Problems In Physics Electricity And Magnetism for JEE Main & Advanced [1 ed.]

Table of contents :
Contents
1. Electrostatics
2. Electric Current
3. Capacitors
4. The Magnetic Field
5. Electromagnetic Induction and A.C. Circuits
6. Solution Electrostatics
7. Solution Electric Current
8. Solution Capacitors
9. Solution The Magnetic Field
10. Solution Electromagnetic Induction

Citation preview

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Preface

~-.·

.-

- -~- -· --- --~

My interaction with students, sincerely preparing for JEE (Main Et Advanced) motivated me to write this boo I< on Problems in Electricity Et Magnetism. Electricity and Magnetism is also as important as Mechanics because in all the competitive examinations, this part is given same or even more weightage than mechanics. This book will help the students in building analytical and quantitative skills, add res sing key misconceptions and d eve loping confidence in prob Lem solving. To make the concepts clear each chapter has been divided into following exercises: •!• 0 nly one alternative is correct. •:• More th an one alternative a re correct. •!• Matching type problems.

•!• Assertion and reason type questions •!• Comprehension based problems.

I sincerely wish that this book will fulfill all the aspirations of the readers. Although utmost full ca re has been taken to make the bool< free from error but some errors inadvertently may creep in. Author and Publisher shall be highly obliged if suggestions regarding improvement and errors are pointed out by readers. I am indebted to my father Sh. Bhavesh Mishra, my mother Smt. Priyamvada Mishra, my wife Manjari, my sister Parul, my little kids Vrishanl< and lra for giving their valuable time which I utilized during the writing of this book and people of Mo rad a bad, who supported me throughout my ca rrer. ln the last, I also pay my sincere thanl-........-

-1 Electrostatics . ···j [A] icoo (OM 9,·s IAw;-ELECTRrc-F·1 E([J"- -:-·------7

!- ---

L. .. _ _ _ _ _ _ _ _ ._ ......... -.-.,

, •.

-·-·--··-------.. ---

--· ......... · - - - - · · · · · · - - · - .......- - - - -

-

·---~-·------ - - ~ - - ·

~Only One Alternative is Correct 1. Four positive charges (2../2 - ]) Q arc arranged at comer of a square. AnoLher r:harge q is

placed at the centre of tht> square resuiling•force acting on each corner is zero. If q is : (a) -7Q/4 (b) -4Q/7 (c) -Q (d) none of these 2. 'I'wo identical charges experience a force f. If half of the charge is transferred from one to another and separation is reduced to half: (a) F/2 (b) (3/ 4) F (c) 2F (d) 3F 8, Four charges are placed on the circumference of a circle of radius R. 90° apart as shown in the figure. The electric field strength at the centre of the circle is : y1,,. i-20

//......~··r··-··-··--.\_ :t9,J,,...

.,M•H ........................

i

\.,. ,. . .1. . . -· · ·/ O!

1

.-!:,~9...,. X

j+2Q

2 ./sQ ( a) -l- -· - - , m aking angle tan -l 2 4m: 0 R 2

w1'th

th e -ve axis .

,-

(b) _l_ 2 'I/ SQ , making angle tan·· 1 2 with the + vc axis 41tto R 2

(c) - 141teo

4-.JiQ , making angle tan-1 .!. with the -ve axis R2

2

.

(d) - 1 - 4 .fi.Q , making angle tan 4n:e 0 R 2

1

.!. with the +vc axis 2

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11-

2

-

(

--------------~---- -

--··-~----------

_.....__P __0>l,le_ms in Electricity & Magnetff!_i": _. _

4. Particle of specific charge 2 x 10 11 C kg-1 is moving through an evacuatL'd vessel in the positive x-direction a! a speed of 10 7 cm s-1 . At x = 0, y = 0, it enters an electric field of 5 V m - t in the positive y-clirection. Its position ( x, y) _after 10 ,; sec is : (a) (10 cm, SO cm)

(b) (10 cm, 25 cm)

(c) (1 cm, 5 cm)

(d) (1 cm, 2.5 cm)

5. Work dn:-ic in shifting" charge q/2 from a point X rn a point Yin the diagram shm-vn in figmc is:

lTI -q

6. A charxe q is plated at the centroid of an equilater;-il triangle. Three equal charges Qare placed a: th.e vc:tces of the 1n ,! r. gle. The sys ter:1 of four charges \ \':.il be i:1 eq u ilib:i um if q is equal to : (a)

-Q/.fi

(b) -Q/3

(c)

(d) Q/ .../3

-Q.fi

·-

7. Two plates A and B are placed one above the otllf'r in the gravitational field and a block of mass m is connected to the upper plate by a spri:s.g of spr:r.g constant k. Its time period is found to be T. Now the space betwi:~1·n the plates is madt~ gravity free ,md a charge l rJ is given to the block of mass m and an electric field E is produced in the di n·ction shown. ·!"he new time period is :

'"

lqE -,--.

(b) I - 2 :c\f

_(a) T

mrl.

. {qE.

(d) nmw of these

(c) 2:-::\, md

8_ 'Iwo small sphere each of mass mart' suspended by light stringlmeter in length ;:is shown in the figure. Sphert-''.i have charges of q and - poL~.: between charges 1 and 2 and also at some point between charges 2 and 3. (b) Th!:-' dectric field i:; zero at some point between charges 1. and 2 but it 1s never zero between charges 2 ,mtl 3. (cJ Tht' electric field is never zero between charges 1 and 2 but it is zero at some point beivveen charges 2 and 3, j (d) The dectric fielrl is never zero between charges 1 and 2 and it is never zero between chmges 2 and 3.

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--Electrostatics ------ - - - - ·-

---------------.~-I

17. '{}:le diagrniu bdow shows the arrangement of thn'(' charged hollow metal ·spheres, A,B and C. The arrows indicate the direction of the electric forces acting between the spheres. At least tv,o of the spheres are positively cha:-ged. Which sphere, if any, coul~

20. A trin non-conducting disk of radius R lie5 mthe .cy-plane wirh ir_,; center at the origin. The disk has a positive charge Q distributed uniformly on its surface, re.'iulting in a surface c:1arge density cr. Which one of the following statements about the resulting electric field is true? (a) On both the +z-axis and the -z-axis, the electric field points in the +zsdireciion. (b) At loca1ions ve:-y near the origin (r .I

q V40m: 0 Rm

~

2

(b) u>

31 rrs 0 Rm

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Cd) u>

9q2 401t&0Rm

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--·=:~:=~-----~-=--·~ -_-.- _. •- ---·--·----_., __ 1_2___,---=

Electrostatics

27. The charge per unit length of the four quadrant of the ring is 2J..., -2l,}. and --J. respetively. The electric field at the centre is :

X

A. ':' (a)---- 1 2n:c 0R

is 2ru:: 0 R

A

(b) - - - - j

.

..fi.-;.. ,:,

(c) - - 1 4:n:e 0 R

(d) none of these

28. Between two infinitely long wires having linear charge densities}. and -].·there are two points A and B as shown in the figure. The amount of work done by t11e electric field in moving a point charge (fo from A co B ls equal to : (a) Aflo ln2 2•o

(b) - 21.%t ln2

(c) ZJ..qo ln2

(d) ''40 ln2

~o

m·:o

29. The follm.-ving diagram shows the electric field lines between two opposite charges. The positive charge is indicated by the black circle, the negative charge by t!1e white circle. An electron starting from rest at the indicated position (X), and accelerated to high speed by the electric field, will most closely follow which trajectory?

(•)O (b)O (c)O (d)O

30. A distribution of charges is held fixE!d by rigid insulators as shown in figure. z A charge Q at (-a,0, 0) and at (a,O, O) and a charge -2Q at (0, 0, O). Which of ~ a the following electric fields will cause a net torque to be exerted on the o Y system of charges ? -2Q ~

(a) E

=

"

....

(constant) j

(b) E

....

I\

(c) E = (E 0 x + constant)k

(d)

,.

=

(E 0 x + constant)i

+Q

X

E=E !xii 0

'-

....

31. A particle of mass m and charge Q is placed in an elect.de field E which varies with time t a~ E ==· E 0 sin wt-. ft will undergo simple harmonic motion of amplitude:

(a) QE5 mol

(b) QE~

mro 2

(c)

(~Q.. vJ11(1) 2

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(d)

9.~~-Q. mco

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·--II' -s-11. 32. A solid conducting sphere having net charge Q and radius 3 a contains a hollowed spherical region of radius 2 a. A point chc1rgc +Q is placed at a positiun distance a from L½e cornmon center of the spheres. What is the magnitude of the c,Icctric fo~ld at the position r = 4 a from the center of the spheres as marked in the figure by P ? kQ

: I

;.i

: I I

~--c-----,

a : a: a:

. t

j

J

I

'

I I

(a)

16a 2 (b) 3k~~

16a~ (c)

kQ . 8a 2

(d) cannot be determined due to non-uniform distiibution 33. In an ink-jet printer, an ink droplr.1 nf mass m is given a negative ~ charge q by a compU1 c~r-controlled charging unit, and then enters at 7 ~ +speed v the region between two deflecting paralkl plates oflenLrt:h L separated by distance d (see figure). All over this region exists a L dov,..nward electric field which you can assume to be uniform. Neglecting the gravitational force on the droplet, 1ht" maximum r::harge that it r::an be given sn that it will not hit a plate is most dosely approximated by :

t d

Ei

2 (a) m1.1 E

(b) mv 2d

dL 2

(c') 2.dmv 2

EL 2

EL2

34. The two ends of a rubber string of negligible mass and having

(d'1 none of t h.ese 24 cm

l

unstrctched length 24 cm are fixed at the same height as shown. A ~ , e small object is attached to the string in its midpoint, thus the depression (h) of the object in equilibrium is 5 cm. Then the small h object is chiuged and vertical electric field (E 1 ) is applied. 'Qie equilibrium depression of the object increases to 9 cm, then the electric field is changed to E 2 and the depression of object in equilibrium increases to 16 cm. What is the ratio of electric field in Lhe second case to that of in the first case (E 2 / E1 ) ? (a) 4.25

(b) 4.20

(c) 4.30

(d) 4.35

85. A proton r:,:its at coordinates ( x, y) = ( 0 ,0) and an electron at ( h, d) 1 where d » h. At time t = 0, a '.' uniform electric field E of unknown magnitude but pointing in the positive y direction is

turned on. Assuming that dis large enough that the proton-electron interaction is negligible, the y coordinates of the two particles will be equal (at equal time) :

(a) at !!.bout y = d/2000 (b) at an undetermined value since F. is unknown

(c) at about y =d/43 (d) nowhere : they move in oppoi:1ite directions

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1

1

I

Electrostatics 36. A point charge +Q is placed at the cent.-oid of :m ec_ui\2.teral triangle. When a second charge +Q is placed at a ver:ex o: the :1iangle, the magnitude of the electrostatic force on fr1e ccn:ral cha:·ge is 4N. What

:I

9

Q

is the magnitude of the net force on the cen:rpJ c·nargc when a third charge +Q is placed at another vertex of ;-he tr.ang:e'? ,:b) 4 N

(a) zero (c)

4.fzN

Q

(d) S N

37. Two electrons are a certain distance apan from or.e ano:J1er. l/lhat is the order of magnitude of the ratio of the electric force between them to t:-:c grav:tadonal force between them? (a) 10 8 : 1

(c) 10 31 : 1

(b) 10 28 : 1

(d) 10 42 : 1

38. Millikan's oil-drop experiment attempts tc mecJsurc r::e charge on a single electron e, by measuring the charge of tiny oil-drops sUS?ern'.ed in ,~:-. elecrrostatic field. It is assumed that the charge on the oil-drop is due to just a small num·Jcr cf excess electrons. The charges 3.90 x 10- 19 C,6.50 x 10- 19 C and9.10 :< 10 < 9 Cf.re :-:--_easured on three drops of oil. The charge of an electron is deduced to be : (a) 1.3x10-19 C (b) l.6x10·· 19 c (c) 2,6x10-19 c (d) 3.9x10- 19 c 39. A 300 eV electron is aimed midway betv:eer. two p2-:·allel metal plates with a potential difference of 400 V. The e:crnor~ is defected upwards 300 and strikes the upper plate as shown. Wha: wo·..::d ·::;e the ldnetic energy -_ of the electron just before striking the me t3 l plate? N cg l ect the gravity r:::e and air resistance. (a) 360 eV (b) 400 eV (c) 50:J eV (d) 700 eV

1 +

:ev 7 4 0 V. ====:=:::::::r

q.t]More than One Alternative are Correct 1. 'lbree charged particles are in equilibrium under their e'.ectrostatic forces only :

(a) the particles must be collinear. (b) all the charges cannot have the same mcJgnin:.de. (c) all the charges cannot have the same sign. (d) the equilibrium is unstable. 2. An oil-drop has a charge -9.6 x 10- 19 C ar,d has arr.ass 1.6 x 10- 15 gm. When allowed to fall, due to air resistance it attains a constant veloc:ty. Tr.en ff a uniform ,electric field is to be applied vertically to make the oil-drop ascend ur, v::tl'. the same constant speed, which of the following are correct ? (a) The electric field is directed upward. (b) The electric field is directed do""1".ward. (c) The intensity of the electric field is

.!. x 10 2 N'C. 3

(d) The intensity of the electric field is ..:. x 10 5 N · C , 6 '

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10 II Prob.~~ms in Electricity & Magnetism ----~==-::::::::f---~--~----"~-----3. "Jwo charges are placed near the origin : charge q1 == -3Q is placed at x == +d/2, and charge q2 == -Q is placed a~ x == -d/2. Which of the following statement (s) is/are a valid 0. Then the motion of P is : (a) periodic, for all values of z O satisfying O < z O < ·'L· (b) simple harmonic, for all values of ::: 0 sa:isfying O < z 3 ~ R

{c) approximately simple harmonic, provided :: 0 « R (d) such that P crosses O and continues to move aiong the -ve z:axis towards x = ----«)

5. The figure shows, two point charges q1 == 2 Q ( > 0 ~ and q2 ""---Q. The charges divide the line joining them in three parts I, II and IIL l +2Q

i:..:

I: -Q

(a) Region-III has a Jocal maxima of electric field. (b) Region-I has a local minima of electric 5.eld.

(c) Equilibrium position for a test charge lies in :-egion-IL (d) The equilibrium for constrained motion H.long tric line joining the cl1arges is stable for a negative test charge. ·6. Point charges are located on the comer of a squa:-e as shown-.. Find the components of electric field at any pain: on r:ie z-2-'XiS •.vhich is axis of symmetry of the square.

+1r1 rx

(a) Ez =0

(b)E,,==0

(c) Ey ===0

(d) none of these

7. Electric field, due to an infinite line of charge, as shown in figure at a point P at a distance r from the line is E. Jf or:e haif of the line of charge is removed from either side of point A, then : (a) electric field at P will be magnitude E/2. (b) electric field at P in x direction vrlll be E/2. (c) electric field at P in y-direction will be E/2 . (d) none of the above

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-1µC

+1!1C

.

,P r:' ''

+++++++++++++ A

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ft: lectrostatics

-----····--··-"--~------·--·--··

~

·-····--

-- - --------- -

.

-- ----- ~----·--

)Only One Alternative is- Correct

1. A proton is released from rest 10 cm from a large sheet carrying ;1 surface chaTgc density of

-2.21 x 1D ~'cm- 2 . It will strike the sheet after the time : (aj 4µs

(c) 2-,./2 ~s

(b) 2µs

(d)

L/2 ~

2. Figure show~ a metallic shell of radiu,; R with a concentric cavity of radius r. A .

point charw· q is placed at the centre. Find the net ckcrric flux emerging from the surface S (Dotted surface) as shown in figure. (a)

q/£ 0

Cb) -q_,'!: 0 (d) Cmnot be defined

(c) 0

, , · · +q . - ::

3. The diagr,1111 shows a 'uniformly charged hemisphen· of radius R. lt bas

A

volume charge density p. lf the electric field at a point 2R distance above its cer:ter is E then wha'. is the elect~ic fie:ci at the point ·Nhich is 2R below its center ?

(a) pR/6': 0

+E

'(b) pH /12e 0

(c) ---pR/6i: 0 +E

.:..

E

(d) pk'/:!.4e 0 +E

B

4. 1\vo identic,il in'b.ite posi'.ive ::ne cl1argcs are placec'. itlo~g the line~

x = ±a, in the X)'-plane. A positive point charge placed at origin i:; restrit.'ted to move along y-axis. Its equilibrium is : (a) stable

(b) neutral

(c) umtahlt'

Cd) none af tr.ese

5. A sphere or rndius R carries charge deI1sity proportional to the squc1rc of the distance from the centre p - Ar 2 , where A is a positiv,~ constant. At a distance of R/2 from the center, the m8gnitudc~ o: tr.e electric :°ield is : ., AR'.\ AR3 AR~ A (a) (e)

(b) - · -(40eo)

( 4n:Eo)

(c) (24e--;;}

(d) - (Seo)

AR:i (3Eo) J

6. In tbe figure below, a point charge+ Q I is at the center of an imagina:1' spherical }:aussian surface and another point charge f Q 2 is outside of the gausfrm surface. Point Pis on the surfuee of the sphere. v\'hich one of the following statements is true ?

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-. - __ 1_=12=:=:-I

·---·-------~~-

--~·-·-·-- ~--~--- -~~- ~----~~---------- ----------·--···------ ____ ~rol>lems in Electricity & .\.fagnetism

(a) Bo! h charges +Q I and+ Q 2 contribute to the net electric flux through the sphere but only charge + Q 1 contributes to the c lcctric field at point P on the sphere. (b) Bo~h charges+ Q 1 am'.+ Q 2 cont:-ibute to the net electric :lux through the .,pr.ere J:Jt only charge +Q 2 contributes to the electric field at point P on the sphere.

(c) Only the charges I Q1 contribu1r>s to the ne! Plectric flux 1hrough the sphere but both charge +Q 1 and 1-()z connibutt' to the electric field at point P. ( d) 0 n !y the charges + Q;:,. con tr; but cs to the ::e1 c lcc.:tric f1 ux. t hrm:.gh :he spi:c re bu:: both charge +Q 1 and +Q 2 contribute to the electric field at point P.

7. The figurP to the rigln shows the potr>ntial due tu cwo similarly· charged infinite sheets with charge per unit arc,t cr 1 and a 2 . From ex.tminir.g this plot we can deduce that : (a) cr 2 > rr 1

(b) G2 < cr1

(c) cr2 --0"1

(d) None of the above

+ - •,

·---t, l

--->-X

V (volts)

;,;(m)

8. Electric flux b a measure of : · (a) the raLe at which moving electric charges are crossing an arf'a

(b) the number of electric field lirn·s passing throllgh an area (c) the surface densiLy of electric charge spread along the area

~d) the rnte ;.t which eicctrlc f.cld lines arc spreading out in space as on moves further and further away frorn t'!ec::ric charg1·s ---j-

A

A

9. A uniform electric field J•: =: a i + bj, intersects a surface of area A. What is the flux through this area if the surface lies in the yz-planc ? (b) 0

(cl) (IA

;J O.

(c) M

The figure to the right shows an l'r!ge on view of three extremely · large, parallel insula11113 sheets positively charged \-vith uniform ;md identic:1 l surface char?,t' densities. In which of the regions shown is the electric field a maximum ? '·

·. (a) B

(b) C (c) A aml D

(d) ThP electric field

is

rhe same in all four regions of space.

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I 2 (d) A-,;a A ~

13

+ b-~ ~

c ~

lJ

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thickness cl,:: 5.0 mm and cross-sectional area A= 1.0 m 2 • The slab has a fixed total charge Q tot = 4.0 nC placed upon it and the slab is then aligned with its area parallel to an infinite sheet of charge with surface charge density T\o =+ 2. 0 n C/m 2 (see figure). Afr er equilibrium is reached within the conductor, what will be the surface: charge densities on the left and right-hand faces of the slab (11r and flR) ?

11, A rectangular conducting slab has

(a) 111 =+2.0nC/m 2

;

(b) 111, :::+2.0nC/m 2

; T\R

(c) 111 = + 4.0nC/m 2

; TIR ::: +2.0nC/m :!

(d) TJr. ::: + 3.0 nC/rn 2

;

+Tio

TIL

TlR =+2.0nC/m 2

T\R

=-2.0nC/m 2

=+ LO nC:/rri2

12, An insulating spherical shell of inner radius a and outer radius bis uniformly charged with a

positive charge density. The radial c.mnponent of the electric field, Er(r) has a graph :

~' (a)

(b)

E

o

E

~

O a

Et!~

o~,

:

:

r

a b

b

@ (c:)

@i .j @

(d)

E~;j 0

i !

••

,

:

r

a b

a b

13. A rod containing charge +Q is brought near an initially

uncharged isolated conducting rod as shown. Regions with total surface charge +Q and -Q are inducctl in the conductor as shown in the figure. The only regions where the net charge in this configuration is non-zero are / indicated by the"+" and"-" signs. Let us denote the torn) ~ flux of electric field outward through dosed surface Si as t1> i , through S 2 as 0 (b) cJ> 2 =

to

->

(a) E must be the electric field due t'o the enclosed charge.

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1·······-···-···········;

.\ . . ./t.

- :

+ -

-.....'-........___ -- -_. ~....,,.·.•

: ...

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I

,I

·-···--------------------

1 ----~-___

1a

__P_.r_oblem.., ill Electricityft Magneti~----->

(b) If net charge inside the Gaussian surface= 0, then E must be zero everywhere over the Gaussian surface. ( c).,Jf the only charge inside the Gaussian surface is an c lcctric dipole. then 1:he integral is zero. ---->

~

(d) E is parallel to d A everywhere over die Gaussian surface. 25. A point charge +Q is positioned at the center of the base of a squa-:-e pyramid as shown. The flux through one of the four identical upper faces of µte pyramid is : Q (a)

(c)

16Eo Q

(d} none of these

8s 0

26. A 5.0 µC point charge is placed at the center of a cube. The electric flux in N-m 2 /C through one side of the cube is approximately : (b) 7.1 X 10 4

(a) 0

· (c) 9.4x 10 4

(d) 1.4 X 10 5

2 7. If distance x and radius R are doubled so that FA becomes FA ,F8 becom Fs (a) FH > F8 28. A body in the fom1 of a right circular cone of dielectric material with base radius R and hejght

his placed with its base on a horizontal table. A hori.wntal uniform electric field of magnirnde E penetrates the cone. 'lbe electric flux that centers the body is : (a) ERfl/3 (b) ERh (c) ERh/6

29. \A.'hat is the flu.x thrnugh the part of surface ~

to the electric field E

x2

+y

2

+

.a: 2

(d) 2ER1i

= I for region x > 0 ,y > 0 ,z > 0. due

~

:=:

(1000 N/C) j.

(c) 125;r (d) 7501t (a) 5001t (b) 25011: 30, You observe that electric field lines are emerging from a dosed box, but every field line that leaves the box re-enters. Which of the following statements is true ? (a) There is no charge in box. (b} The net charge in box is positive.

(c) The net charge in box is negative. (d) There arc bot11 positive and negative charges inside box but net chilrge is zero.

31. A charged spherically symmetric body has a charge density that varies \'lith the radial distance (p = f(r)) from the centre. At the centre of the body the electric field : (a} is non-zero irrespective of the function f(r) (b) is zero irrespective of the functfon j(r) (c) mar be non-zero depending on the function f(r) (d) cannot be. predicted

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-.,.-;·,-·----~~= i

-------

___ _______

Electrostatics . ,

.

---·-.-···--

32. Two imaginary spherical surfaces of radius R and 2R respectively surr(?,und a positive polnt chargE~ Q located at the ce1,1ter of the concentric spheres. When compared to the number of field lines N 1 going through the sphere of radius R, the number of electric field lines N 2 going through the sphere of radius 2R is : (a) N 2 .:::: 1 N 1

4

1 (b) N 2 ""'2,·N 1

(c) N 2 =2N 1

(d) N 2 =N 1 ->

•

33. In a region of space, the electric field is in the x- direction and is given as E =Eo xi. ConC =-Wn----l-C

(d) Ac point C, the force applied by external agent is maximum.

4. Consider a gaussian spherical surface, covering a dipole of charge q and -q, thC'.11: (a) qin =0 (Net charge enclosed by the spherical surface) (b) cj, net

8

=0 (Net flux coming out: the spherical surface)

(c) E ""0 at all points on the spherical surface ....,)

(d)

....

---,.

JE · d s =0 (Surface integral of E over the spherical surface)

5. An electron is placed just in d1e middle between two long fixed line charges of charge density+,,. each. The wires are in the xy-plane (Do not: consider gravity).

(a) The equilibrium of the electron will be unstable along x-direction. (b) Tl1Ei equilibrium of the electron will he neutral along y·direction.

(c) 'lbe equilibrium of the electron will be stable along z-dircction. (d) Tlui equilibrium of the electron will be stable along y-direction.

6. In which of following cases, electric field is uniform ? (a) Inside a uniformly charged spherical shell (b) In any cavity inside a unjformly charged sphere . (c) In front of an infinite sheet of uniform surface charge density (d) At a distance X from a point charge q 7. A larg-;:

-

-

-

•

-

\ '.

', "'~ ........--~·· . j 'Ur.iformly charged sphere with an empty spherical jcavity in it. S 1 and S 2 are concentric the center-of !spherical cavity. 5'3 is concentric to the charged 'sphere. (B)'

(Q) S 2 is an. equipotential surface.

I

[ ::c~_:: ···-:: 'Thin non-conducting cylindrical shell of finite !.lengtli with uniform linear charge density. S and 1

'S 2 are coaxial with cylinder.

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---,si---'-----..1•-._.....------..,.7---,,~---~--;:, ·.

22· __; : .. •·.

.

.

Probl(!,mS inEJectricity &•Magn~ti$~

(C) ..

••1 •

.

/

CR) :M:agnitude of electric fieid' oh surface S 3 ,is uniform.•·· .

•. -~

~ .,:

··.--·.:Ii"

. ---~:

-

..,.

.:.- . .;

-.. -:_---=~ R t lll' electric fit' h.1 of given charge distribution is identical to a point chargt'..

(d) Elecrr'r field at ~he centre of given spherical charge distribution is zero.

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~-·-~

· · · -· ------ ------·----------------I -.------ -- ------· ------· -------· Problems in Electricity & Magneti.,;m --~--" - - ~ --------·" ••• - -

----·--·~-~·- -~-~--- •-• -•• •••

•• "• - - -

" - I · - - - .. ______ .. - - - ~ - " " - -

___ ---~~-~----~-~::- --=\[C] jELECTRI(POTENTIAL_ ~ - ~~:~----- ---~:--~~-- --~~__ ?]only One Alternative is Correct l. Three identical charg a), such a way that their surface charge demities are equal. The potential at the common centre is given by: () (a+ b) (b) _ (b-a) _

g__

(a)

4rn:o (a 2 (c)

+ b2 )

,J11t O (a 2

(a+ b)

Q

(a.,.

4ni; 0

(d)

b/·

+ //)

g_.

(b - a) Lr:cu (a+/JJ2

18. Two point charges are kept at a certain dist,mcc from one another. The graph represents the variation of the potenti;1J

along the straight line connecting tht' two charges_ At what point is the ei('ctric field zero ? (a) 1

(b) 2

(c) 3

(d) none of these

19. A very large sphere h;1ving charg(· Q uniformly distributed on the surface is compressed uniformly till its radius reduces to R. The work done hy electric forces in this process is : --Q"

Q_2,

M-8rrs R

00--· 8m:uR

~o

~~

0

2 0. A non-conducting ring uf radius R has two charges q and q/2 disr ributed uniformly on two half of it. A negative charge q/2 (mass '-- m) is placed ar a distance R from the centre of the ring on :t3· ax:s at a point P anc: reieased. If :his C'.'.arge is restricted to move freely on1y along the axis of the ring, find the speed of this charge when it crosses the centre of the ring :

3Kq2

(a) [ --(-./2 - l) 2·./'J.Rm (c)

[3·J2

Kq z (-.J2 -

]1/2

(b)

]) 711-2

r:1Kq2

l-(-h. - l) Rm

(d) l' 3 Kq: (-.J2 -

Rm

]1/2

2Rm

l)l

1/2

21, In an ekctric field the potential at a point is given by the following relation ~

~

/\

/',

electric field at r = 3 i 1 2 j+ 6 k :s : /\.

I\

I\

/I

/I

A

(a) 21 i+ 14 j+ 42k

(b) :Ji+2j+6k

1 ,, /I /I (c) -Cl i+2j+6k) 7

(d) -(3 i+ 2 j-6k)

I\

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"

,..

v· = 243 . The r

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___ I

Electrostatics ----,,

s-..

A

31.

ii __ _

•

22. Let VO be the potential at the origin in an electric field E =Ex i + E Y j. The

poten1 ial

at the

point (x,y) is : (a) V 0 -xE_\- -yE 1 (c) xf?x + yE 1 -Vo

23. The work done by external agent in canying a particle of a charge 2 C from B(l m, O, l m) to

" N/m along the str_aight line A(0.8 rn, 0.6 m, 1 m) in a non-uniform electric field E ;:; (y "i + x j"+ k) path from B to A is : (b) + 0.96 J

(a) -0.96 .J

(d) -0.48 J

( c) zero

24. Consider rhe potential at the corner of a uniformly charged cube of dimension L ro be directly proportional to pL 2 , where p is the volume charge density. What is the value of the ratio of the potential at the center to the potential at the corner of the cube ? (a) 4 : 1

(b) 3 : 2

(c) 8 : 1

(d) 2 : 1

25. Two positive charges +Q and +4Q are placed at the ends of a straight line of length L. A negative charge -Q is plaC'.{~d between the first two charges on the straight line at a distance 'r (0 < x < LJ from the charge + Q. Then, the graph of (electrostatic potential energy) of the system of three charges versus xis :

u

2U3

L

/\I

(a)

X

Cb)

(c)

VI

0

L/3

LI

(d)

L

J3 L

0

=

u

I

LI~

X

U3

L

(\I

X

l

X

26, Two circular rings A and B having the charge +Q and-Qare located at a distanced apart as shown. RadU of both the rings is R. The minimum potential on the line joining their centres is:

_---_a

++. -+

~

-

A +

_ B

+

+

+1•

-

d

~

= '..

_-

(a) at the centre of coil A (b) at the centre of coil B (c) at the midpoint of the line joining their centres (d) at a distance

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-:I

I

32

Problems in Electricity & Magnetism

27. An electron travelling in an uniform electric field passes from a region of potential V 1 to a region of higher potential V 2 • Then : (a) no change takes place in velocity component parallel to interface of two regions. (b) direction of its motion remains unchanged but speed increases.

(c) direction of its motion may change but speed must be decreased. (d) decrease in kinetic energy is proportional to ~V2 - V 1 •

28. In an electric field shown in figure three equipotential surfaces are shown. If function of electric field is E = 2x 2 V /m, and given that V1 -V2 =V2 -V3 , then we have:

y

_g___,

-·

-;

I

r-H X :X1:X2: > X2 (c) x 2 > x 1 (d) data insufficient z 29. 1\vo equal drops of water having the same and similar charge combine to form one spherical drop. Considering drop to be conducting and spherical, the ratio of electrostatic energy of single drop to the combined drop is : (a) 1:25/'3 (b) 1:2 4/ 3 (c) 1:2 4' 3 (d) none of these (a)

X1

= X2

(b)

X1

v1 Vz v~

30. The linear charge density on a di-electric ring of radius R is varying with e as

>.. =>.. 0 cos Q. Then the electric potential at the centre of ring is : 2

(a) ~

(b)~

2m:o (c) lo &o

21>0

(d) zero

31. 1\vo charged sphere A and B, shown below are isolated conductors, A having + Q charge and B . having+ 4Q charge and radius rA =1/2 r 8 .OX is a straight line passing through their centres. ·

9."x B(+4Q)

(J°-e~~!.....

The potential 'V' at any point on OX, plotted against the distance ' x' of the point from O, will be nearly: (a)

1

v

IA (1 /

oµ_L-1-b

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',·Et~ctrostatic_·~-·_. · - - - ~

-~-----------~-~--1

33

I'~ ,:

32, Two· concentric sphet1tal shells have· radii Ri (m) and R 2 (m) [R 2 > R.i]. the inner sph.ere carries a charge -q cdulomb. 'The velocity of an electron (charge e, mass m) starting from rest from the inner sphere and striking the outer sphere is : (a) / (R2 -R1) (b) /-q-e-(R_2___R_1_)

qe

I 2m; 0 m (c)

R 1R 2

qe ( 1 47tto

,

1 )

(d) /

41te 0 m

qe

~ 41ti::om

Rf - Rf

R 1R 2

R 2 -R 1

Rf

33. The· electric potential at a point P, which is located on the axis of synimetty a distance x from the center of the ring, is taken by :

(a)

(e)

Q 4·m: 0 x

~ Q

(b) 4rtE 0

' 2

-vR

+x

2

(c)

Qx·

4m: 0 (R 2 + x 2 )

(d)

Qx 4m:o(R 2 + x2) 'J/2

QR

4ns 0 (R 2 + x 2 )

34. Two fixed charges -2 Q and Q are located at points with coordinates (-3a,O) and ( +3a,0) respectively in the .l)'-plane. The points in the .l)'-plane where the electric potential due to the system: is zero lie on a circle whose centre and radius are : (c) (3a,0);3a (d) (O,O); 4a (b) (0,0) ;3a (a) (Sa,0); 4a 35. Without producing ionization of air, the maximum electric field that can be supported in atmosphere is 10 6 Vm ""'1 . Using this criterion, the maximum potential of a conducting sphere of radius O.Olm in the same atmosphere will be : (a) 10 4 V (b) 2 x 10 4 V (c) ld 5 V (d) 10 6 V 36. 1\vo tharges lie on the x-axis. A rough sketcli of the equipotential lines of these two charges is shown. Which one of the following statements is true ?

(a) the two charges have opposite signs artd the charge on the left is srnaller in magnitude than the charge on the' right. (b) The two charges have opposite signs and the charge on the left is larger in magnitude than the charge on the right.

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~==-:=!'---------------~·P_r_~~[ems in Electricity &:Magnetis,ij. (c) The two charges have the same sign and the charge on the l~ft is" smaller in magnitude than the charge on the right. (d) The two charges have the same sign and the charge on the left is larger in magnitude than the charge on µie right. · 3 7. Consider the following conclusions regarding the components of an electric field at a certain

point in space given by Ex ;::-Ky, Ey =Kx, E 8 =0 (I) The field is conservative. (II) The field is non-conservative. (III) The lines of force are st[aJght lines.

(IV) The lines

of force are circles.

out of these conclusions : (a) II and IV are valid (c) I and IV are valid

I~ :

(h) I and III are valid (d) II and III are valid 38, Suppose a region of space has a unifonn electric field, directed towards the right; as shown below. Which statement is true ? (a) The potential at all three locations is the same. '

E

•A

----.-:-c+ B

•

I

(b) The potential at points A and B are equal, the potential at point C is higher than the potential at point A. ·

--,---·

_

_

(c) The potential at points A and B are equal and the potential at point C is lower than tne potential at_ point A. · '-, · (d) ,The potential at point A is the highest, the potential at point B is the second high~t and the potential at point C is the lowest. , · 39. The electrostatic potential is measured be V ( x, y, z) = 4 Ix I+ VO, where VO is a consta~t. The ch:arge distribution responsible for this potential is : (a) a uniformly charged thread in the ;zy-plane (b) a point charge at origin (c) a uniformly charged sheet in the· yz-plane (d) a uniformly charged sphere of radius l/1t at the origin _ 40, · Consider an arrangement in' which a point charge has been placed at the center of charged ring. The magnitude of the point charge is Q1 and the charge present on the ring is Q 2 • Which of the following graphs showing the variation potential as a function of the distance X from the center along the axis is/are correct ?

to

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Elec.tr.ustatics-~ ·'

: _,.

~

.

01==+5G and Or10G

tyx ~x

•'-·· - ·(a) I, Iv, V and Vlll .

~

M

Qt=-5C and 02:0+10C

• ·1

(c) I, III and V

I

I

35 -------------------------===~

1

(b) II, N, V and VI h

-II

..

(d) I, lY, V and VI

41.

'IWo concentric spherical conducting s.hells have radii r1 and r2 and charges Q 1 -· · ·· and Q2 , as shown. Let r be the distance from the centTe of the spheres and consider the region r1 < r< r2 • In this region, the electric potential (relative to infinity) is proportional to :

·,.

(a) Ql + Q2

ri

r2 "

(c) (Q1 + Qz)

(d) Q1

+ .9-.~.

· r

r

rz

42. An infinite thread of charge density J,,. lies along z-ax.is. difference between points A(4,3,4) and B(3,4,0) is:

(a)

_J,,._ln(-141) 2n:& 5 0

.."C'' :,

'

(b) __!::_ins · 2u 0

The potential

+ + + + +

+

(c) zero

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71

3~ , ·-~-~~------------P_r9.blems in Elec!!i!:_i_!y & 1\lagnetism

43. Consider the two large oppositely charged plates as shown in the diagram. At which of the marked point.c; shown in the diagram would a negatively charged panicle have the greatest electrical potential energy ?

C•

D• +

(a) A

+

+

+

+

+

(c) C

(b) B

(d) D

·I -·-;

44. A rod AB of length J. and mass m is uniformly charged with a charge Q and "it is freely suspended from end A as shown in figure. An electric field E is suddenly switched on in the horizontal direction due to which rod get turned by a maximum angle 90°. The magnitude of Eis : ·· B 2~ 4~ 3~ (d) Mg (a) ...................... (b) (c) ·Q Q Q Q

••

.:.--::::..E

45. The linear charge density on a dielectric ring of radius R is varying with 0 as k "",. 0 cos(0/2). The potential at. I.he centre of the ring is : (b)

(a) 0 (

A

(a) 2 p cos3O° (i + 2j)

,.

(b) 2 p cos30°(i) :c

~

(c) 2 p cos30°(2})

(d) None of these

5. The equation of equipotential lines in .'9'-plane for a dipole kept at the origin and oriented along x-aYis is : '· (a)

x = const· cx2 +i2J312

(c)

· y (x2 + y2)312

2

=canst

(b)

y

(y2 + x2:)3/2 2

(d)

X ,

(x2

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+ y2)3/2

=const

=':canst

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----),

6. A tiny electric dipole (H 2 0 molecule) of dipole moment p is placed at a distance r from an ----),

infinitely long wire, with its p normal to the wire in the same plane. If the ~ear .charge density of the wire is )..., the electrostatic force acting on the dipole is equal ·to ·: ->

(a) _!:L · 41rn 0 r ----),

7. Electric field at a distance r from an electric dipole on its axis is E 1 and at ,distance 2 r on its ----),

perpendicular bisector is E 2 then : ----),

(c)

IE2l=~

----),

(d)

8

IE .

2

I=

IE1I

16

8. An electric dipole, consisting of two equal and opposite point charges at the ends of a insulating rod, is placed in the electric field of a stationary positive pomt charge, as shown. The dipole is free to move. The dipole

will: (a) rotate (b) rotate (c) rotate (d) rotate

clock.wise and move to the left counter-clockwise and move to the right clockwise and move to the right counter-clockwise and move to the left ----),

-

9. A water ,~olecule as shown is in a region of uniform electric field E = 1000 i V / m. This m?lcculc experiences :

--••-------1.-.---..-.E 0-2e

~

._-Eo

I~·; ~ ~

'•

~

m·:~-~m#tlin;~~n 0

\}lAssertion and Reason Type Questions --+

L

Statement-I : If a dipole ( p ) is moved along rhe line normal to the axis (dotted line 1

,

--+

•

shown) of another dipole ( p :'. ), their :nteractiur. energy does no: change. --+

--+

-+

Statemcnt-2 : Electric field ·of p z at the positinn of p 1 is normal to p .

~-·P,· -· ·-· · -· · · · · · · · ·-· · tp~

1

(a) Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-L (b) Staternent-1 is true, Statement-2 is true and Stan'.ment-2 is not the correct explanation for

Statemt·nt-1. (c) Statement-: is

trUC',

Stater..ent-2 is false,

(d) Statement-I is false, Statement-2 is true. 2.

Statement-I : An electric dipole placed in the electric field of a point charge can never experi1'.ncc zero resultant force. Statement-2 : Electric field o~ a pnint charge is mJn- uniform. (a) Statement-I is true, Statcment-2 is true am! Statemcnt-2 is correct explanation for Statement- I. (b) Statement-I is true, Statement-2 is true and Statcment-2 is not the correct explanation for Sta:l'nwnt-1. (c) Statement-I is true, Statemcnt-2 is false. (d) Statement-I is false, Statement-?. is true.

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1· -~· ~-

~ , 46

.

.

.

Problems in Ele~!ricity &Magn~~_;:,_·

f]comprehension Based Problems Comprehension - 1 •

"p:

'i R)_ "lne force of 11\lraction (F) lwtween them is : KQ 2 (b) -- (r+2R) 2

KQ 7

(a) - .

r7

KQ:,

KQ1.

(d)

(c) ·- >F>--- r 1· (r+2K) 2

KQ 2

> F > KQ

(r-2R) 2

0

r2

22. A thin conducting spht>rical shell carries a charge of surface chargt> clemiLy cr. A ? small elemental part nf the shell is removed from ii-. Consider two points P and Q located very dose to the spherical shell. The point· J-' is in the nf'ighbourhood of the ,~lementary cavity formed and Q_ is just outside the shell ;1s shown. Let •0 E? and Fri_ be: r:~.e magnitudes of electric field ~tr:·113th ""' P and Q respect:vely. Tr.en tht>. ratio of P..p /FQ is eq:..:al to : (a) zero (b) 1 (c) 0.5 (d) 2 23. Consider two concentric conducting spheres as shown below. The ·outer sphere is hollow and has a total charge of +SµC charf;e on it; its inner radius is R, = 9cm a::d :ts O'..!ter radiu5 is R 2 1Oen. The inne:- sphere :'. from the co::".mon centre : (a) :he highes: elcctm: field magni1ude E occurs immediately outside the sm;-illcr (R = b) shell. (b) the highest electric field magnitude E occurs immediately 011tside the larg:/C exists in horizontal direction_ The bah is released from the position when the string is vertical. lf the length of the string is lrn, then : (a) the bob will perform ,SI-IM of time period ne:irly 2s. (b) the bob will havc maximum vdodty nearly U.lm/s. (c:) th!' mn..x.inrnm a:--.glc th~_t the siing will make wi~h tl}e venical

(d) it will not perform SHM.

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:s r.early 3.6 degrees.

-

.~

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l__s~_J1-.

; .Electrastatics ----~-~---·-·----0

,8. You are moving a negative charge q < 0 at a small constant speed away from a unifonnly charged non-conducting spherical shell .on which resides a negative charges Q < Q_ lbe

electrostatic field of Q is E. Let Ube the total energy of the system, W., the work done by the force Fa you exert on q and WE the work done by the electrostatic force FE on q. Then, as q is being moved. (a) W11 =--::WE, therefore U remains constant

(b) Fa "';-FE (c) U increases ( d) U decreases to fonn a composite bar, one end of which is heated. After some time has elapsed, the temperature gradient along each rod is found to be uniform, but greater in X than that in Y. which of the following can be inferred ?

9. Two metalrods X and Y having equal cross-sectional areas are joined end to end

(a) Both the rods are well lagged. (b) The heat current is the same in both the rods. (c) Both the rods are of equal lengths. (d) X is a better conductor of heat than Y. 10, Mark the correct st'aternent(s) for the situation shown:

NNlrul l50latf!d spherlcal conduc1,;1, wilt, spherical

"""ily

(a) If a point charge q is. placed inside the cavity but not at centre, then potential of the

conductor is--q4 n&0R

(b) If a point charge q is placed at the centre of cavity, then potential of the conductor will be zero. (c} If a point charge q fa placed inside the cavity, but not: at centre, then potential of the conductor will be __ q_ [~ + 4m; 0R R

! - _!_]r

r1

(d) If a point charge q is placed inside the cavity but not at centre, then potential at the centre of the conductor due to charges on the outer surface of co~ductor is __ q_. -

-

4x& 0 R

11. An isolated syscem consists of two concentric thin metallic spherical shells A and B having radii

The shells are neutral initially. A point diargc + q is placed at the centre of the s_hells. The shell A is earthed.

11 and 2a respectively.

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=._~1

58

JI .::==~=:___ ___

_-_-_-_--P-r_o_b-le_m_s-,-.11~E-le-c~t-,~--;;;,,-.ty___&__

~~~:-~-;~:~

_a_g_n_·e-ti;;;,,~==

.-Mi·_-

(a) There exists an electric field in the cavity of the shell A. (b) The charge density on the inner surface of the she}] A is non-unifom1. (c) There is no electric field in the region a< r < 2a. (d) There exists an electric field at r > 2a.

12. In figure, we have 2 concentric conducting shells, the first is thick and second is thin. TI1eir total charges and radii are indicated below. At the common cencre, we placed a point charge Q. At what distance from centre will the potential be zero ? (Assume V =0 at oo) (a) 19 R Ol) 1.SR 8

(d) ,6R 7

(c) 2.25R

13. Three metallic plates out of which mMdle is given charge Q as shown in the figure. The are~ of each plate is same. d

o

3d

a

0

(a) The charge appearing on the outer surface of extreme left plate is -~·(b) The charge appearing on the right surface of middle plate is ~. ·

(c) Each of the facing surfaces will bet equal and opposite. (d) The charge on surface with separation 'd' is more than chaton other two charge surfaces. 14. A conducting sphere of radius a is concentric to and inside a hollow sphere of inner radius b and outer radius c. The central sphere contains charge q and hollow sphere contains charge 2q. (a) The electric field at a point ( a < r < b) is equal co 0. (b} The potential at a point ( r < a) is 0. (c) The electric field at a point ( b < ,. < c) is O. (d) The electric field out:sid": the sphere at r > c is 3 Kq/r 2

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~E-le-c-tri-_~ii;if~i.:~~---· ~~-=-=-~~--~. - ~- _ ------------·---_--.. . . ______ . _____I !~. -.. .1-----15. In the

=x I + y J is

present in 1he XY-plane. A small rL,g c;-mying charge , Q, which can freeiy s:.ide on a smooth non- ~nducting rod, is projected along the rod from the point (0, L) such that it can reach the other end of the rod. "'1hat minimum velocity should be given to the ring ? (Assume zero gravity).

2 2. Electric field. 'given _by the vector E

[a) (

(c)

~,r·

---------',...._+X

(G, L)

4r~? r2 I

[ 2m211/2

(d) Qr.

I

_I

1.

y

23. A sphe.re cuntains charge at uniform charge density p. "'1hich of the graph correctly c:escribes potential as a function uf distance from its centre? (x-axis is pa;;;sing through centre, which is

origin).

. 'V

(a) ~ x

t '

V

,

o,J _)

r l_.,

V

',l

(c) ~ x (d}

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~x

[ -_.

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- _ 'I 100-_ .1

Problems in Electricity & Magneii-sm

24. Jn. wliich Qf the following cases potential energy increases ? _(a) A sp~g-is-compressed-from its naturallen$1h. · (b) 'rwo opposite charges are brought ·near each other. , (c) Block is moved on rough horizontal surface. ' . (d) Air bubble .rises up in water. 25. In the electrostatic field of a point charge_q from point 1 (fi&1:1J"e) we moved one and the same charge to points 2, 3, 4. Flnd work done on the charge during the movemerit in each case and compare them. ·(a) ,W2 .< W3 > W4 . · (b} W2 < W3 < W4 (c) ·W2 = W3 =o/4 (d) W 2 =W 4 < W3

1 ...•..... , ..

~\

) . 4

3···-.............

,.

'

26. · An infinite conducting plate of thickness 0.0200 m is surrounded by a uniform field E = 400 '{/m directed left to right_. .See ·me figure. Let the potential VO= 0 _at di,sqmce O.Q200 m to the right of the plate. What is V 3 , the potential 0.0300 m to the left of the plate ? ~

§... V1 V

0.0300 m

0.0200m 0.0200m

, (b) -20 V (c) +20 V . fd) +28 V _ 27. A uniform electric field points in the positive x direction, as shown below. Along the two lines fi, Ji we plot the electric potentials as a function of distance. Choose the correct plot. (a) -28 V

'i

---./

/f2

/

/

......•··

··";

E (

i~~ --·······--... f,

...

X

2 ~

ro

1. 2

E (a) .:planation for Statement-1. (b) Statement-1 is true, Statement-2 is true and Statement-2 is not the correct c>:planation for

Statement-1. (c) Statement-1 is true, Statement-2 is false.

(d) Statement-1 is false, Statement-2 is true.

2, Statement-1 : An electric charge is fixed in free space, producing an electric field around it. No work is done in displacing another charge from its position to any other position. Statement-2 : Electric field is conservative. (a) Statement-1 is true, Statement-2 is true and Statement-2 is correct explanation for Statement-1. (b) Statement-I is true, Statement-2 is true and Statement-2 is not the cqrrect e>:planation for

Statement-1.

'

(c) Statement-1 is true, Statement-2 is false.

(d) Statemcnt-1 is false, Statement-2 is true.

3. Statement-1 : Electrostatic field at a point inside a uniformly charged spherical shell due to it,;;elf is zero. Statement-2 : Electrostatic potential at a point inside a unifmmly charged spherical shell due to itself zero.

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Electrostatics··

I 101 _jl--

·--~-----------

(a) Statement-1 is true, Statement-2 is true and Sratement-2 is corre a). What is chf! electric field at a distance r(a < r < b) from the centre? (a)

2

Q 2 ne 0 r

(b)

3Q 2 4:m: 0 r

(c)

3Q 2 41tt: 0 r

(d) None of these

5. A hollow, insulating spherical shell has a surface charge distn1mtion placed upon it, such that the upper hemisphere has a uniform: surface charge density +cr, while the lower hemisphere . h~s a uniform sutface 'iharge density -er, as shown in the figure. Their interface lies in ' xy-plane. Which of the following starement (s) is/are correct? · ,(a)' The field at all points of xy-plane within the sphere points in the -ve z l \ ',~· -z-direction. -, (bJ J\U poiilts qf the xy-plane within die :;phere are equipotential. (c) The field at all points on 2-axis outside the sphere point along positive z-direction. (d) The field at points on z-axis which are on either side of origin outside the sphere is in opposite directions. 6. Two large conduccing sheets are kept parallel to each other as shown. In equilibrium, the charge density on facing surfaces is a 1 and cr 2 . What is the value of electric field at A ?

.

•A +a2 i (d) cr1 ····0"2 i ~o ~o 7. Two large thin conducting plates with small gap in between are placed in a uniform electric field'£' (perP,endicular to the plates). Area of each plate is A and charges +Q and -Q are given to these plates as shown in the figure. If points R!:S and T as shown in the figure are three points in space, then the : (a) li~l4 at point R i,!> I? (b) - field at point S is E

..

(c)

o1

(c) field at point 1' is (E + _

(d) field at point

_g__) e A 0

Sis (E + _g_) Ae 0

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I

I 8. 1\-vo concentric: shells and (f)v respectively. Now shell R

(a) 4A

c=:1

qB

2

qA qh

=l

Cb)

---------

--·-

- - - .f!.!oblems in. Electri~_!y .& Magn:!ti_sm __

124

ZR charges qA and q8 and potentia]s 2V and

B is earthed and Iet charges qA and q8.Then :

(c) potential of A after earthing becomes(}) V.

(d) potential difference between A and B after earthing becomes V. 2

lf]Matching Type Problems 1. Column-[ shows graphs of electric potential V versus x and y .in cenain region for four situations. Column-II shows the range of ang]e which the electric field vector makes with positive x-direction. ~

•

' ••

~

4

•-

•

, •

- -

Column•I

·-· . (; - cy versus _x) -- (V versu~ r)_

;-

• I/

,1

l

11

;!

~

q

- •• •

• - •-• • I

Column-II

.

" ·O::::i 0 < 45°

(A)

(P)

(B)

(Q)

·4s0 ::;e < 90°

(C}

(R)

90° 5: e< 135°

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_ _ _-·-_--··_---·---- E,_~_)I:__

Electrostatics

'(D)

(S)

· fiComprehension Based Problems Comprehension -1

--

-----

______________ ..

;~int

·1~;ere is a .cubical c~~ity inside a conducting sphere of radius R.A positive c_harge q_ isl _placed at the centre of the cube. and another positive d1arge q is placed at a distance l (> R) I the centre

'.

Upper

...• -.

.

_...;. .-·-...::_.

_,

. . . ''

• puncv. -

..

t., BelI-

.}:,

. ..-

r:

111oGround ·(

The electric potc1itia,i-of the dome is V ""Er where Eis electric field just outside the dome and ,

:r 1s 'the-.!adius. ·111e ~~arge_s on ihc s_urface· ofthe dnmc. d~ n?t affect the _electri~ field inside .) lthe C~Vlty. 'fh,c P?tent1al that_ c~n Imtld up on the dome 1s ]lll)lted by the d1clectnc :strength of ! the air; ·Which_ is about. 3~,00_°.-V~cm fo~ dry aJt. a,t- rQom t~pe~atu~e. _When the. el~c~ic fie}~ [arqu:n~ -th~ -dome reaches· tit~ q1clcctr1c_ stre~g~h .of the au:, air mol~cules are, JOQJ.zed. Tim; .! ~na~l,~t the air to· conduct· electricity. Van de Gra.~ff generators are to~tindy used hi. college pliysics laboratories. Wh,~n a student gees within? few inches of a Van de Graaff generatoi;

l

l

1she_·r:i'.l-3-~}l~w. a spar~·~th an 'instantaneous cup-ent-of 10 amp 1m~t~n,.~~n~ous cunen~ i~ th~ -~ansfer !)f charge wi~in 1~. _

a~q· remains uninju~ed. Ju}_ ·

4. The 660 V rails on a subway can kill a person upon contact. A 10,000 V Van de Graaff generator, howevei:, will only give a mild shock. Which of the followin1 best explains this seeming paradox? (a) The ·generator provides more energy per charge, but since it has few charges it transfers )esser amount of energy.

a

(b) The generator provides more energy; but since there is little energy per charge the current

is small. (c) Most of the energy provided by the generator is dissipated in the air because ·air presents a smaller resistance than the human body. (d) Most the energy flows directly to the ground without going through the human body since the generator is grounded. S. What is the maximum potential the dome, with a radius of 10 cm, ca_n sustain in dry air? (a) 3 kV (b) 5 kV (c) 300 kV (d) 500 kV 6. Why is the potential of t11c dome limited by the dielectric strength of the air ? (a) Once the potential of the dome reaches the dielectric strength of the ail:; charge fro·m the belt is repelled by the charge on the dome. (b) Once the potential of the dome reaches the dielectric strength of the ait; the .air heats the metal of the dome and it is no longer a good conductor. (c) Once the air molecules becomes ionized, charge on the dome can leak into the air. (d) Once the air molecules become ionized, they no longer conduct electricity.:

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--- -

------------ --~----~-

Electro~tatics

-

---

7. Why docs negative charge from the outside of the belt continue to build up on the outside of the dome instead of being repdled by "the charge that is already there ? (a) The potential is zero inside the dome. (b) ·i11e rnnducling dome shields the effects of the charges on tJ1e surface. · (c) ··1bcre is only positive charge on the outside of the dome. (d) Charge. does not build up on the outside of the dome. 8. What is the work required to move a charge q from the top of the belt to the surface of the dome, if the amount of charge on the dome is Q and q was the only charge on the belt ? - (a) ·O

(b) kQq

2r

(c) kQq

r

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r

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c-- ·=I IATTfl!l!l!~B'S [AW~__-ELECT~C~~~-Q_-__··-=--=---~~-·--1 Only One Alternative is Correct

j2.

1.

(a)

9.

(d) . 'i 10.

17_

(a)

25.

(~) 126.

'a.

(~)

4.

(a}

.....

·Is.

(c)

11.

(t:)

12.

(d)

118, ,-~c)

19.

(c)

20.

(d)

21.

lb)

27.

I(~).-..

i28-

(d)

29.

c~J. ··ia4. I-ca)

85.

{-car . J36.

•

33. -

(d).

: .-1

.-l

l(d)

lea)

. 13.

,,

.

I j 6. , !(a) I 14. · f(a)

IIcc)

22.

I(a)

jk)

30.

(c)

(b) __ '. 37. !(d)

38.

.Ca)

I 7_

I

15 .

· J 2:-1.

l

-r·· , 39.

.lta)

ls.,. .(a).·:-q .

Jcai j1Ch (b)_ 24

_(b)-,32. (c)

!

More than One Alternative are Correct

II · - - ·.1! (a,d}____

_ 6. ·

I

(b). ~(r.) -.

I

l

(i:) ' '

f:· ... ·1'

(~,_b_,c) / ;J

-,

: ·. ·. "i

Only One Alternative is Correct I

[b) 14.

(b)

.(d) . 12.

(b)

1.

(a)

12.

(c)

9.

(a)

\ 10.

(c)

17,

(b) '· 18.

(c)

19.

(d) . 120.

1311.

I 5.

lia.

(b)

25.

f(c)

26.

(c.)

27,

-Cd)-

l2s.

(b),

33.

l(t.l}

34.

(b)

,as.

(b)

}a6.

(d)

l[b)

I

(b)

21.

l'(b)

29.

!Cb)

I

!cc):. ··i 7,

6.

14.

(a)

22.

(c)

J30.

! 15.

(d) 16.

123.

(d) 24

.i

.(d) '

i-(a) 8.

:n .

Is,. lcdJ I

l(b)

7.

I

l

(ii..~.d)

· 3.

I ·· 1(a,b)

·1

(a,b,d)

J9,

lca,b,c)

! 10. k~,c)

14.

l

,.~a,b,d)

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(b).:_ lI

(~ (c} ··j . (d):

I

. ' "· 1

More than One Alternative are Correct t.

32.

i

Is.

11.

l{a,b~c)

,ca~b.cO

l 6.

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j j

---=-=~==~~~·-·

_ _E_le~c_,_.trost~~i£1!~---~~-,__,~~-:_·_--_Matching Type ProJJlems

·1

~~-~-1[1 ?i_11.

l. (A) .-P, R (B}->Q (C)->P, S 2. (A) >P {B}--+P (C)--+P, Q

Assertion and Reason Type Problems 1.

I(d).

l

I 2.

I.(d) .I3.

,1

L ..1

I l'·

l,(e)

l

II (b) ·

l.

.Comprehension Based Problems

2: 11,(a) 13. I

1.

[ (c)

\

9.

lea)

J 10. , ca·,c,d} 11.

I

r-·--··~-

I

.

17, 25.

I

j

l l

,I I' t

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1'

' - "II 130 I .;L,-_·______-_-_-_--P-_ _ ro-,-b-le-,-n-s-in._:_E-ie_c_t~r,-.c-i_o/,~.-&----1Vi-a~g-n-e-iis-:_-;;-_-_ .

!

More than One Alternative are Correct

f'~ '.)

14-

..

':._ 1,·.-

~ ~

,(b,c)

1·· ,{~;C' .. -jI~-.

~.

.

...

,i

I

Matching Type ProbleTs .':

..

. 1. (A)->P, Q, S (B}---,-P, R, S (C)-41? Q (D)--+Q

Assertion and Reason Type Problems 1Ca)

1.

_I 2.

~ca) f

I

'

l

(

J

I_

·

1

Comprehensi~n Based Probl~~~

··:...

•

••. ,;'I,

Only One Alternative Is Correct · l(b)

·•

(d)

6.

(b)

7.

(b) 8.

12,

{b)

13.

(rl)

14.

(cl)

15.

(b) 16.

(a)

20.

t(a)

21.

,{c)

22.

(c)

23.

1(a). 24

(d) --

28.

29.

;(d)

;JO.

(a)

: .31.

I-cc)_ .32. .

2.

9,

(b)

10.

(d)

11.

{b)

17, ·

(b)

18.

(a)

19.

25.

(d) •126.

(a)

27.

l(a)

i

(a).

More than One Alternative are Correct

12.

1,

7,

13.

-.

(a,c1d)

(b;d} (c,d)

..

5.

(b)

r)::t:~:~.-

,4.

(d)

I.

3.

,._1,_'

I --13.

; 1915.

(b,c,d) (a,b) (c,d)

4.

·(a,b}

10.

!(~;d)

-

I

t--------

j

S.

11.

lca,c,d) _lca,cJ. . J

:.,-•

•

-~~r

rj·1I - -.

_I

[c)

f(J:

-·,

(C} - I,

..

tca;h> . ·,· j

E_;

6.

12, -

.• J

.:I

.

Matching Type Problems ·1.

(A)4Q (B)_:__,.P, S (C)4Q, R (D)-4 Q, R 3. (A)-+P, R (B)4Q, S (C)4Q, S (D)4Q, S .. 5. (A)-;+P, Q (B}4Q, R (Ch,Q

2.

(A)---tP, S (B)4P, lf(CJ->P.

s· (D)---t Q, S

4. (A)--+P (B)-,.Q, R (C:::)45 . . _ •6. (A)-41~ R, S (B)~P,'i~:R; s.. T (C}-,(fT (D}->ll, S . '

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Electraslcitics ·

I

.

Assertion and Reason Type Problems 1.

I(iJ) I2 ..; Ice) Ia. Ica).

i-1.

I(d) l s. Ica) l

I

J

Comprehension Based Problems 1.

Ica) ·I2. ICd) . is.

!.cc>.

i4. ICb)

Is.

l6.

t.fo}

!Cb)

I1. lc.o Is. i(b>

:1

_ _ _ _ _ i. J-=--[F. .:_j(:~~-~_TllJNJlLP~~O_b_lE_M_S ] _ _ _ _=3 Only One Alternative is Correct 1.

(d)

9,

(c)

17.

j2.

!(bl

(d)

3.

10.

(c)

11.

-(d)

18.

(d)

19.

led) -

25,

(c)

26.

{d)

27.

33.

(a)" • 34.

i-ta>

'.4.

Ch)

(e)

12.

(a)

20.

t(a)

Ice, .'.. 2s.

(d)

I " >•.:>

'

Is.

6.

(c)

14.

(c)

21, . (d}

22.

(b)

29.

30.

(b)

13.

.

I

(e) (1:1)

..

1~h1 . .

I'·

;

O!) l 8.

(a)

(b) 16.

·(d)

I 12s.

(a) 24

(c)

'

(d) 32.

;

15..

I

31.

! I

'

l(b) ; • ·I

,:'(''

More than One Alternative ,are Correct 1. 7.

(a,b,d) (a,c)

2.

l("b1l

!

3.

I

I(a,b,c)

4.

(11;b,c,d)

I

s.

l(a,dJ:

. 6.

l

(a,b)

i

Matching Type Problems 1. (A)-+P, T (B)-+P, R, S, T (C)-+P, Q, R., T (D)-+ Q, R

Integer- Type Problems 1.

lo.osi I

I" ·· I

I _I

Assertion and Reason Type Problems 1.

ICd) l 2. ICa) i s. !(d) - l

I.

I I

,

. I ..-~·., ,

.

,

I

Comprehension Based Problems

·I

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Only One Alternative is Correct 1.

l(a) j2. ica)

3.

' (c)

!

9. 17.

25.

Cc) (c)

,Cd)

j 10. {Cb) I

11.

f(d}

19.

](c)

27.

l

18. 26.

(b) ·"

14!12.

' . 7.

(c) .

5.

(c)

6.

jS, Q (Il)----J>P (C)----J-H. (D)-:i-Q

1.

r

Comprehension Based Problems

lCb)·_..j2. !cci .' la.

1.

1·a,j-._-1-4.-(-Ca)-,-.

ls.

j

!cc). ·l6. lee): :, 7.

l(a),:,-j,' . '

.'

)'

]•

i.,,1

j"

l

••

-

•.

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.

..

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,....,,.,------- ;n.-•·--- ·-------~-~,__..-.........,.---------,--_ •-•- •...,.'":._,u_ " ~ - - - - - ·

~--

.1·2·---~' m.

Electric Current

... i

...

•

I

I

~

·'.r •

lf··1on1y One Alternative is Correct 1. Both terminals of a battery of e.m.f. and internal resistance r are grounded as shmvn. Select the correct alternative. (a) Potential difference across A and Bis E. (b) Current across AB is zero. (c) Current across AB is E / r. (d) None of the above 2. Five cells of e.m.f.'s lV, 2V, 3V, 2V and lV and having internal resistances 1,2,3,2 and 1 ohm respectively are connected as shown in figure. (a) VA> Vs (c) VA y > z (c) y > X > Z (d) X > Z > y 48, In the circuit shown in the given figure, the resistances R 1 and R 2 are respectively:

B

A

D

R1

20n

69V

(d) 14 n and 30 n 49. 'Two cells of the same e.m.f. E have different internal resistances r1 and r 2 • They are connected in series with an external resistance R and the potential difference across the first cell is found to be zero. Therefore, tI,ie external resistance R must be: (a) r1 - r2 (b) r1 + r2 (c) 2r1 - r2 (d) r1 -2r2 50. In the following network of 5 branches, the respective current are i 1 , i 2 , i 3 6 etc. Given that i 1 = 0 .SA, i 4 = 1A, and i 5 = O.SA, the remaining currents are: (a) i 2 ,..-1.SA, i 3 =0.SA, i 6 =0.SA 4 (b) i 2 = 1.SA, i 3 =-0.SA, i 6 = O.SA (c) i 2 = 1.SA, i 3 =-0.SA, i 6 = -0.SA (d) i 2 =1.SA, i 3 =0.SA, i 6 =0.SA 51. In the house of a person who is weak of hearing, a light bulb is also lit when somebody rings the door-bell. The ring can be operated both from the garden gate and from the door of the house. Select the correct possible circuit (s) required. (a) 14 n and 40.0.

(b) 40

n and 14 n

(c) 40 n and 30

n

·[21)· ~

~.

.

' (a)

(b)

(d)

(c)

t--{•}-{.

~->- ·

_ _ _ _ _ _ ............/ . · . · · - ~ - - - - - - - - - . - .-· ---~..-i-:: . . .

~

52. If M = mass, L = length, T = time and I= electric current then the dimensional formula for resistance R will be: · (a) [R]=[M1L2T-Jr2J (c) [R]

(b) [R]=[MlL2T·-3I2]

= [M 1L 21' 31-2 ]

(d) [R] = [M 1L 2T 3(']

53. A conductor of resistivity p and resistance R, a1; shown in the figure, is connected across a battery of e.m.f. V. Its radius varies from' a' at left end to 'li at right end. The electric field at a point P at distance x from left end of it is:

(a)

(c)

vz2r

2Vl 2p

(b)

rrR.[la + (b - a)xf

nR[la

Vl 2 p

+ (b- a)x] 2

(d) none of these

2nR[la + (b - a)xf

54. A piece of conducting wire of resistance R is cut into 2n equal parts. Half the parts are connected in series to form a bundle and remaining half in parallel to form another bundle. These bundles are then connected to give the maximum resistance. The maximum resistance of the combination is: (a) R (1 + ~) 2 n2

· (b) R (1 + n 2 ) 2

R

(c)

·

2(l+n 2 )

55. In the given circuit, when key K is open, reading of ammeter is I. Now key K is dosed then the correct statement is: (a) If 6 1 > IR, reading of the ammeter is less than I.

(b) If IR < e 1 , reading of the ammeter is greater than J. (c) If 6 1 < 2JR, reading of the ammeter will he :r.ero. (d) Reading of ammeter will not change. 56. In the circuit shown., the batteries have e.m.f. E 1 = E 2 = lV, E 3 = 2.5 V and the resistance R 1 = 10.0., R 2 =20n capacitance C = 10 µF. The charge on the left plate of the capacitorC is:

¢

~~-

(a)

+ 2 µC

(b) - 4 µC

(c) - S µC

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57. A wire has linear resistan4)

(a) 2E n

(b)

2E(l- ·q

(c) 4£

n;

(d)

/l

2E(

l

128. In order to determine the e.m.f. of a storage battery it was connected in series with a standard ce1l in a cc>rrain circuit :mci a c1.:rrem I 1 w2s oh:n:ned. \Vnen tJw 'battery is connected '.:o the same cin:uit opposite Io the standard cell, a current I 2 flow in the external l"ircuit from the positive pnle of the storage battery was obtained. What is the e.m.f. i; 1 of the storage battery? (The e.m.[ of the standard cell is E 2 ) (a)

129. Two current elements P and Q have current voltage characteristics as shown lwlow:

Ip

I

~--10

P.D.(voI1)

f 10

P.0./v,;,lt)

Which or the graphs given below represents current voltage characteristics when P and Q arc lr: sc:ies7

t

0.

'

( b) ~

{a)

2li,

.. -..

-_.-

--

-;o 20 P.D. {volt)

•

1 --------- : ' . :

I"

j

: '.O

-----20

P.D. (vol~)

2

ci:

I

-~ 0.

. :

~2 1 : ~ ,,; '


and i are electric field at, cµrrent density through, electric flux through and current through shaded cross-section respectively as shown in figure. Physical quantities jn column-II are equal to those in column I. Match the expression in Column-I with the statements in Column-II. shaded cross·

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----------------1-~·-··----------------~ Electric Current . . ~-- ..... ... - Ir - . .. .. .-- !,~· .... ..,_,. Colµh},n~l~ ' . • . ·r • I, • - - .. • . . -...

____

,_

__

....

'Ill

_...

....

_,,..

~ 111'

.....

--

_.,.....,,.

. • ... ~J"

I

ol

.. .,._

j_ .

(A)

..

.

(B)

(C)

(P)

..

. "'"···

E.

,!

-

.

-

(R)

Resistivity ofto~

(S)

Power :delivered to rod·

V

-

.. ~,

-

.. ·' ..

(Q) Resistance'. of ~od

·rnpv

'

'•

'

I


V 2 ,R 1 -> R 2 , C1 ... c 2 (c) V1 < V:i,R 1 < R 2 , C1 =C 2 (d) V1 < V2 ,C 1 < C21 R1 = R 2 36. In the given circuit, the capacitor of capacitance C is charged by c R closing key 'K' at t= O. Let the maximum charge on the capacitor be Q and the initial rate of charging be i 0 , The capacitor is now removed from the :,circuit, discharged and charged again by a constant current i 0 to ·maximum charge Q. Find time required. (a) RC/3 (b) 3RC/5 ~ (c) 2RC/3 (d) SRC/3 E K 3.7. In a discharging RC, circuit (a) V1

= V2 ,R 1 > R 2 , C1 > C 2

R

(a) .R:~tio of charge pn capac~tor and current in resistance increases ¥(ith _tiµi~··· '.. ~:_ (b) Ratio of charge .on capacitor and current in resistance decreases wit;h ,time. • (c) Rado of charge on capacitor and current in resistance remains constant. ·.,: :· · · · (dJ Ratio of charge on capacitor and current in resistance first decrea.~es; then increases with time.

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W_-_-_-_----~---_-_-_________P_ro~~;-s-in-Ek~tric-it_y_&-_M_a_g_n_e-ti_s_m__ '38. An uncharged capacitor and a resistor of big resistance are connected in;series to a battery of electromotive force 4.5 V. The voltage across the capacitor is 3V one minute after the dosing

the circuit. What will the voltage across the capacitor be 2 minute. after closing circuit? (a) 6V (b) 4.5 V (c) 3.SV (d) 4V 39. The diagram in figure show Resistance of resistors R 1 = 8 ohms, R 2 = 12 ohms I R 3 = 10 ohm, the potential difference between points a and bis 60V. The potential difference between points m and n is: a

b

(a) 16V

(b) 60V

(c) 36

'(d) 24V''

te]More than ·one Alternative are Correct 1, Capacitors C1 = ljJF and C 2 ""2 µF are separately charged from the same battery. They are then allowed to discharge separately through equal resistors.

(a) The current in the two ,discharging circuits at t = 0 is zero. (b) The currents in the two discharging circuits at t = 0 arc equal but not 1.ero (c) The currents in the two discharging circuits at t = Oare unequal. (d) C1 loses 5.0% of its initial charge sooner than C 2 loses 50% of its initial charge.

,,,,.l?:-:-:-:1Fl

2, In the circuit shown in the figure, switches S 1 and S 2 have been 82 1011 closed for a long time. .L~1 2v 60 (a) Charge on We capac is 100 µC. _ 21' 70 (b) Charge on the capacitor is 20 µC. _ T4V _ (c) Charge on the capacitor increases to 120 µC if one third of the gap of the capacitor's plates is filled with a dielectric (K = 2) of same area. (d) Charge on the capacitor remains unchanged if one third of the gap of the capacitor's plates is filled with a d_ieleL'tric (K=2) of same area. 3. A capacitor C charged to a value Q = eC is connected to a batt~ry of e.m.f s as shown in the figure. .

(a) Charge on the capacitor is zero at time RC ln ~ a~er the switch S is closed. (b) . -·· _1_2_54---...JI-_·-•.-.----.. ·-····.

:P_roble_ptj_i_n_E_le_c_tr!rs ar~ _ initially w1chargcd. 12ui::-, 4Q

.

3Q

1=

f-

l

,,_, I ''

"SIJ

3µF

24V

~A

- - - - - . . . - . . - , ~ ~ • • • • • u + 1 1 t 1 1 ~ - - - - = ~ = - ~ - - - - - -........INHIIIIMIIIIIIIII),,,,..,~ - - -

1. At time t-=O. the switch S in the circuit is closed. At that instant, what _is the equivalent resistance of the circuit? (b) 1.20Q (a) 9.00 Q (c) 1.80 n Cd) o.92 n _2. After the ~witch has been dosed for a tong time, h9w_much charge is on the positive plate of the 3µF capacitor? (a) 24 µC (b} 32 itC (c:) 56 µC (d) 72 µC:

-- ----· ·----·--· - .........

Comprehension· 2

!.. -

________

A capacitor with square plates of side l has a charge Q. A protoi1 enters the unifom1 eiectric fieJd'·of the capacitor after being accelerated from rest through a potentfal difference V. The. protc;in:(tjlarge +t, mass rr,J'.enters the capac;jtor·parallel to the plates and is deflected by a' distanced/?-(where dis the gap between the plates.) · N'owthe switch Si is dosed for some time t 0 and reopened when the heat generated in the 2R' resistor is'o~e third of the ipitial stored energy of capacitor. Switch S 2 is now dost·d for a'Jong t4n,e but the ·capacitor finally attains only 81 % of its initial energy. . S 2 is n'ciw ripened and gap between the plates is changed so that the stored energy in. cap~cito~ ~ecomes equal tn the initi~~ store d~~ergy. Neglect the effect of gravity. , 1

I

l

0

-·

I

\

\

i

'.

\-

0

l ~a;: "· :I,

.''-l ·

2R

R

.,,~a

e,m_~·-··-···········

I

"J\t,/',.,-----

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_"""'"Capacitor_s_ _ 3. Time spent by proton between the plates of capacitor is (a) l

~

1J eV

(b) l /mdEo eQ

(c) l /l2mdEo \ eQ

v

(d) l

/2m

VeV

4. Energy gained by the proton in this time is: (a) eV

(b)

e(v +

~i 2Eof 2

eQd

(d) none of these

(c) -- ----2E 0 I 2

5. Correct expression for charge on the capacitor Q is: (a) 2E 0 Vd

(b) VI2E O

(c) 2c 0 VZ

d

(d) none of these

6. Time 't 0 ' for which S 1 is closed (here C is the capacitance of the capacitor.) (a) 3RC In 3

2

(b) 3RC ln 3

(c) 3RC In 2

(d) 3RC ln 2

2

7. Graph of current i vs. charge (q) on capacitor before t < t O is: (a)

i~q lL.q (,)'~q

(d) '[ " " -

(b)

•

q

8. Heat generated in R in this time (t 0 ) is: Q2 (a)--

4C

Q2

Q2

(d)

(b) 6C

(c) 24C

(b) BlQ lOOC

9 -1 ~ (c) ( 10 ,,fi_ C

Q2

12C

9. E.m.f. of the cell is: (a) 9Q lOC

)Q

(d)

none of these

10. Work done by the cell is: 9Q2 (a)-----lOC

(b) ( _2_ 10

__!_)Q2 ./2 C

(c)

_2_( _2_ - _!_) Q 2 1010

,J2

C

(d) ,none of these

11. Final gap between capacitor plates is: (a) 10d

9

(b) 9d

10

(c) Bld 100

12. The ratio of final to initial energy density is: 81 9 (a) 10 (c) 100 (b) 10 9

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(d) 100d 81

(d) 100

81

:.2_

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I

I . ,·.

:I 256 I ·~______.,__________P_r_o_b_l_e_m_sJ..n Electricity'---&_Mi_a_.,,,g,_n_-e_t~,~''!1- -~ . _-__-.:-~:~:= -:----==~--..:::.=.-_-_:::_________ , '.-1 -

Comprehension - 3

---~----~---.,,,,..====-=-----==-·,::::::::::::::. . :.:.::::~~

e:::::::::::::::::::::::::,.,,,- ·- - - - - - ~ -............

Consider the circuit in the fii;ure·. The switch is initially in position A _ R · _for_ a su_ffitjently long ti~e to esrablish a s~eady st~~e. At t "'' 0, the_ . - ~

1 8 CLiiTA

sw1t:ch 1s turned to pos1t1on ~- The capacitor 2 C did not hold any · · charge before t=O. · -

ri:-i .

·

E

J.. 2C

·

2R

13. 11le magnitude of charge which each plate of capacitor C ho1ds before t =0 is: (a) CE

(b) CE/R (c) RC/E (d) RICE 14. At r -+- oo, when a new steady stare has been established, the charges held by capacitors C and 2 C will respectively be: (a) CE and 2CE (b} CE/2 and CE (c) CE/3 a.nd 2CFJ3 (d) 2CE/3 and Cf: 15. The current decreases exponentially between t = 0 to t:::::oo_ The time.-constant is: (a) 9RC (b} 2RC (c) 3RC (d) 3RC/2 16. The energy lost between t =0 to t =mis: (a) CF. 2 I 3 (b) 2CE 2 / 3 (c)CE 2 /9 (d) 8CE 2 /9

17. The time, at which charge in t.he capacitor C is reduced to half of the value, it had at t = 0, is: (b) 3.RC]n 2 (c) 2RCln 2 (d) 4RCin 2 (a) 6RCln 2 Comprehension -4

~

--__ -_--:_--- ·:-: _--. :_-::-.:-. ·::. ._. . ._.. ______-~.:.__ --------_J~

A circuit contains a battery, a capacitor and a resistor as shown: The capacitor is inir.iaHy uncharged and the switch i:. dosed at time t .= 0.

OR=4Q e=12V

,.·

.. -1

18. At

c , , , 0, the current in this drcuit is:

(a) zero (b) its maximum possible value (e / R)

(c) somewhere between zero and maximum, depending on R,C 19. At r. , , , 0, the voltage drop across t.he capacitor is: (a) zero

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"__,,_~,_2-apacitor~_ ..:~~~- - __:,. _____ .__ _____________ - - - - - -

~£:_ -

IL~I.~

(b) its maximum possible value (Qm;"" / C) (c) somewhere between zero and rndx imum, depen, Ii ng on R, C

A%,Mt4MMW

. -- - -_ -------- ----····· -- - ---::::=i

'

In the c~~nection shown in the figure, initially the switch K is open and-the capacitor is_·) L.nc.hargc{'.._T!1en the swi:ch is c:osed and :he capacitor i.~ charged U? to the steady ~tate and : the switch is opened ar,ain. Determine the values indicated by the ammeter. j G~ven: V 0 :-30 v, R 1 = lOkQ, R 2 ~skn

I

20. Just after dosing the switch:

(a) 2mA

(h) 3m.A

(c) OmA

(d) none of these

(c) 6mA

(d) none of these

(c) 6rnA

(d) none of these

21. A long ti:::c after the switch 'N2.S closC'd:

(a) 2m.A

(h) 3::-j\

22. Just after reopening the switch:

(a) 2mA

(b) 3mA

=-====:_:j

Compr~h~Qslo.n __ .6~-

f;

T~e circt~ir s~own i~ fi~ure _1 _consist:~ or a r_esistor. hayi~gxes~staJ:(:: connected in.seri~~ j W1th a capacitor, havmx- capacitance(., ;md·an e.m.f. i:. A short prcmt ts mchtd.ed that makeslt·I possihie to t·xclude the vnltage source c fro!:". the circuit by throwing ,he switch s to posi~ion·; B. In'. this position, the capa~itor completely discllargcs through the resistor. . i When thP :;....;;itch is thrown to position /\' the e.m.f. produces a current I t}J.at'.p;is, i 2 ). When the currents are in the same direction, the magnetic field at a point midway between the wires is 20 µT. If the direction of i 2 is reversed, the field becomes 50 µT. The ratio of the currents i 1 /i 2 is : ,(a)- 5/2 (b)- 7/3 (c) 4/3 (d) 5/3 25. Constant current I is flowing through a circular coil of radius R. At what distance from the centre will the magnetic field (on the axis) be maximum : ~ R {a) -

(b) 2

(c) R

(d) zero

./2

~

26. A conductor carrying cur;ent 'i' is bent in the form of concentric semicircles as shown in the figure. The magnetk field at the centre O is:

uptom 4a

2a

(b) µoi

(a) zero

80

(c)

6a

µoi a

27. The figure shov.-s four different sets of wires that cro~s each other without actually touching. The magnitude of the current is the same in all four cases, and the directions of current flow are as indicated. For which configuration will the magnetic field at the centre of the square formed by d1e wires be equal to zero?

(a)

Io-4t, : ,to'--t, (b)

----. I

(tl)

+-I

28. The figure shows two long wires carrying equal currents l 1 and I 2 flowing

in opposite directions. Which of tlle arrows labeled A to D correctly represents the direction of the magnetic field due to the wires at a point located at an equal distance d from each wire ? figure (b) B (a) A (d) D (c) C

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12

I1

G·---~----® ••

B .'

C

r,

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t .

I

12as

f

'

-

~

29. In the diagram shown, a wire carries current I. Wl1at is tl1e value of the B - d s (as in Ampere's law) on the helical loop shown in the figure? The integration is done in the sense shown. The loop has N turns and pan of helical loop on which arrows are drawn is outside the plane of paper.

(b) µo(O

(d} zero

(c) ~lo (NI)

30. Two mutually perpendicular conducrors carrying currents I 1 and I 2 lie in one plane. If l 1 is taken along x-axis and I 2 along y--a.'tis, 'the locus of points where maguetic induction Is zero, is : (a) a straight Jine passing through origin and having slope l 1 /l 2 (b) a straight line passing through origin and having slope J1 /! 2 (c) a circle (d) a hyperbola (e) A straight line passing through origin and having slope 45°

.

Y:

31. Fig. shows a t.hin metal sheet in the plane y =D, for which the current of constant density flows in the positive x-direccion. It is in a constant homogeneous magnetic: field of value =(0, 0 ,B 0 ). As a 82 result of superposition of magnetic fields in region y > 0, the induction field B1 =(0,0,B) and in y B 2 • Spedfy the correct statement (b} Bo "'(Bi + Bz)

(a) Bo"" CB1 -· H2)

2

2 (c) B0

=B1 -t· B 2

(d) B 0 =B 1 -B 2

32. The diagram shows three arrangements of circular loops, centered on vertical axes and carrying identical currents in the directions indicated. Rank the arrangements according to the magnitudes of the magnetic fie)d at the midpoints between the loops on the central axes. (From minimum to maximum)

1

(a) 1, 2, 3

2

(b) 2, 3, 1

3

(c) 2, 1, 3

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(d) 3, 2, 1

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· The Magnetic .Jlield 33. We have a uniform current carrying wire loop bent in the form of a semicircular cylinder, as

shown in the diagram. The magnetic: field at the origin is : Y.

l.

(a) directed along x-axis

(b) directed along y-axis

(c) diret:tl"d along z-axis

(d) zero

34. ·rwo unconnected circular loops of wire lie in the same plane with the same cent:re, as shown in the diagram. The outcrloop carries current of 2A in a . clockwise direction and has twice thEi radius of the inner loop. 1f the magnetic field at the centre of the loops is zEiro, then the current in the inner loop must

©o

be;

(a) 2A in the counter-clockwise direction (b) 2A in the clockwise direction

. (c) IA in rhe counter-clockwise direction (d) 1A in the clockwise direction

3_5. The magnetic field due to a current carrying square loop of side u at a point located symmetrically at a distance of a/2 from its centre (as shown is) : (a}

:fi_µ_ 0 i_

(b)

-,/~i°M

~ ~1ta

2µ 0 f . (c) ........................

& ,

a

{d) zero

../3rra

36. A thin, straight conductor lies along the axis of a hollow conductor of radius R. The two carry equal currents in the same direction. The magnetic field B is plotted against the distance r from the axis. Which of the followint~ best represents the resulting curve ?

r--.

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_______ --·-· .,...

_______________ Problem.!!.l!!..!:;}'!.._t;.tri~!!Y & Magn:~~m~--

~--270

B

(d)

37. The dimensional formula for the physical quantity E 211 ?e 0 is : (E = electric field and B = Bz magnetic field) (a) LOMOTO 38. A wire carrying J is shaped as shown. Section AB is a quaner drde of radius r. The magnetic field at· C is directed :

A-------- C

(a) along the bisector of the angle ACB, away from AB · (b) along the bisector of the angle ACB, towards AB (c) perpemlicular to the plane of the paper, directed into t.he paper (d). at: an angle

rr./ 4 to the plane of the paper

39. A direct current is passing through a wire. It is bent to form a kctrodes must lie : (a) QEJii{ln3)/M (b) (}B 2 R 2 (ln3)/2M (c) QR 7 R 2 ~:.n3)/!IJ

(dJ none of '.:hese

71. A particle of charge q and velocity v passes with constant velocity through a space 1,-vith non-zero electric field !'. and magiwcic field B. The undeflecting conditions will hold if: (a) signs of both q ;iml E are reversed. (b) sigm of both q and B 2.n: :·evc:-scd. (c) bo1b Band E arc changed in m;-ignitudc, bui- keeping the product of IBI ;-ind IE I fixed. (d) both Band E an: doubled in m:ignitude. 72. A mass spectrometer is a device which select particle of equal mass. An le> 6 0 0 0 iron with electric charge q > 0 starts at rest from a source S au':l -292---1_ --->

-

5. A particle of mass m and charge q moving with velocity v enters a region of uniform magnetic --->

field of induction B. Then ; (a) . its path in the region of the field is always circular. > ->

(b) its path in the region of the field is circular if v - B =0. ...

--->

(c) its path in the region of the field is a straight line if v x B ~o. --->

(d) dist;1nce travelled hy the partide in time T dc)('s not depend on the angle between v and --->

B.

6. 1\\'0 particles havi.ng the same specific charge ( q/ m) enter a uniform magnetic field with the same speed but at angles of 30° and 60° with field. I.et a, b and c he the ratios of their pitches, radii am! periods of their helical paths respectively; then : I (a) abc=l (b) a+b=:2.;1c (e) a 7 ::a:c

(d) ab-c

7. A long s:raight cylinc!rical shell has inner radius R, and outer radius R O , lt carr!es CUtTent i, uniformly distributed over its cross-section. A wire is to be placed parallel to the cylinder axis, in the hoJlow region (r < R, ). (a) The magnetic field is zero everywhere in the hollow region. We conclude that the wire is on the cylinder axis and carries current i in the same direction as·the,current in the shell. (b) The magnetic field is 2ero everywhere outside ihtc shell (r > R 0 ). \·Ve conclude tr.at Lhe wire is on the cylinder axis and carrie:; current i in the direction opposite to that of the current

· in the shell. (c) The magnetic field is zero evel}'\vhcre in the hollow region. We conclude that the wire may be anyv,·here :n the hollmv region but must be carrying current i :r. d,e sa:ne direction as the rnrrent i2 the shell. (d) The magnetic field is zero everywhere in the hollow region. We conclude that the wire does 11ot carry any current.

8. A charr,cd rod having charge as shown is rotating with angular velocity rn about cm hinge at its centre. At the instant shown rod is along x-axis, Car.sider effect of :icld at the imtant sho½-n.

~----(!): .... I\

(a) A magnetic field H i ,\ill slow rlnwn rod. 0

I\

(b) An electric field F. 0 j will slow down rod. A

(c) An electric field F.,,(- j) will slow down rod. (d) A mag11etic field

c;1'1..'lOt

slow down rod.

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--- - - - - ---·- .- --~~:-____ .---_----1 293 1--

_T!_i'! .A-~ag_'!:_e_t_i!'-_ Fi.eld

\3 )Matching Type Problems 1. A charged pattidc having non-:r.ero iuilial vehwity is snhjccted to l:crrnin conditions given in

column-I, column-II gives possible trajectories of the particle. Match the conditions in column-I with the results in column-II.

·- - .... - plates that create the electric field in the

selector "? (a) Nothing (b) RedL!l"e its magnitude (c) Incrt>ase its mag:1:tntlc (d) Rewrsc the polarity; and reduce its magnitude 28. Two particles, each of w;1ss m and charge q, arc attached to the two ends of a lighL rigid rod of length 2R. The rod is rotated at cuns1ant angular speed about a perpendicubr axis passing thrnugh its centre. The r:n:o of the magnitude~- of the :::~ag.:-1etic moment of the system arid its angular momerr:um c.bout :he cemn· of the :od is : (h) 51. (c) 2 'l (d) ...:L 2m m. m rrm 29. A thin uniform rod with negligible mass an D > A

(b) B>C=D>A

(c) H >A>C =D

(d) C>ll=D>A

31. A positively charged tli.sk is rotated clockwise as shown in the figure below. What is th(' c:redon of the mag:-.etic field at point A in t:;e pla:1e of the disk ? ~+++ +; '+ + + +-+-+

A

•

~

(a) ® (into the page)

(b)

(c) (-

(d; 0 (ot:.t of the page)

3 2. What an· 1he directions of the magnetic field bctwei·n and outside a pair of two parallel large

sheets carrying currents in the same directions, as illustrated in figure?

(2:

Tow;i.rds us between t:1e pktcs arnl 8',Vay fror:'. us above and below the plates.

(b) Towards us above the plate.~ and away from us below plates and zero between plates. (c) Towards us above and below th~etrically.

· -,

1· ••• _.

"

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._

I

'· • .

•

•

Column-II . •

I

-

-

The force on AB is zero,

ii'

•

'

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~~-~-~-~_JI_~-----'-· (B)

®

'

(Q)

J A""'"-·------B

_,

The torque on AB about it's centte; is zero. .. -

·· infinite wire carrying current inro ·the· pI~ne.

..

I-----+...---'·-',,'··---~·--"··~·-c--c-~·-------,---.+--+-~-...,--,----~-...,.--

(CJ

..

11=,

...... - -- . "'

. "'

" ... .,

'

(RJ

Thc force oµAIHsrion-~e~~--

--~ ~-

.-.:

.

-.,

. ~.A>

•i

··B:

..

-.... - ..... AB is kept inside an ideal solenoid along the ·.. ¢lfameter. · ~

(SJ

The torque ·on ~ about its centre of mass is 'non-zero ..

lf]Ass~'}iQn an~ -Reason Type Questions ,,',-

•

•

--,.

·~~.>

...

·i'-·

a

1. Sti\tement-1 : When lightning strikes a metal pipe, the pipe tends to contract. St?-t~me~t-2 : Parallel current attract each other. (a) St!3teme!}t-l js true, Statcment-2 is true and Statement-2 is correct explanation for Statcmcnt-1. (b) StatelJ].ent-1 is true, Statemem-2 is true and Statement-2 is not the correct explanation fi:>r S~a!emenc-L (c) Statemcnr-1 is true, St~tement-2 is false. (d) Statement-! is false, Statcment-2 is t~~-

~--}Comprehension Based Problems Compref-!ension· - 1

--

..

--- ~

-

-

.

--·· --.. rh~-ii;;;e;i~-Fi~ld _______

\

·::= -_

I

j

., 1

.;

I

-_--r·------·

~-I a11 1:~

•

jphot~ as ,constant while increasinr, the external magnetic field. The en~rgy ~hsorbed by -1 is plotted,

j

I ethanol a•. different Brn i

.'

-g.

t·

OH

'CH2

CH3

·'

1

Grouµ Group Group

"'ro

.0

>-'

2' -0:

i:: . ..___ _ _ _ _ _ _ ,..... 1..:.1

B.,xt

This spcc1 rum is unique to every group. This graph forms a signature by which we CB.11 identify the groups of organic atoms. If the net magne:ic field due to all tlw atoms is in the same directiur. as the exu·:.,al ~agnetic field, choose the correct statement. (a) Internal magnetic ridd at· H of OI I group is rn;iximum. (b) Internal magnetic field at Hof CJ 12 group is maximum.

16,

(c) Intemd magnetic fidd at H af CJ l 3 g:-oup is maximurr.. (d) Internal magnetic field atH of all three groups are equal. 17. A hydrogeu atom can be in 3 different positions ill a variable magnetic field whose lines are shown below. In which of the case will the rnaxiinum photon

.....

cne rgy 1:; c re quired to reverse ~c spin 7 (In all 3 positio:is :\: is

-}

p;1 rallel

to B)

. (b) 7.

(a) 1

(c) 3

(d) All 3 require same energy

1 R. The magnetic dipole moment of proton in H-ato_Il} pf water rnolecuk is 1.5 x 10-zr, J/T . Internal

magnet:c :·ield is negligible. \\'":iat is the ..:va,1ekngt:'1 of photon rt'qni:-ec. for reversal of spin af proton, if external magndc field is 221 ·r: (a) 1m (b) 2m (c) 3m· (d) 6m

----

Comprehension - 8

______

]

l

I Like many other galv;mometers, a ballistic galvanometer has a coil which - rotates between magnets. The ballistic galvanometer \1as the speci;1lfeature that its rotating coil has a large :

!

momem of inertia. It is used to measure quantity of r:harge rath~r than currents, for the large :no:-:-ient of inertia permits the· pas~age of-g-. q"i1antity of cbrge before the coil moves I 1 1,significantiy. The passagt! of tht:. cha:·gc produces an_ impube, a momc1taty torque, whic9- .i causes the coil then to ~wing to some maximum position. For the ballistic galvanometer, the.! damping is made negligible. Such a g;1J vanometer was often used to standardize capacitors. ••· _ j

l

I '

'

~==-

--=-----=~===----====

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AM Problems in Electricity and Magnetism with www.puucho.com

_I 319 I _

__ ----· _'f..lt~ Magn~t-~P, T (D)--+P, Q, H, S, T

2.

(A)--+Q (B)--+T (C)~P (D)-)R

-Assertion and Reason Type Problems

-

J.

j(b)

l

I

I

I

1

I

Comprehension Based Problems 1.

ICd)

12-

9.

, (dJ

, 10.

!Cd) (d)

j a.

!

--Ice) 14. (d) 1

---'---

(s. j

l(d) ! i

-

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Icci !

I,. lc•iw I , .

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i

;

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-

~~-

-~

. ~-

~

~

-

-

--_--...------...r-

l~---:-

· · The-llfagnetic:·Field · . . ·. · .·:_..-.-,..-~· ·~-~-~-~---_-......_............ _- - .

. .LJ• [C] •jMAGNE!J~FFEC~]).f_ CURRENT -· . _ _ _j

"'----~~-'·

Only One Alternative is Correct 1.

lb)

9.

Ca)

17. 25.

33~

!ca)

2.

(a)

5.

lcb)

13.

'(b)

• 7,

i(c) J8.

6.

(c)

(b)

14.

(b)

15,

(c)

16.

(c}

12.

(d)

19,

(D}

20.

(b)

21.

(c) -

22.

(b)

23.

(d) 24

{cl

(b)

27.

(c:)

28.

(a)

29.

(a)

30,

(c)

31,

(d) 32.

'(b)

·1s6.

(d)

37,

'(d)

38.

(d)·

ls!i.

(c),

18.

(c)

26.

.(b)

35.

I

(c}

(c)

Meire than One Alternative are Correct -----,------,,------,-------,,-----,,---~

1, 7.

12.

I- (aA)

B.

{a,c}

1

I (a,c) (a.,d)_

, 3.

I (b,d)

!

4, I (~ 1b 1d)

5.

l(a,b,~;.d)

.1

6.

I(b,c~d)

1

_,:__--'-----=---............----'----=----

MafcH1ng Type ·Prob.lems 1. (A)-+!? Q, R, T (B)-+Q, R (C)-+Q, R (D) >l? Q, T 2.. (A)-+R (B)-+P, Q, S (C)->P, Q, R, S 3. (A)-+~ S (B)-+R, S (C)->Q, R

Assertion and Reason Type· Problems 1.

Ica) I

I

I

I.

t

Comprehe~5!ion- Based Problems 1,

(~}

2.

9.

(b)

17.

(a)

10. 1(b) '. • 18. I1.(c) •

l(d).

·(al 11. (dl

3.

19.

(b}

.

'

s.

'(b)

12. (d)

13.

i(c)

20. (-a)

zi.

lw

4.

(a)

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(a:)

,.

(f)

8.

(b)

.114.

(d)

15~

(b)

1-6.

(a)

I

I I

11.

(b)

10.

34.

lcaJ j4. (d)

(d)

(a)

3.

f

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AM Problems in Electricity and Magnetism with www.puucho.com

---------------· ·----------

'

.'

Electromagnetic Induction and A.C. Circuits --~

T°',Only One Alternative is Correct vb=2 mis 1. A conducting thin rigid rod oflength 1 m. The diagram shown in the. figure shows the velocity of ends a and b of rnd. If a uniform v=-,/3mls / =--=====ih magnetic field of strength B (in SI unit) is existing perpendicular to ai::::·

the p1ai1e of rod then induced emf developed across the ends ob of B(in SI :.ir't)

:-od: (a)

7.

_JJ

-.,/3

(b)

./3 B 2

(

/j

cl. 7

(d) none of these

2. 1\vo coils of wire are arranged so that a changing current in ont-'. will induces a current in a second, resistive coil. If the curre.:-.t in the firs: is illcreas:r.g clockvvisc by 1.0 A every second,

the induced current in the second rnil : (a) will also increase clockwise

(h") will be increasing counterclockwise

(c) stays constant

(d) stays zero

ft .

3. A flat rn :: of wire :s rotated a: a frequc ncy of 10 h f'm: in the mag 11 etic f:eld G r s ~N producec'. by three pairs of ::iagnets as shown. The axis of rotation of the N s coil lies in the plane of the coil aml is perpendicular to the field lines. What i.~ the frequency of the alternating voltage i11 the coil ? U(a) 10 Hz (b) :rn Hz ~~ (c) 60 I lz (cl) 10/3 Hz · ~

4. The fignre shows a conducting ba.r moving to the right 0.11 two condm1 ing rails. To make an induced current i in the direction indicated, in what di rcction would the rp;agnetil' field be in t ]l(' area contai11f'd within the conducting rails ? ·

(a) Out of the page

(b) ln~o the page

(c) To 1he right

(d) To the left

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1 323 1___ _

__ ··... Electromag11,etic Induction and!'· Q. Circuits . .. 5,

If a bar-magnet is falling through a loop of wire, the induced current in the loop of wire sets up a field which exerts a force on the magnet. This force between the magnet and the loop will be attractive when : (a) the magnet enters the loop {1)) the magnet is half way through (c) always attraction (d) the magnet is leaving the loop

.6. Consider following coils one tum carrying current I. The magnitude of the magnetic induction at X, Y, Z are B 1 , 8 :i. and B 3 respectively. Then :

p:-1 I

I

r.:7 LJ

L___________f?..~1 a

A

a

7. In a cylindrical region having radius R, magnetic field varies ·with time as B =a+ bt_ OPQ is a triangular loop made of wire having resistance per t.tnit length 1,,._ Cummt induced in the loop is: (b) -------~-bR_ _ l2..J3 ( -./3 + l)t..

(a) nbR(~-1) 12,J31.

(c)

p

n:bR( ,J3 -1)

(d) none

6-./i,_

of these

8. The magnetic field in a cenain cylindrical region is changing with time according to the law B =[16 - 4~ :1.l tesla_ The induced electric field at point P at time t "' 2- sec_ (a) Bvolt/m (b) 6volt/m (c) 4volt/m (d) None of these 9. The dimensions of magnetic flux is : ( a) ML2 T 2 I (b) ML-2 T 21"'1 10. In the diagram shown, a time varyini non-uniform magnetic field passes through a circular region of radius R. The magnetic field is directed outwards and it is a function of radial distance ' r' and time 't' according to the relation B = B Ort. What is the inr.luced electric field strength at a radial distance R/2 from tl1e center ?

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.·. =:Fz4 ) _____________ ---~- ____ Problems in Elcct~:;city & M~gneti~m 11. The current through the coil lm the rightin figure l Vilries as- slmwn in figure 2. Which graph in best shows the ammeter (A) reading as a funcLion of Lime "? 11

·N: '. > .. . .'

s

' '

Fig. 1

fir].

,,

'

2

. .

kLU '

(b)

' '

t

12. A wire moves through a magnetic field directed into the page. The wire experiences an induced charge separation as shown. Which way is the wire moving ? xxxxxxx

I-

X

X

J(

X

J:

>;

+t

){

(a) to the right (b) out of the page (c) toward the top of the page (d) toward the bottom of the page 13. For the solenoids shown in the diagram (which are assumed to be close to each other), the resistance of the left-hand circuit is slowly increased. in which direction does the current flow through galvanometer in the right-hand circuit ?

~ °ff Rra11

(a) B ta A (b) A to B (c) there is no current (d) cannot be determined 14. The total charge, induced in a conducting loop, when it is moved in a magnetic field depends on: (a) the rate of change of flux (b) Lhe initial magnetic flux only

(c) the total change in magnetic flux

(d) the final magnetic flux only

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---·--~

-

-~----~---·---

--·~ f,;[ectromagnetic Induction and A.C. Circuits_ · - - - - -

__ I

~2s.____

.1· ~-

15. A circular loop of wire is positioned h:ilf in and half out of a square ·->

[3

yt

-

region of uniform B field directed in 1h1· +z direction, out of the p.iper,

):,

X

ll:

M

Z(~[Q

BvrrR :i

'k A

-

l"- ."( J(

,:

Q

a:i.d M is at higher potential

(c) rrRB1.' am: Q is at higher potential (dJ 2RH1,, am'. Q_ is at higher potential 37. A t:i:n c:n:dar ring of area 10

1

m 2 is held perpendicular tu a uniform magnetic field of

ind:.ic:ion 0.1 '"'.'. A small cut is made in the ring and the galvanomet'er is connected across the c.nds such that ~he total resistance of the circuit is 0.10. The ring is squee'.led to area 0 .5 x l O- l m 2 i:1 time O.1 sec. The ave rage induced current in the circuit is :

(a) :.nsuocient data

(b) 0.05 A

(c) 0.5 A

(d) 5 A

38. A Jong straight conductor is placed along axis of a circular coil of radius R. If ':he curre::.t, as shown in figure, starts decreasing with time, the current inc'..!ced ::'. loop wouid be : (a) clockv,ise (ACBJ (b) anticiockwise (ABCJ

(c) cannot be decided (d) there will be no induced current.

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39. In a long hollow vertical metal pipe a magr.et is dro:i?ec:. During its fall, the acceleration of magnet: (a) will decrease linearly (b) will decrease upto a value which is less tha:, g

(c) will decrease to zero and will attain a terrr.:r.al spe.ed

Cd) may increase or decrease 40. A bar magnet is released from rest along the axis o: a very long, vertical copper tube after some time, the magnet : (a) will stop the tube

(b) will move with almost constant speed

(c) will move with acceleration g

(c) will oscillate

41. A square coil ABCD is lying in xy-plane v.-ich ::s cer.tre at origin. A long straight wire passing through origin carries a current i == 2 t in negative ::: -direction. The induced current in the coil is:

(a) clockwise

01)

: c) alte,,~ating

antic\oclavise

(ases and then increases B (c) rem:1ins constant (d) decreases continuously 18. The ma/;netic flux through a srationa1y loop \.vit:, resistance R va:ks duri::g inte:-val of time T as¢""' at(T - t), The heat genera:ed during ±is tlm~ neglecting tlw inducta::ice of loop will be: (b) a2Ti

(a) a2T~ 3R

3R

(d) a2T:i

(c) a2T JR

R

19. A long ~ttaight wire is parallel to one C 2

C3

R2

(d) C 3;., L'1 > C:i

(c)C 2 >C 3 >C 1

37. The currt'nt ! ir: t'.1e straight conducrnr varies s:r.muidally with t:me 2s shovv11. (A positive value of I is in tiH' direcdon indicated). At time t 1 , the induced current in tlu~ rectangular

loop is clockvvise. Wh;ll is the currem in the rectangular loop at time t 2 and time f 3 rc. . : Problems; in ElectricitY. & iflagnetisin· . ~s·...,_........,..._,_.....__,..,_,..-~----.....,_,....;,;,_.....,_ ------• ,~~~-~~---··~....,._,,,__ J o . - " ' · .. .. .._

~ ]More than

One Alternative is/are Correct

1. A conc.ucting ri.--i.g R is placed on the axis of il ba:- magnet.I\.!. Th~ plime of R is perprndicu]a:- to this axis. M can move along this axis :

(a)

M will repel R when it is moving roward R.

(b) M will attrac·t R when it is moving toward R.

(c) .1\.-f will repel R ·.vhen it is mming away from

R

(d) M will attract R when it is moving away from U _ ·--->

2. A conducting rod AC of length 4l is ·rotated about a point O in a uniform magnetic field B directed into t:he paper. AO == l anc UC: == 31. Then : " X

•

-·

!l

X

X

A__'.:'_'~__, .........._ _ _ C X

X

Q

X·

~

. (b) 1/ n

Vo"" B©l2

(a) VA

X

2

(c) V,;-Vc=4Bool 2

- Ve

9 ~ =-Belli· 2

Cd) Ve -V0 =~B{),1 2

lf]Matching Type Problems 1, Match the following and select the correct altemativ~s glven below :

(A)

Unit q_f magnetic·; ndi.Jction (Bl ,..

(B) Dimensions of R

---------!

---~

(C) Unit of /1;~- (permi ability)

(R) _Ncwtop!Amp-111l"l er, :

(D) 'Di ITH'~Si~IlS ofµ o

(S)

•.,

(E)

~

Ncwton/(Amp);,

----~----+---.-(T) rv1° t?T OA~ : ,

Dimc1isions:of m,1r,neti~ momcm , .. ~

~

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, ___ Electroniag_n_e-ti_c_!_n,_d_u_c_t_io_n__.;nd.A. C.-C-i-,-~;-its__________===-------------.____

IL~~-!JI__

~Comprehension Based Problems ,Comprehemslon ·- 1 '=====--

The figure below shows a rod having initial velocity u on smooth conducting: parallel rails in horizontal plane. B .--) uniform constant magnetic field .intensity

:,1;; x·

~-

I--t cunent

X

-•·-u• "

R"'

~ B

'"·--------''----' X

~-

"

-•f

R --t resistance

m--) mass of rod 1--) distance betWeen parallel rails

·v,:

1. Give the correct order of initials Tor F for following statements. Use T if sratemep.t is true an-~--"----·

_.13s2

_____________ --·-···-

.

.

.

4. Potential difference across be at time at t =-l- : . 2v : 3m,l Bvl () (b) Bvl a (c) -···· 4 4

.

.·

~-,-.-

-

(d) none of these

5. Find the applied hotizo ntal force on be ( F) as a functio 11 of time •t' (t < .?.J V

~

B 2 vl ( a) -t

.

"Problems i,1 Electricity __.__ ~----.....-& Magi,,eti;;n,.-~ ....:-------------·

(b) B 2 vl

:

(c) B 2 vl

(d) none of these 41. 6. If resistance of wire frame is negligible and self inductance of loop is L, then current in wire

2}.

"-

frame at t =-l : 3v Bl 2 (a)

Bl2.

(b) -·-··

L

3L

(c) infinite

(d} information

.. --·--·

-~--~.,,,,,,.--, -

·.c

-·- ·-

are insufficient to decide

____

-· - ··------··----------- .. ··-----·-··---.--

__..._.

,.

·The-·oonclµcting connector ab mass m and length L cari freely slide a -_ I o~-'-.a -h(?tizontril long c9nducting parallel J°ails c~mnected by .------.--i~-- ' 1 ': capac,itor.¢ one ends (as· shown in figure). A. non-conducting . ~ L light sp·npg{spring con~t. K} connected to the connec:t.or ab and it is- m.- a f'eJaxcd srate. The whole system is placed in uniform magnetic field of strength B directed into the plane of rails (as . I!'...... shown in figure). Now at Jimc t = 0, connector is suddenly given a x=O velocity.11 0 in rightward direction. If resistance and se]f inductance of circuit is negligib]e d1en: : ' ·-

:at

'

7. The magnitude of acceleration of connector as a function of x : (a) Kx

(b)

m

K~

(c)

m -B'iL2 C

~

m +B 2L2C

(d) none of these

8~ The maximum compression in the spring:

(a)

1m=n 21?c

Vo~~

9~ The rod will

K

-

(b)

VovIm·+ BK L C 2 2

(d) none of these

execute (after prujet.:ting it at t =0} :

(a),.S~IM

(b)'harinonic motion but not SHM (c) · The rod will come at rest at certain position then afcerward it will not move (d) nmie of the above

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-_·- ·j ·;-

I I

~ \Only One Alternative is Correct_ 1. A current I i.s circulating in a super conducting coil of induci:.ance L. The temperature of the coil is now raised above the critical temperature so that the coil acquires a resistance R. Then, the total heat energy dissipated in a time At =L/R after the critical temperature is crossed is : · (a) 11 2/4

(c) LI 2 [1- (1/e 2 )]/2

(b) U 2 [e -1]/e

(dJ nohe of these

2. in the circuit sl~owri, the switch is dosed at t = 0. The current through: inductance L· varies with time as : L

inductor of

2L

R

,..___...._.....l\r.JV1.,....--'

fa) (2V /3R)[l -cxp(-3Rt/2L)]

V

. (b) (2V i3R) exp(-3Rt/2L) (d) (V /R) [1-exp(-Rt/2Lll

(c) (V/R)[l-exp(-3Rt/2L))

3.

ilie

In the circuit of the previous question, the switch is opened at t =o. after being closed for a long tiine. The current through the inductor of inductance i at any time t > o

is :

. (a) (V/3R)exp(-3Rt/2L)

(b) zero

(c} CV/R)exp(-3Rt/2L) (d} w 4. A solenoid has an inductance of 10 henry and a resistance of 2 ohm. At t = 0, it is coruiected to i (i volt battery. If at t = t 1 , the energy scored in the magnetic field of the soi~noid reaches

¼

of its maximum value, the value of t1 is_: (i) 1.5

s~c

(b)

0.35 sec

(c) 0.14 sec

(d) 3.46 sec

s·; Jn the circuit sliowr.1 irt figure, switch s is dosed ar rime t =bj current ittrougii. inilucmr after iong tilfie of closing of switch :

.L,. R

R

~

-s

E

.

E

(a) 1[

. k

(b)-,..

2R

(t) zero

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------:-·-·----

Problems in Elect,:icity & Magnetism-

- - - - - - ... --

·-··-~ - · - ·

• - - _ _ _ _ .., - - t..--F-""·•----~-

_ ....... _ . _ , . ~ . . _ - - - - - - - -

I -

a,_ .___ ,._ _ _ _

6_ A coil of wire having finite inductance and resistance has a conducting ring placed coµially \v:ithin it. The coil is connected to a battery at time t = o. so that a time-dependent current I 1 ( l) starts flowing through the coil. If I ;i(t) is the current induced in the ring, and B(t) is the magnetic field at the axis of the time (t > 0), then as a function of time (l > 0), the product I:i(t)B(t):

(a) increases with time

(b) decreases with time (c) does not vary with time (d) passes through a maximum and then decreases 7. A rectangular lonp of sides 'a' and • b' is placed in xy · plane. A very long wire is also placed in xy-plane such that side of length' a' of the loop is parallel to the wire. The distance between the wire and the nearest edge of the loop is 'd'. Tiu~ murual inductance of this system is proportional to : · (a) a (b) b (c) 1/d (d) current in wire 8. The switch in the circuit pictured is in position a for a long time. At R ab L t· ;,; o. the switch is moved from a to b. The current r-hrough the ~ ~ -, inductor will reach its first maximum after moving the switch in a 6

T

time: (b)

(a) 21r..../LC

(c)

Tc

_

]_Jic 4

!:..JLG

(d)

2

rr.../iE

9. In the LC circuit above, the current is in the direction shown and the charges mi the capacitor plates have the sign shown. At this time : C

I

+o -a

L

',. ·-~

...

•

L

(a) I is increasing and Q is increasing

(b) I is increasJng and Q is decreasing (c) I is decreasing and Q is increasing (d) I is decreasing and Q is decreasing

10. In the circuit shown in the figure, R =

i.

Switch S is closed at time

.-~

-R

t = 0. The current through C and_ L would be equal after a rime t equal € ''

to: (a) CR

(b} CRln (2)

L (c) RJn

.. -

(d) LR

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V

' _

'R __,,'/

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'

I

I I 11. A small square loop of side' a' is placed inside a large square loop of wire of side' L'. The loops are coplanar and their centers coincide. The mutual inductance of the system is proportional to: (a) a/L

2 I

(b) a /1,

(d) Lja

12. Tn the circuit shown. the capacitor is initially charged with a 12 V battery, when switch S 1 is open and switch 8 2 is dosed. S 1 is then closed and. at the same time, S 2 is opened. The maximum value of cunent in the circuit is : (a) 10-6 A (b) 72µA (c) 7.2 x 10-4 A

E=12V C=9µF

L=2.5mH

(d) 360µA

13. In ari T,C circuit, tl1e capacitor has maximum charge q0. The value of d{I is : dt max

;;.1 356 I. in .Electricity--~~ & Magneiism - ___-_______ - - - - - "Problems _

-·-----

...

- -

......... ....

-

.

16. A dosed loop of cross- sectional area m which has imluctance B{T) L "'10 mH and negligible resistance is placed in a time varying 0.1 magnetic field. The figure shows t.he variation of B with time for the im:ernal 4 sec. The field is perpendicular to the plane of c.hEi loop (given at t =0, B =0, i = 0). The value of the maximum {'.Urrent induced in the loop is : t(secJ (a) 0.1. m.A {b) 10 mA (c) 100 mA (d) data insufficient 17. A coil .of inductance L = 02 H and of resistance R =; 62.8 n i:; connected to the mains ,ihernating voltage of frequency 50 Hz. What can be the capacitance of the capacit.0r connected in series with the coil if the useful power has to remain unchanged ? 10-2

2

(a) lOµC (b) S01iC {c) 25µC 18. In the figure shown the battery is ideal. The values are £ ""1.0 V, R through the battery at t =2s is :

R

(d) lOOµC =;

sn, L =21-I. The current

l

(b) 7 A (c) 3 A Cd) none of these 19. In the LC circuit, the current is in the direction shown and t.he charges on the capacitor plates have the signs shown. At this time : (a) 12 A

C

+O -0

(a) I is increasing and Q is increasing

L

•

(b) I is increasing and Q is decreasing

(c) I is decreasing and Q is increasing (dJ I is decreasing and Q is decreasing 20. The circuit shown in the figure rs in a steady state with the switch Dpen. When the switch is closed, which of the following will change immediately ? (All of them eventually change, bm three of them stay the same for an inst-ant.) (a) The potential difference across the capacitor C. (b)_ The current through the inductor L

(c) The pmential difference around the resistor R 1 . (d) The current through the resistor R 2 . 21. A capadror of capacitance 2 i1F is charged to a potential difference of 12 V. It is then connected across an inductor of inducu:mce 0.6 mH. The current in the circuit when the potential diffcrcnce across the capacimr is 6 V, is : (a) 3.6 A (b) 2.4 /\ (c) 1.2 A (d) 0.6 A

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-'~~~'- 'J,;[;~troma~ne-tic

_,---' 357

Indu;~ii~~-:~~a"i~ C. Circuit;-~=-=--------- _,__: ____ I

-1-~

22. Refer to llu~ circuit diag:ram and the corresponding: t~raphs. The current rises when key K is pressed. With R °" R 1 anc.l L =L 1 the rise of current is shown by curve (lJ, while curve (2) shows ,he r:se of current whe:-, R = R 2 and L = L:,· The maximum cur'."ent is sarn~ fo'." both curves, then : I_

R

i~l-. ---·-·· ....... (1

.

0

(a) R 1

Timc (t)

U 2 ,L 1 >L 2

(b)R 1 >R 2 ,L 1 =J, 2

(c) R 1 > R 7_, L, < L 2

(d) R 1 =R 2 , L 1 < I, 7

23. In d1c given circuit, the ~witch is closC'd to the position be from the tV11 b. ~

(b) I is from a to band decreasing. (d) I is from b to a and .decreasing.

(a) I is.from a to 11 and increasing.

Cc} I is from b to a and increasing.

(p]Matching Type Problems 1. A homogeneous magnetic field B is perpendicular to a sufficiently long track of width l which is horizontal. A frictionless cond ucring resistanceless rod of mass m srraddles the two rail of the track as shown in the figure. Entire arrangemen1 lies in horizontal plane. For the si111ation suggested ·in column-II match the appropriate entries in column-I. The rails are also resistanceless. ' '

.

(A) A is battery of emf V and internal resis- (P) Energy is dissipated clnring the motion.

r~ce

R.

.•

Th~~:' rest

'4., • :

~

.

•

'I,

'

~

!-

C

(B) -A is a chargf:!d ~apacitor.. The syste!Il has (Q) .the· ~ad m~;~s with. a: constant velo,city. no :resistance. The rod is initially at rest:· ;-after a long time. ·

~D

(C)

~ is an

.

:th

inductor initial currenr1 0 is having no resistance.

.•.

."i (R) ~ .• ~ n ti;;,.· lnteivaJ roil :.W~ change it1rdirection of motion. '

.. _ ' - ~ "

-

J

I

.

'

. !

C

•

,

.. .

·

. . '

,

"'.'

(D) ·A. is a resistance. The rod is projected· to (S) lf tl·constant force is appJied on the rod to the right with a velocity VO , .the right, it can move with a constant

,velodty.

.

, ... _, _ _ _ _ _ _ _ _ _ _ _..___ _-+----+-----,-

(T)

'. .

The rod stops after some time in absence

- - - ~ - - - - . . . . __ __,___ _,_o_f_an_:ex~t_e_rna.!_!.orce.

l

. . . ..

.

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·_

- .

I

AM Problems in Electricity and Magnetism with www.puucho.com ---- _

• ..,,..._.... ~•~' ......,.- - - - - - ~ . , , - - -

.. -,....,...,~.,.,.,..,_ ,,n~-'- ---• ~ - -

1-~~~_jl

·Elec_t~!!!!.t:!_Cnetic Induct__i_q_~-~!1..~. .A._f:..2.irc..u_Y_f!_ -~ 0

2. •

lj:.

i •

•

•

•f

Column-I •

~

IJ

. · •

,1

2 X JO -3

· -

I

!lo

-

•

• -1,

., ~I

(A) A wave pulse is given by Y·=

't.

It

Colu'nm-II -

,

.-

~

,..

..,

(P)

. 1 • di trave s m +vex- -

(x-2t) 2 + 1 ·

rection.

(B) The switch is closed at c , , , 0,

Lr= magnep.c t1eJd ~nergy,

(Q)

y

x =time.

D

X

(C) A uniformly charged ring kept in (R) dy cix = 0 at: x = O_as weU as approaches tQ yz~plane with centre at origin. y = iclet::tric field ata point Ott X-axis, X = X Zero at large values of x. ;coordinate. ··

j

C.;.-~

---+----....-'--'~--'-c---- .........................._______ _. __,_,.

...... --;~:·--·-... "'" ,;....~ _ - - - - , - ·..··•- :1

(D) A 1iquid drop falling starts down in (S) presence of air restsfancci y = kinetic energy of the drop. x ""time.

!

X , "--·-"-------.-.---c--------t---+---'o----•------,.a--;---------

(T)

y

X-

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---·•h .............mnuu

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\:ilj_3__!£J--~---------- ____________ _____P_.r,_oblems in Electric~ty,_& Magnetis_rri_i_ _ 3. Column-I describe the value of variables jndicated in column-II. As:5WIJe potential energy in gravitation and efoctrostatics to be zero at infinity. If the quantity mentioned in column-II is a vectm:, positive and negative refer to the direction and increasing or decreasing refer to magnitude. Match the appropriate entries.

A body of massm is projected upward from-surface. of a planet. 111e gravitational potential energy of the system (B)

Positive and decreasing

(Q)

In the situation shown, energy of the magnetk field just after closing. ·

-----,-,-'-----+-~---(C)

Negative and increasing

(R) An air bubb:le is rel~ased from middle of a column of viscous liquid. Upward direction is assumed to be positive. The velocity of the air bubble

(D)

Negative and decreasing

(S) A point source is moving along the principal axis

------1

of a stationary convex 'lens. The direction of velocity of the source is pqsidve. The velocity of unage i-----~-~-----------------+----('O Two balls of opposite charge are released in vacuum. As time passes, their electrostatic ·----potential energy

. J

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·'-·-3~s I._

. __Elf!clro11_i~g'!et_i(! lndu~tion and A.C. C!rcuits 4. Match the column : .

: '

'

. ..

•

, ~.J:i:

I~

Column-l

>

Column•ll I

(A) The pressure on walls is tending toj (P) A soap bubble present in ak rontaining air. i The temperature inside and oucside air is the contract rhcn1'

·same.

0 Energy: Internal energy of ::1ir.

J

> - - - - - - - ........................... _ __

(B) The pressure on walls In tending to (Q) Current flowing in a thin hollow pipe

iexpand thr.111_

radius r.

i

Energy : Magnetic fielq energy. .

.

{C) The energy/volume inside the walls {R) A hollow conducting shd1 with a charge on

is more than outside.

-

- --

it.

0f~-~~.~!. ~.~.~:~~Y..-....,___

;Energy: Electrostatic

................ ...... .. · - - - - ~

~

(D) The eneri~y/volnrne outside the (S) Point source of light is present at: the centre of a spheri.:al shell with both surfaces walls is more than inside. j perfectly black.

;

r½) \ 3

i I

t - - - + - - - - - - ""

" ............... ,r.,, ___________

~Energy : Light energy. -

-

-

(T) A cubical container has adiabatic: walls. The temperature of air inside is less than the temperature of air outside. The density of air'

is same on both sides.

D

Energy: Internal energy of air-

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__________

--, 1 Js6 I~~- __

___,..,......,.-,..-__

Problems in Electricity_ & Magnetism·' -~~---·---------- -_____=..,_--~-

5. Match the column :

Column-I

Column-II (P) Time constant is the time in-which currem drops to 37% of its initial v~lue.: _.

(A)

0

(B)

(Q) Time constant is the rime in which rnrrent increases to 63% of its steady state

value.. . Initin.l charg!! on capaciror ::: O_

f -------+---------'-------_____,__---'---~-

- ---+-'--------'----,.,--'--~..,._

CJ

(C) :

(R) Time constant.is the time in which cur-;' rent increases to 37'% of its steady state

value.·

·

·

. I---+----------------------------------------'---'~ Initial current in ipductor -= 0

(S) Time constant is the time in which current decreases 'to 63% of its initial .value.

(D)

.

.

Initial current'in.indut:tor ::,i 0

- - - - - - - - - - - - - - ----+-----------,c-~'----~~-(T) Time constant is the time.in which voltage across resistance increases to 63% of its steady state value.

f .'

~Comprehension Based Problems

- --- ... --::·=----_ -=-- -::::-.::~:-.:...-_-_- - - - -...... :J

Comprehensioi1 -1 .

'

In the circuit ~~own, rhe switcJi is. closed,at t Q m~ '=100µ·C> 1·""40 mH > C =lOOµF

c=

0.

='-L~~~

l~;,·=\;.,.,C=-t:.~,_,~~"')~·

l.,..,.,,,,,,._ ,_ _............... ·• -----~

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17

----i--3-6_7_.,__II

_-_. ---,_E_l_~_c_t_r_a:_m_p__g-_!}___!;_fi_"c-,1-_.!!,-d--~-.~-t-io-.!'--.~----a=n-;]

B -dl along z-axis from

- l/wc1C

= 1/(JldC (d) o> 4 L > R 34. A capacitor and a coil in series are connected to a 6 volt AC source. By varying the frequency of (c) ©,1L

the source; maximum current of 600 mA is observed. ff the same coil is now connected to a cell of e.m.f. 6 volt and internal resistance of 2 n, the current through it wm be: I

(a) 0.5 A

(b) 0.6 A

(c) 1.0 A

(d) 2.0 A

35. In the figure, if l 1.. = 0.8 A,Ic = 0.6 A, then I=? le

C

---,..ti-----11 I-·

(a) 0.4 A

(b) 0.2 A

(c) 1.0 A

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(d) 1.4A

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_ _!}!__'!_£ frOf!l_llf!.~_!-~ic Induction and_!l: _C.

Circuits

36. In the figure shown hot wire voltmeter and hot wire ammeter are ideal. The reading of voltmeter is :

Xc=20

(a)

S-,/2 V

(b)

sv

(c) 1.0 V

(d) none of these

3 7. A coil, a capacitor and an AC source of r,m.s. voltage 24V arc connected in series. By varying the frequency of the source, a maximum r.m.s. current of 6 A is observed. If coil is connected to a battery of e.m.f. 12 volt and internal resistance 4 n, the current through it in steady state is : (a) 2.4 A

(c) 1.5 A

(b) 1.8 A

(d) 1.2 A

38. A coil, a capacitor and an AC source of r.m.s. voltage 24 V arc connected in series. By varying the frequency of the source, a maximum r.m.s, current of 6 A is observed. If this coil is connected to a battery of e.m.f. 12 V and internal resistance 4 Q, the current through it will be:

(a) 2.4 A

(c) 1.5 A

(b) 1.8 A

(d) 1.2 A

n

3 9. An AC-circuit having supply voltage E consists of a resistor of resistance 3 and an inductor of reactance 4 D. as shown in the figure. The voltage across the inductor at t = is : R > -Uo == -j,E cos "O -( -pE) = pE (1-cos 0) _ 2kpcos'O . E _ kpsin9 17. Er • or3 r3 .

E:r =E,cos8-E· 8 sin9

= kp{2cos 2 8-sin 2 8)

I

4V0 = -pE

. ~More tlian .One.Alilihu,tfve ire Correct

2

tana. ==

, 7V0 cos0 2 ""-.-, . pE

.

1. E due to righqlipole"Js:along aiis and as (-} ve o~, left 4,ipole is ·closer to right dipole. it expefi:efices greater.force. Hence net force is toward~ riglit.' . As both forces are along axis ofleft dipole, . ' torque is. z~ro. 3. Since, electri~ same work

26. E go es from higher potential to lower potential

E

= .1.V =_V3 -Vo Ax _9.Q~ - 400 x.0.05 = 20V

1. Point A and B a're equipotential, work done by electric field is path independent and Ve> V,1-

. 2. Using law of conservation of energ,;

.

,dire.ction of decreasing elecoic potential, the potential decreases as , Y one trave,ls -·

from

initial

/ ,.

- E

•

..__A

.

m,q

a

. -~

'

E-,.,_ =E 8 1

2

-m11 0

~-

,. point to final point on each i / ------ •• ~ ··---- f1 line. Sim:e, the electric' . ·is field uniform and in the x-direction, . " ..cq1:iP.o,rcp.tial li:1tcs .wil.lJ]e .11,qpeq,dicular ··_ ·-i~- the .taxis. Therefore," final position .of each : line_ J:\a.:-,_ the same x-rnordinate, each .v.:ill ha".~._ t_hc same

• B

a•...

=> V3 2 7 . . Since, · electric. ·field lines point in the

b Vo

2 [·.· .

6a

I

kQq -

a. ·

kQq

= -

b

a

'-

I

6a b

b 6

a

7

At infinity,£ A

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kQq

At B, u =0 and zr kQq

.. · -

stncc •die

kQq a

+ - =0+-

=-

E ...,

0

b]

-

,•,

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---~~----

Electrostatics' .. · .. , .y··, ''-

- - - · _ _ ..........,___.T-.,1,,...,,;..•..;i,.,._......,__.__. _ _ . ......_........ _ _ _ _ __

1 ' '.

2

-mvo

2

·kQq 1 ' '2 +--= -mv '+o· 2

a

"·

r

kQ · ]· L.,. ~ 4 0 ~sr~o:,

7 2 -rr.v 0 2

1 2 = -mv

u.,.,

= -.;?vu

~

3. (a) EF

2

,----

""

directed perpendir.:ular to ~quipote1:tial surface and from high :s

potential to low potentiaL (b~. Force on a charge is perp~ndicular to the equipo:endal. , (c) Because we have zero potential not , -a: rn so, charge cannot be corr.men te d.

~Integer Type Problems 1. From equilibrium of' Qi

[-l_ 41tea

=mg]

Q1Q2

h3

· In COM frame FP is pseudo force.

(d) \Vor:.; done on an equipotential line is zero. CT ' ;, • _. CT y " -y '>"

I

6.

(CJ

1) .

--,0-y)=

2;: 0

•


VI

=V I 3

Also

R1 +R3

_Pr =P3 a:::;, R 3 =9.0. R 3 =R 2 =90 I -an d 1 =l I =a

:::::;,, V /2 i = 22~ =0.02A

8.

8

and 11 = length from one end in second Ii .X 12 case--=-1-li R' 8 21.

R =2000 + 9000 = llOOOQ

= rzl 1 = 0.01 x 80 = 0 _062 .Q I2

r2 =r1 ~ -

cq

is very-very small

rgl 1 =l 2 R

=>

R

R

= BA (app )' as I 1

Vl =Vz

7.

. ":.,__,_J

.

10 =0.0l(R + 100) => R =900Q

· 9.

To increase the range upto n times, the . resistance S (shunt) used should be such that lg ""l/n S= (I /n)Ro = ~ I n -l l--

n

17.

Ohm's law V =iR·· =>

V cc i (for ammeter) V2 i? ~ . R c;::...:C:. =2 => 10 =2 x 10 x - V1 i 1 · 2+R

·::::, R=20

After dosing the sv,ritch VA =VB =12,V, so, VA increases. But VB decreases. Hence, PA in?"eases and P8 decreases. 24. The voltage of battery is lesser, so power dissipated is lesser and hence temperature of bulb is lesser. So resistance is lesser. 26. {a) R x 3 ) Q = I.SQ

=p

0.6-

. p 0.6 or 1 = / v =~ = 0.2A R 3 Reason with temperature rise resistance .

V

I "" -

increases.

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Electr.ic Current

-~-·.. -~~.-~------

(b)(i) Due to r of battery I can be reduced to zero a,'1d a potential drop across it 0 G = rn n

X

2

2n

3it5 12n

I

=) -

13

J.

1®-~

45.

r=__!_I

L.w

,~v-)4 l = --

l'=--1 = > - - = 4+G 4+G 5 4D

13

VA14 iRAR =- =L,w

R 0t

4

3

1 1 I -I' =-I=-- x0.65mA=0.05 mA 13 13

Rt= 65 . 0

a=Rr -Ro =8.3x10--1K-1 38.

41'=l';;;;:;., 4J,,,,l3I':::::,.J',., 12 1

4I

=--

Ro

:::.;,

I 0.6 2 x 0.6 X

0.4

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30

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.j I

1

i

i

---~ _Electric Current 3R =R 2 +R 1

r:]More than One Alternative are Correct 3.

(i-ig)R=igx96

R =2R 2 -R 1

R

U -10--4)R =96 x 10--4

4R =3R 2

Q

SR

R1 = 3

4R

4.

Potential V

across

drop

Rz=-

ffi

wire

3

B

=(___.5_J_JR1 r +R1

R 1 : Resistance of wire For the direction shown of current E'z>V so correct options arc (a), (b) and (c).

A

8.

C

•

Equivalent diagram is as shown, if P is moved 2 cm right then R1 = 12,R 3 =31 R2 -R1 = -(Hence Wheatstone will be R3

R4

balanced.)

6.

lf Sis moved left~ cm then R 3 = I.Q and 3

3

R4 =20

3-

For null point current flow in the loop CD

R

3V i:=---=lA 2Q+Hl 10.

VCD ""lV-1(1)=0

R

1 = - 2 (Hence, Wheatstone will hcnce,R3 R4 be balanced.) x = deflection 1

only.

+-©-----

:. option (a) is correct 1

is VA> Vv When jockey touches to B current from A to B to increase the p.d. across the secondary circuit. .·. Option (b) is correct. 7.

Case-I :, 1(4)_. ¼= G+4

R L/4 :=-R1 + R 2 3L / 4 '

G + 4,,,,20 G=16Q

3R =(R 1 +R 2 ) R +R 1

Case-TI

2/ 3

=-)

1.

¼

I

E1 ~ .

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)

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1-

!

I I

,----- -~~------==~~~~-=-~-P_-_ro_ _

.

ti__.-le_m_s_i_n_E_le_£__t_tf_'s_i_t_y=·=&~M~_~a-g~n-_e-~-i~~==

_ I( 4 / 3) _ 1 I ,----H:i + i 13 3

11. .--j ,__ ,._,"',........, I 1 ~v 2.sn 100:

t.-. i=4A

rl.....-,,,..,vv--,. l, 10v 2.sn

sn

Ti =2A

~Jaximum

V =wJA 2 -x 2 Q ==mStiT

Miriirnum

Pt :mStiT

p 1-1.T=-t

Tl.Matching Type Problems 1.

ms p

R, 1 decreases=:;, it:::> Vt

Tr

=-t

ms

On closing s-v1itch S right hand side resistance get short. This equivalent resistance decreases, voltage across left side resistance increases and current decreases

hand

2.

(A) Effective resistance of the circuit

f]lnteger Type Problems 1.

=40

=100 3.

_,

=i[(~) ~] 2

g

3

... (1)

1+2 l l+R

l

j-

... (2)

Dividing eq. (1) by (2) and on solving, we get resistance of wire w 2 == 10

Ossertion and Reason Type Questions 2.

.

VA 1 (t1) V =SR~ S = - :::> Sr..(; -

el

For w 1 ,f:

Forw~ = 2l[(-2-)R

(B) Potential difference across

3 0. =20V -BV == 12V (C) FL'1d currencs in resistors using Ohm's law and series parallel and then use Junction law to find current in ammeter. (D) Effective resistance of the circuit

+ T0

X

When battery is supplying power, inside battery positive charge moves opposite to _ electric fidd. So work Eledro~tatic field done by electrostatic forces in negative.

~Com_l!!ehension Based Problems 1.

. C 1=---

Rg +R 2.

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-, ·· Electric Current ;

I 443 I~

' .. iR = 3(n - l)i :.R =3(n -1) From (1) and (2)

,,,,5 mA

l

3.

I=

5.

20-'- 80 -'-100 Q.No. 4 and Q.No.5

(R+27)-=R[; +

R

~ 1 27Q

i (R + 27) =O iR

0

R =90 and n =4 ... (1)

6. 40 3

1)

(~ -1)i

378V

,:

),

j

G

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... (2)

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- ~ - - · - - - - ·

· - · - · - - - - - ~ .. - - - · , - - - - - -

L_:_±J- Capacitors

-·-·-·--·---

_j

r5ov

~Only One Alternative is Correct 15,

,7

Due to increase in distance benveen the plates, ca?acitance increases.

lS, G: =3C

2C 3C C C 2 = 3 C:, = 2 C4 =·

3

19, Wl:e:i. ap;:ilied p.d. is V across A and B assuming 1/,\C = V 1 and Veil = V 2 VA =2SV

r-f~-7_r

A---L .--J ,

U o::- 1 / C. 2 C Hence stored energy will decreases. 40.

Q =BOO x 10 x 10-6

800

X

.!cv 2 = pt 2

C=~pt =:2x2000x0.0i y2 106

10 X 10-6

50 X 10-6 29.

I

)

41.

11

3µF

Q=CV=3x10- 6 x12 Q =36µC

C:J

(x + 13) x 3 = (27 - x) x 1

3x + 39

36-q q ~~=-

V

So, Va -Vb =27 -(x + 13) =17 42. From charged is tribution Q 1

3

"" Q 4 ,

electric field between plates is E x d. :::;;, 36-q = 12 µC

= 36 - q = 12 =4 C

-x + 27

X=-3

3 6 ·72-2q=q 72 q =-3- =24µC

Charge on 3µF

c=

Potential Difference

= Q2 -Ql.d,,,, Qz -Q3_

volt

· 2AH 0

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2C

net

l.J

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.Proble~s in.Electricity' & Mag!!etisin ·

446

2q

43.

.. !I 8

I N-1

__ N_-2_,l

1··-- ----- - ----- ·-·---- ----- ·:

\16

lT

I

l~IP

1\3

I

2

. . . .-1----11 16. . . _ _....113 I

ql Iq lq

I I T

Tl

!-----. -----------. ------. ---.---···- i -

N

(N-2')

bala noed Wheatstone h adgo

(N-1 ')

N'

Similarly charge between I and 1'

Ir"

aT _______.4T

C 8 q=14/5

==:,

q

2(11-l)

=Q

(given)

44.

r---:

cc:>

~~

Vi

( q

1

=-E 0 ~

2

Ai: 0

v1 =-1 ( -2q - -)

46. Let q charge flow through the circuit then using Kirchhoff's law

)2 Ad=-q2d

19 + 15 + !I

'

2Ai: 0

i: 0 Ad

+!(_q_)

2

2 3Ai: 0

2q2d

q2

47.

q2d

Q=6coA

45.

I'TT~·:. ·:· .·r~ l

2 2C

3

t,.1_

1 2C

1'

2' ·· 3'·

',(N--1j

Let charge on last branch let q 2C N

.

N

2

..

=0

=:, q

=30 µC

~., 1•50-q

100 - q 5 X 10-6 ~

=IOV

q'

J _,,,T

N

T cJ cJ cJ _ _ ·:_Tq J~;,

_9 + !I == 0

P.O. across 3µF _is V == 3 0µC 3µF .

e 0 A(2d)

=--+~ 9As 0 9

2C 1 2C

3

Sq 25 + 6

2

2 3Ai: 0

q=_g__ 211-l

+ 50 - q

=O

20 X 10-6 -'6

q==90x10,'_ C :. Final charge on SµF top plate is

.N'

lOµC.

49. V AC + V DB == __g_ + __g_ CAc

Cv:a

-l~Ilq' lTC

=Q[ cdCA + i:dDBA J=Q

- - ~ - - - - ' \Q)

=Q ~ +dDB s0A

0A

N'

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I

Capa-ci,tors, , ~-0 =+1r,C

-1nC"

A

-2nC

C

.

8

=Q (3) = Q ~ X ~ = lnC EoA EoA 5 20PF

X

4

~

1 59. E x K ==> ;I,,V

5

V AC + V DH = 30V

Vw

=_g__=

... (1)

2"C'

,:c;40V

... (2)

20PFx.. ~ 2 Add (1) and (2) V Ail = 30V + 40V = 70V

61.

1

.

C2

Electric field

2rtt-

At the mean position of plate A

2A;.0k

1

----'---- < - and -~~ > C 1 +C 2 2. C 1 +Cl 2

74.

Qlmax

=:

500 X C

C

Ci +C 2

C 1 +C 2

2

Similarly C < C 2 2

Q 2 m~x =lOOOC

51. C 1 Q on both =500 C = ZC xv

+C 2

1 and 2 parallel and in series with 3 and combination is parallel with 4

54.

2C

C

C:.C 2 -C C2 C1 - C--- l ---->-

c,,,,c 1

1 K ==> E3 < E 2 < E1 and

spring will be elongated b y ~ -

C 1 l)

(Q

and Q after > Q befCb,fore

CV

2 3

2

"''c +(kC)

.

,,,,..!.cqv2 ,,,.! sc vz = scv2 2

t]More than One Alternative are Correct

e

3

When K 2 is closed no increasing in energy When K 1 is dosed,

:. q2 ""70; qi = -2625 .·. q~43.75

4, On insenion of dielectric, capacicance increased k times, thus , for syst V1 (As. q=CV = constant)

2

==> U ,I, and U = Q 2C

::::>

C1>C3>C2

.ct

f:0A1

E:0A3

E:0A2

d

d

d

-->-->--

11. Q =CV= soAV d

A1 > A3 > A2 3, V 2 >V3 >V1

I ,.. \I d+::=:-Ql,E=-=- Et, d

V = constant

E 2 d > E 3d > V 1 d

(V = F.d)

E2>E3>l1 or E1 E 3 ·

5, C 3 -> (tJ

l.~~I

1:JA i j 1. (A) .C, =--u

d

_;, ct~

c

~

C 1 -! C

y_Q C

c,,v ,!,

Q

2

==> V on /4 r.d c:apJ

==> C:

t : : -,

'

C eq t

~

d,. Q t

(C) (D)

C ~

~~ =

==> V t

No effect

C

Vt and

:

Q ,._

fJAssertion and Reason Type Questions

t

==> .. . C 2 :=2

••

4

• •

.· and C1 =8 µF out of.options given ·6. ,-111idirection cif current is considered the direction of movement of ( -r:ve).charge, as moves from ·left to right-and ...:ve1 diarge ,moves from .right to . ·1eft (which is ~quivaleht to ( +ve) charge mdviilg from . l~ft to right.

c

,._ ==> C tq

2, Q = CV ~ C ,,.. V

... (2)

C 1 =4C 2

(B) C.-t~AA1'

d

Ci

s c1

==> Q_..,

A->R

... (1)

for C 3 =U -

=,_c1c . .i, ~q

lc 1

vl

~-\MalchiI!9._}"Ye!: Problem~ .

==>. _shorte·d

7. ,E.tectridield ios·ide capacitor=~+.::.::... .,

2c 0

[FtC,m (+ve) plate to -Ve plate] , · · 8.85 X 10--6 8.85 X lQ--6 •

=

----- + ----2 x8.55 x 10-12 2.x8.85xl0- 12

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~ 1450·.

I

Problems in Eiectricity .& Magnt!tisrii~

..,

=lx 10-6 ,= lx 10 6 volt Work done by electric field

=increase in kinetic energy

So distance travelled by bullet in 2 ms =(lo'O m;secx2 x 10-3 sec)=20m/s Distance as seen on film=.! x 20 =-10 cm 2 . ;

J

(qE)d=!mv 2 . 2

·•._;:

10. Q =Q 0 e-r/RC RC= time constant =2 ~s

After one time constant Q =037Q 0

=> (lxl0-a)(lx10 6 )(.!x10-2 ) :·

2 .

=Q2 =(037Qo)2 =037x0.37Q2

(U )

2C

cf

=.!(1 X 10-3)(v 2 )

2C

2C

2

2 V

If T

10--4 10-J

1 10

(Uc) 1 =(0.37 x 037)(Uc)

=--=-

rest energy is lost to resistor =3.45 J

= tension 2

11. Initial p.d.

•

T - mg= mv R R T=llxl0-5 N·

= length of string

2C

Whole ent-"rgy is losL into thermodynamics internal energy which equally distribwcd bcLl"".ccn two pldtc.~.

is

.=>,

U

.

'

=,3.Q, • • /vi 15 30

20. 1 am pcre dl'pc nd.~ on unit of forrc i.e. , newton au maximum

C -minimum

d '

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_ _Q_ap_a_c_i_to_~_s_ _ _ _:,_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

1·

I

~I 453, I

[C] jR.C. CIRCUITS •

io~

1.

0

21:

22.

= V ·e-c/(Rc)

log I =log (V) __t_ 4 R e RC

.

When t :::0, loge I :::log.{~). which is

I

same for both circuits. Hence, if one out of V and R is different, then another also has to be differenr.

C

. I q L==---R 2RC

=C2

· · ·. ~1

also i = dq dt q

. . J(

r

a: E __ q_ R 2RC

)=I

and

IC

V==dqR+i dt G =t

::::) dq =...!...ccv -q) dt,,RC

.3

=--t

·-----~::·_· -?

dq CE dt'RC

-:;RC

~ -t/RC =-···e

,.

-: ~ ... .

=

R

1

dt.

-~-~1· ·. ·_ ·· . == ~-

3

CV_ CV.

RC .

t 1 =RC In 2

Now at 2

!!.9.a = ... J de

C

CV

3·- l

1

'2

J ····dq=---f de 2CV q RC 0

I""'m

2

C

=V1!

ti

3

t:-0 i=-··· R 10. A wlll read p.d. across 'C' and B will read p.d. across resistance R. By kirchoffs law

.VA

·.·.

;~q::: Re

..-ln -

J:

at

-·r·· · ·

l

CV--

8. When switch is shifted to position b discharging will take place q =q0 e-t/RC =CTe-11Rc and 1:0-~·············e

l

-~ : Lcv·-·q_

2RC

q ::= IC(2 -e-,/1RC)

.

·

xv

q == 2IC - I:Ce _, nRc

and

hence V1 < V 2

23. When at 1

2RC/

1

RC

R1