Electrostatics Mtg

(1)

l.

Five

identicalcapacitorplates,

each

of

area

A,

are

arranged

such

that

adjacent plates

are

at a

distance

d

apaft. The

platbs

are

connecteci

to

a

source

of

emf

Z

as

shown

in

the figure

2. Figure

shows

line of

constant

potential in

a

region

in

which

*tr'o\

_t

ttu

an electric

field

is present.

The

to

u

-

\

\ \r\

values

of

the

potential

are

₎

_{) j^i'l}

written

'-'-*.

in

_:1

brackets.

-l-

-''

Of

-'-.- /

the

'--/7

I

points

A, B

and

C,

the

magnitude'of the electric field is

greatest

at the point

The charge on

plate

I

is ...

and on plate

4

is ...

(1984 - 2 Marks)

(1984

-

2 Marks)

Two

small bails

having equal positive

charge

f

(coulomb)

on

each are suspended

by

two

insulating

strings

of

equal length

L

(metre)

from

a

hook

fixed

to

a

stand.

The wirole

setup

is

taken

in

a satellite

into

space where there is no

gravity

(state of weightlessness).

The

angle between

the two

strings

is

... and

the

tension

in

each

string

is

newton.

(1986 - 2 Marks) TWo

parallel plate

capacitors

of

capacitances

C and2C

are

connected

in

parallel

and

charged

to

a

potential

difference V. Tbe battery

is

then

disconnected

and

the region

between

the plates

of

the capacitor

C

is

completely

filled with

a

material

of

dielectric

constant

K. The

potential

difference

across

the

capacitors

now

3.

4"

5.

becomes (1989 - 2 Marks)

A point

charge

q

moves

from point

P

to

point

S

along

the path PQRS

(figure)

in

a

uniform

electric

field

E

pointing

paralleX

to

the

positive direction of

the

X-axis.

6.

7.

,S

are

(a, b,

A), (2a,

0,

0),

(a,

b.,

0)

and

(0,

0,

0)

respectively- The

work

done

by

the

field in

the

above

process

is

given

by

the

expression

(1989

.2

Marks) The

electric potential

V

at

any

point

x,

y,

z (.all

inmetre)

iri

"pace

is given

by

I,'=

4.r:

volt.'fhe

electric field

at

the

point

(i

m, 0, 2 m)

is

,,...

V/m.

{1992

-

l

Mark)

Five

point

charges, each

ofvalue

+q

coulomb,

are placed

on five

vertices

of

a

regular hexagon

of

side

I

rnetre"

The magnitude of the

fcrce

on the

point

charge of

value

-q

coulomb placeci at the cenffe of the hexagon is ...

newton.

(1992

-

1 Mark)

8. The workdone

in

carrying

a

point

charge

from

one

point to

another

in

an

electrostatic

field

depends on the

path along

which

the

point

charge

is

carried"

(1981 - 2 Marks)

9"

TWo

identical

metaliic

spheres

of

exactly

equal masses

are

taken. One

is given

a

positive

charge

_Q

coulomb

and

the other an equal negative

charge.

Their

masses

after

charging are

difFerent" (1983 - 2 Marks)

10. A

small metal

ball is

suspended

in

a

uniform

elechic

field with

the help

of

an insulated thread.

If

high

energy

X-ray

beam

falls

on

the

ball,

the

ball

u.ill

be

deflected

in

the

direction of

the field"

11. Two

protons

A

and.

B

are placed

in

between the

two

piates

of

a

parallel

plate

capacitor

charged

to

a

potential

difference Zas

shown

in

the figure. The

forces

on the two

protons

are

identical.

(1983 - 2 Nfarks) 3 Marks)

ti

I

+l

dl

li,

I

+ll

llrn*l

(19E6

(2)

-14.

204

12. Aring-ofradiirs.R caries

a

uniformly

distributed

ch41ge

.'

+,Q;\.;Pojqt

charge --q is

placed

on

the axis of the

ring

'

_'

_at_a_distance_2R

_fro{n

_{the centre}

_ofthe

_ring

_{and released}

from

rest. The particle

executes

a

simple

harmonic

motion,along the axis of

the

ring.

(198s - 2 Marks)

13. An

elebtric

line of

force in

the

x-y

plane is

given

by the equation :r2 +

f

=,7: Aparticle

with

unit positive

charge,

initialiy

at rest at the

point x

:

|,.y:

0 in

the

x-y

plane,

will

move along

the circular line

of

force.

A hollow

metal

sphere

of

radius 5

em

is

charged such that the

potential

on

its

surface

is

10

volt.

The

potential

at

the

centre

of the

sphere is

(a).zero

(b)

l0

volt

(c)

same as

at

a

point 5

cm away

from

the

surface

(d)

same as

at

a

point 25 cm

away

from

the

surface

(1983

-

I

Mark)

Two point

charges

+q

xd

_-q

arc held

fixed

at

(J,

0)

andid,O)

respeciively

of

ax-ycoordinate

system. Then

(a)

The

electric fieid E

at

all

points on x-axis

has the same

direction

(b)

Electric field

at

all

points

on

y-axis is

along

x.axis

(c)

Work

has

to

be done

in bringing

a test charge

from

oo

_to

_the

_origin

(d)

rhe

dipole moment

is.2qd

"** T;;:T"",

A

parallel

plate

capacitor ofcapacitance

C is connected

to

a battery and is

charged

to

a potential

difference

I/.

Another

capacitor of capacitance 2C is

similariy

charged

to a

potential difference 2V.The

charging battery is

now

disconnected and the capacitors are connected in

parallel

to

each other

in

such a way that the

positive terminal

of

one is

connected

to

the negative

terminal of

the other.

The

final enerry

of

the configuration

is

q.).5"s

(a)

zero (b) ;rr"

(c)

-"cv'

(d)

tCY'.

(1995 - 2 Marks)

An

electron

of

mass mu,

initially

at rest, moves

through

a

certain distance

in

a

uniform

electric

field in time

/1.

A

proton

of

mass mo, also

initially

at rest, takes

time

12

to move through an equal distance in this

uniform elecffic

15.

16.

17.

(1988r 2 Marks)

18. A

non:conducting

ring

ofradius 0.5 m

carries

a

total

charge

of

l.i

I

x

l0-r0 C, distributed

non-uniformly

on

its

circumference,

producing an

electric

_field

E

/ =0

everlnvhere inspace.

Thevalue ofthe

integral

_I

-Eai

' _{-: -} :: l:q ':

.(I

:'0

being

centre

of

the

ring) in

volt

is

field.

Neglectin!.qhe effect

of

gravlty,

the

ratio

of

t2lt1

is

nearly equal to

(a)

I

7c)

{m"lm)tt2

(a)

+2

(b)

_-1

_@)

1 (d)

zero.

(1997

-

I

Mark)

A

parallel combination

of

0.1

MO

resistor

and

a

l0

pF capacitor is connected across a 1.5

V

source ofnegtrigible resistance.

The

time

required

for

the

capacitor

to

get charged

up

to

0.75 V

is

approximately

(in

seconds)

(a)

*

(b)

ln2

(c)

logie2

(d)

zero.

(1997 -

I

Mark)

Two identical

metal plates are

given positive

charges

Ql

and

_QzG

_Q)

respectively.

If

they

are

now

brought

close together

to

form

a

parallel plate

capacitor

with

capacitance C, the

potential difference

between them is

(a)

(Q

+

_QilQC)

(c) (9r

_-

_Q)tc

For the

circuit

shown

in figure,

which

ofthe

following

statements

is

true?

(b)

(m/m")ttz

(d)

1836

$ee7

-

l

Mrrk)

(b)

(9r

+

_e)tc

(d)

(gr

_-

_Q)t(zc)

(1999 - 2 Marks)

s,

k3ov

s,

_.,

vr:2oY

_{*_}

,r-"2

I C;2pF

C;3pF

I

II

=

19.

20. 2t.

(a)

With

,St

closed, Y,

:

15

Y,

V2:

20 Y

(b)

With,S, closed,

Vt:

Vz:

25 V

(c)

With

,S1'and ,S2

closed,

V1

= V2:

0

(d)

With

^S1 and 53

closed,

Vr:

3A

Y,

V,

=

20

Y.

(1999 - 2 Marks)

o

22. Tlvee

charges

_Q.

+

q

and

+ q arc placed at the

vertices

of

a right-angled

isosceles

triangle

as

shown.

+q

The net electrostatic energy

ofthe

configuration

is zero

if p

is

equal to

q

(A)

_GT

(c)

_-

2q

-2a

(b)

_t+-E

(d)+q

(2000-2Marks)

(3)

23. A

parallel plate capacitor

^

of

area

A,plate separation

i

d

and

capacitance

C

is

i,

d

llled

with

three

different

,

dielectric materials

having

i

dielectric

constant

Kt,

Kz'

and

K,

as shown

in

the

A=AteaofPlate

figure.

If

a single dielectric material is

to

be

used

to

have

the

same capacitance

C

in

this

capacitor,

then

its

dielectric

constant

K

is given

by

(")

_=l

_t.+0)

+

="+i.+

(c)

r

: ,!r!l

+

2\

_(d)

_,<

₌

_Kt

₊

_Kz

₊

_2K3

Kt+K2

,

::

(2000,- 2 Marks)

24.

Tbvee

positive

charges

of

equal value

qr are

placed

at

the vertices

of

an equilateral triangle. The

resulting

lines

of force

should be

sketched as

in

-ti

-a)

_i'l

-t

t,

(d)

2q.

Ql{lr -

r

uaft<)

A uniform

electric

field pointing

in

positive x-direction

exists

in

a

region.

Let

A

be

the

origin, B

be

the point

on

the

x-axis

at

x

:

+l

cm and

C

be

the

point

on

the

y-axis

at

y

:

+l

cm. Then the potentials at

the

points

A,BandCsatisfo

(a)

Ve

<

/,

(b)

Ve> Vn

(c)

Y1<

V"

_{d)

VA>

yc" (2001

-

I

Mark)

25.

Consider the

situation

shown

in

the

figure. The

capacito r

A

has

a

charge

q

on

it

whereas

B

is

uncharged.

The

charge

appearing

on the capacitor.B

a

long,time

after

the switch

is closed is

27,

Two

equal

point

charges are

fixed

at

x

₌

_-a

and

x

::+a

on the

axis.

Another point

charge

_{Q is}

placed at

the

(b)

ll'

li

_,

26. .':

origin.

The change

in

the electrical potential

energy

of

p,

when

it

is

displaced by

a

small

distance

x

along the

r-axis, is

approximately

proportional to

(a)

x

(b)

x2

(c)

"3

(d) llx.

Q002

-1

Mark)

28. Two identical

capacitors have

the

same capacitance C.

One

of

them is charged to

potential Vl

andthe

other Vr.

The negative ends

of

thp

capacitors

are: cotrnocted

together.,When

ttte positive

ends are

also

connected,

the

decrease

in

energy

of

the combined.system

is

29. a> IcV?

'v')

(c)

_{IrM -}

,;f

30.

Six charges

of

equal magnitude, 3

positive

and 3 negative are to be

placed on PQRSTU

comers

ofa

regular hexagon,

such

that

u

field

at the centre is

double.that

of what

it

would

have

been

if

only

one

,-ve

charge

is

placeci

61 _f,c(f

+ rt;)

1^

@

_;c(t4

*

vr)'

:

A

metallic shell

has

a point,charge,q kept inside

its

cavity.

Which

one

of

the

following

diagrams correctly

represents

the

eleciric

lines

of

force?

(2003 -

I

Mark)

at

_.:

R.

(a)

,+,,1, 4,

_{-, -,}

_-

(b)

_-,

+,

(c)

_-,

+,

*,

_-,

*,

_-

(d)

+,

_-,

+,

31. AGaussiansurfaceinthe

_ft"'

_i;::'i...q'

,

, figure is shown by

dotted i

"

line.

The

electric

field

on

i .

_{'''Jt J}

j

the

surface

_will

be

""..."

(a)

due

to qy

and

q2

onl;y

(b)

due

to q2 only

I {2004 -.

I

Mark) t

(d)

due

to

all.

(2004

-

I

Nlark)

(c)

zero

(4)

206

32.

33.

Three

infinitely

long

chaqge sheets are placed

as shown

in

figure.

The

electric

field

at

point

P is (a)

(c)

?:r

tg

-2o

i

o0

4a:

(b)

uo

"

4<s

:

(d)-^k.

c0

Consider

a

neutral conducting

sphere.

Apositive point

charge is

placed outside the

sphere.

The

net charge on

the

sphere is then

(a)

negative and

distributed

uniformly

over the surface

of

the

sphere

(b)

negative and appears

only

at the

point

on the sphere

closest

to the point

charge

(c)

negative and distributed non-uniformly over

the

entire

surface

ofthe

sphere

,:

(d)

zero..

QooT - 3 Marks)

A

long, hollow

conducting

cylinder is kept coaxially

inside another long,

hollow

conducting

cylinder

oflarger

radius.

Both the

cylinders,are

initially

electrically

neutral.

(a)

A

potential difference

appears between

the two

cylinders

when a charge density is given tb the

inner

cylinder.

(b)

A

potential difference

appears between

the two

cylinders

wheir a charge density is given to the

outer

cylinder.

(c)

No potential difference

appears

between

the two

cylinders when

a

uniform

line

charge is

kept along

the axis

ofthe

cylinders.

(d) No potential difference

appears between

the two

cylinders

when same chargg density is

givento

both

the

cylinders.

(2Q07 - 3 D{arks)

the emptied

space

is

(a\

zero everywhere

(b)

non-zero and uniform

(c)

non-uniform

(d)

zero only at its

center.

34.

35. A

spherical portion

has been

removed from a solid

sphere

having a

charge

distributed

uniformly

in

its

volume

as

shown in

the

figure.

The

electric

field

inside

(2007

.

3 Marks)

36. Positive

and

negative point

charges

of

equal

magnitude

/

_^\

(

_-n'r

arekeptat

[0,

o.

!)

and

[o,o,TJ

respectively.The

work

done by the

electric field

when another

positive

point

charge

is

moved

from

_{l-a, 0, 0)}

to

(0, a, 0)

is

(a)

positive

(b)

negative

(c)

zero

(d)

depends

onthe

path

connectingthe

initial

and

final

positions:

37.

Consider a system

ofthree

charges

ao

2a

i,

,ana

-

3.

Rlaced

at

points

l,

QO$X

-

3'Marks)

B

and

C, respectively,

as

shown

in

the figure.

Take O

to

be the

centre

-c

of

the

circle of radiusR

and angle

CAB:60"

q

(a)

the electric

field

at

point

O

is

_*ogt

directed along

the

negative

x-axis

(b)

the

potential enerry

ofthe

system

is

zero

(c)

the magnitude

of

the

force

between

the

charges at

2

s

C

and

B

is

:;-=

_-r

)47[eol(-q

(d)

the;potential

at

point

O

ir

_f

_Z".oR

(2003)

38"

A

parallel plate capacitor

C

with

plates

of

unit

area

and

_a

separation

d

is

filled

with

a

dI

liquid of

dielectric

constant

:,,!(:2.-The

level

of liquid

is

dl3 initially.

Suppose

the

liquid

level

decreases

at.a

constant

speedV,thetime

constant as a

function

of

time

lis

6a"R

(a)

_saizrt

6eoR

\c)

_sd.1w'

(15d

_+gVt\eoR

(b)

-

=3dw:9v't

-

-- -'r

(l5d -gilr)eoR

\d)

_;F

_+zai:;/rF

(20CIs)

39.

A

disk

of

radius

al4having

a

uniformly

distributed

charge 6 C is placed in the

x-y

plane

with

its centre at (-a12, A, A).

A

rod

of

length a carrying

a

uniformly

distributed

charge

I

C is placed on the

x-axis

from x

:

al4

to

x:

5a14.

Two point

charges

_-7

C and

3 C

are

placed

at

{a14,

-s/4,0}

and

(-3a14, ,3*14,0),

(5)

respectively. Consider a cubical surface formed

by

six

surfaces

x

=

*

al2,y

=*.

al/,7=*.

al2. The

electric

flux

through

this

cubical

surface is

t2c

(d)

%

(2oob)

40.

Three

concentric metallic

spherical shells of

tadii R,ZR,

3R, are given charge s

_Q'

_{Q* Q,}

respectively.

It

is

found

that the surface

charge

densities on the outer

surfaces

of the

shells are equal. Then,

the raiio of the

charges

given to the shells,

Qr:

Q,

is

(a) I :2 :3

(b)

I

:3

:5

(c)

I

:4

:9

Two equal negative

charge

_-

q

arc

fixed at

points

(0,

_-

a) and (0,

a)

on

y-axis.

A

positive

charge

p

is

released

from

resl at the

point

(2a, 0) on the

x-axis.

The

charge

p

will

(a)

execute

simple

harmonic

motion

about

the

origin

(b)

move

to the origin

remain at

rest

(c)

move

to

infinity

(d)

execute

oscillatory

but not simple harmonic

motion'

(1984 - 2 Marks)

A

parallel plate

air

capacitor is

connected

to

a battery' The

quantities

charge,

voltage, electric

field

and energy associated

with this

capacitor

are

given

by

_Qs,

Vs, Es

and Us respectively.

A dielectric

slab is

now introduced

to

fill

the

space between

the plates:with battery

still in

connection.

The

corresponding

quantities now

given

by Q,

V,

E

and

U

are

to

the

prwious

one

as

(a)Q>CoG) V>Vo

(c)E>Eq

(d)U>Uo.

(1985 '' 2 Marks)

A

charge q is placed at the centre of the line

joining two

equal

charges

p.

The

system

of

the three

charges

will

be

in equilibrium

if

g is

equal

to

1C

2C

lOC

(ar-F 0) r.

(c)

%

(d) 1:8:18

(200e)

4t.

42.

43.

44. @)

-z

(1987

'2

Marks)

A

parallel plate

capacitor

is

charged and

the

charging battery is then disconnected.

Ifthe

plates

ofthe

capacitor

are

moved farther

apart by means

of

insulating

handles

(a)

the

charge

on

the capacitor

increases

(b)

the

voltage

across

the

plates

increases

(c)

the capacitance

increases

$)

-x

(")

*7

o

_@.?

45. (d) the

electrostatic energy stored

in

the

capacitor

-

_increases.

(1987

-2

Marks)

A

solid

conducting sphere

having

a

charge

p

is

surrounded

by

an

uncharged

concentric

conducting

hollow

spherical shell.

Let

the potential

difference

between

the

surface

of the.solid

sphere and

that of

the outer surface of the

hollow

shell be

V.lf

the shell is

now

given a

charge

of

-

3Q, the new potential

difference

between

the

same

two

surfaces is

(a)

v

(b)

2t/

_@)

ar

_@)

_-2v'

(1989 - 2 Marks) Seven

capacitors,

each

of

capacitance

2 pF,

are

to

be

connected

in

a

configuration

to

obtain

an

-effective

/ro\

capacitance

"f

[."J

pF. Which

of

the

combinations

shown

in figure

will

achieve the desired

result?

46. ':--.

A

parallel plate capacitor

of

plate

area

I

and

plate sparation d is charged to

potential difference Zand

then the banery is disconnected.

A

slab

of dielectric

constant

K

is then inserted between the plates of the capacitor so as

to

fill

the

space

between the plates.

If

_Q,

E

and LV

denote respectiyeiy,

the

magnitude

of

charge

on

each

plate, the

electric

field

between the plates (after tire slab

is inserted), and the workdone on the system, in question,

in

the'process

of

inserting

the

slab,

then

:

,,,-(),,"

q<>HHHF

(b)

s:

t#t

(d)w:+1,-*]

{1991 - 2 Marks)

.

qQr

_-

QzJ1ll

-

tl

(b)

-

_--GE;c"R)

(c)

47.

(^)'a=

"e*v

@

E=*

48.

TWo

identical thin rings,

each

of

radius

R

metre,

are

coaxially

placed a distance R

metre

_{apaft.If Ql}

coulomb

and Q2coulomb, are

respectivelythe

charges

uniformly

spread on the

two

rings, the

workdone

in

moving

charge

4 from

the centre

of

one

ring to that

of

the

other

is

(a)

zero

(6)

208

sa@t+

02)

(c)

_(4"€oR)

:

_.

(1992-2Marks)

49.

The

magnifude

of

electric

field

E in

the annutar

region

'of

a

charged

cylindrical

capacitor

'

1a1

is

same

throughout

(b)

is higher near the outer

cylinder

than near the

inner

cyllnder

(c)

varies

as

llr"

where

r

is

the distance

from

axis

(d)

varies

as

llf

,

where

r

is

the distance

from

axis.

'

(1996

-2

Marks)

50. A

metallic

solid

sphere is plaCed

in

r

a

uniform

electric

2

field.

The lines

of

3

force

follow

the

4

path(s) shown

in

figure

as

(a)

I

(b)

2 (c)

(d)

4.

(1996 - 2 Marks)

(d)

51.

A

dielectric

slab

of thickness./

is.inserted

in

a

parallel

plate

capacitor whose negative

plate

iS

at

x

:

0

and

positive plate

is

x:3d.The

slab is

equidistant from

the plates. The

capacitor

is

given

some charge.

As

one goes

from 0 to

3d,

(a)

the

magnitude

ofthe

electric

field

remains th'e same

(b)

the

direction of the

-electric.field remains

the

same

(c)

the

electric

potentlal

inCr,eases

qoptinuoosli

(d)lheeleitricpot@tinCEdei4rllsi@lgcreases

anci

again

increases.

(1998 - 2 Marks)

A

charge

+4 is

fixed at

each

of

the points

"

:

"0,

x

₌

3Jc6,

x:.,5xs, :.,.;X

₇

€

.,orr the

_aaxiS,.a4{

a charge

-q is

fixed

at

each

of

the

points

x :

Zxs,

x

:

4x6,

x

:

6xs,....1,

x=oo.

Here x9

is

a

positive

const4qt.

Tale

thq electric potential

at a

point

due

to

a

charge

_Q

at a distance

r

from

it to

be

_Ql(4neor).

Then,

the

potential

at

the origin

due

to the

above

system

_of

charges is

ftt

_**fril

q ln?

(d)

4"eo"o ,52.

(a)

o

(c)'o

(1998

_:2

Marks)

A

postively

charged

thin

metal ring

of

radius rR is

fixed

in

the';cy plane

with

its

centre

at

the

origin O.

A

s(q+

e)d-z

+

r\

(4tl2rnsR)

53.

54.

I IT- J E E C h ao te ruii

se Soluti.6ns

negatively

charged

particle

P

is

released.from

rest

at

the

point

(0,

0,

zs)

where

zo>

0.

Then the

motion of

P

is

(a)

periodic, for all

values

of

zs

satisfying

0 <

zo

1 a

(b)

simple harmoinc,

for

all

values

of

zo satisfoing

0<0<n

(c)

approximatefy simple

haqrnonic,

provided

zo

<< R

(d)

such

thptPcrosses

O

and continues

to move along

the

negative

z

axis

towarcis

z

: -

.o.

.

A

non-conducting solid

sphere

of

radius R is

uniformly

charged. The

magnifude'of

the

electric

field

due

of

the sphere

at

a distance

r

from its

centre

,(-4-)

increases

as.r..incr€ases, fo1 7

(

lR.,.;r:

,

.

.,.;;

{b)l,decreses-as:=r ingreasesr'fof , _O

<

_{.r...i: o,,,}

(c)

decreases as

r

increases,

_{for R <}

_r

<

o

(d)

is

discontinuous at

r

=

R. (1998 - 2 Marks)

55. 'An"'ellipsoidal

cavity

is

carved

within a

perfect

conductor

(figure).

A

positive

charge

q is

placed at

the centre

of

the

cavity.

The points

A

and

B

are on

'

the

cavity

surface. as

shsivn

in the

figure" Then

'(a)

electric field

near

I

in

the cavity

:

electric field

near

B in

the cavity

(b)

charge

density

at

A

:

charge

density at B

.{c}

pofpqtl.al

*,1.,.;' potantid

ut' E .

:-,',-,,'-'.,

(d)

total

gtectric

field

flux

througtr

the

surface

of

the

,

,. ,

cavrtf is

q/en.

(tlll

-i

Marks;

56.

A

:spherical

symmetric.

charg.e,sy6ten is, centred

,at'orrgin.

Given,'

electric

potenlial

57.

o

=,#ffik

<

_&),

4:

&(r

>

&r

r?o

,'

'(a)

within

r:'2Ritotal

enclosed

net

charge

is

p

(b)

electric field is

discontinued at

r

:

Ro

(c)

charge

is only

present

at

r

=

Ro

(d)

electrostatic energy

is

zero

for

r

<.R6.

(2006 - 5 Marks)

Underthe

inflyence

ofthe

Coulomb

field

of

charge

+e,

a charge

_-g

is.morring around

it

in

an

elliptical

orbit.

Find out

the

correct

statement(s).

(a)

The angular momentum of the charge

_-q

is constant.

(7)

(c)

The angular

velocity ofthe

charge

-g

is

constant.

(d)

The

linear

speed

of

the charge -.4

is

constant.

(200e)

58. A

rigid

insulated

wire

frame

in

the form

of

a

right

angled

triangle

ABC,

is set

in

a

vertical

plane as shown

in fig.

Two

beads

of

equal masses

m

eachand

carrying

charges _Q1and

q2are

connected

by

a

cord

oflength

/

and

can

slide without friction

on the wires.

A

59.

60.

D

Considering the

case

when

determine

(a)

(i)

The

angle

a

(ii)

The

tension in

the

cord

(iii)

The

normal reaction

on the beads.

(b)

If

the cord

is

now cut what

are

the value

of

the

charges

for

which the

beads

continue

to

remain

stationary

? (1978)

A

charged

particle is

free

to

move

in

an

electric

field.

Will

it

always move along an

electric line

of

force

?

(19?9)

A

charge

_{Q is distributed}

over

two

concentric

hollow

spheres

of

radii

r

and

R

(>r)

such that the

surface

densities are equal.

Find

the

potential

at the common

C

the

beads are

stationary

(f981 - 3 Marks)

centre.

61. The

figure

shows

two

identical

parallel plate capacitors

to

a

battery

with

the

switch,Sclosed.

The

switch is now

opened and

the free space between the plates

62. of

the capacitors is

filled with

a

dielectric

of

dielectric

constant

_{(or relative permittivity) 3. Find the ratio}

_of

the

total

electrostatic

energJ

stored

in

both

capacitors

before and

after the introduction of

the dielectric.

Two fixed,

equal, positive

chargesn

each

of

magnitude

5 x

10-5

C

are located at points

_A

_and

_B

_separated

_by

a distance of 6 m.

An

equal and opposite

charge:moves towards

them along the line

COD,

perpendicular bisector

of the

line

lB.

+q

the

(1983 - 6 Marks)

63.

The

moving

charge,

when

it

reaches

the

point C at

a

distance

_{of 4 m}

from

O,

has

a kinetic

energy

of

4

joule.

Calculate the

distances

of

the farthest

point D

which

the negative

charge

rvill

reach before returning

towards

C.

(f985-6Marks)

\

Three

point

charges.g,

2q

and

8q

are

to

be placed

on

a9

cm long straight

line.

Find the positions where

the

charges should be placed such that the

potential

energy

of this

system is

_{minimum. In this situation, what}

is the

electric

field

at

the

position of

the

charge

q

due

to

the

other

two

charges? _{(f987 -}₇Marks)

64.

Three

particles,

each

of

mass 1 g and

carrying

a charge

q,

are suspended

from a

cornmon

point by

insulated

massless

strings, each

100

cm long.

If

the particles

are

in

_{equilibrium and are located at the comers}

_of

_an

equilateral

triangle

of

side

length 3 crn,

calculate

the charge

q on

each

particle.

(Take

g:

_l0

m/s2).

(1988 _ ₅Malks)

65. Three concentric spherical

metallic

shells

l,

B

and

C

of

radii

a,

b

and

c

(a

<

U

.

c)

have

surface

charge densities

o, --o

and

o

respectively.

(i)

Find

the

potential of

the three

shells

l,

B

and C"

(ii)

If

the

shells

A

and,

C

are

at the

same potential,

obtain

the relation

between the

radii a,

b

and c.

(1990

-

7 Marks)

66. Two

fixed

charges

_-2Q

and

_e

are located at the

points

with

coordinates

(-3a, 0)

and

(+3a,

O)

respectively

in

thex-yplane.

(a)

Show that

all points in

the

x

-

y

plane,

where

the ,

.

r

electric potential

due to the

two

charges is zero,

lie

on

a

circle. Find its

radius and the

location

of

its centre.

(b)

Give

the

expression

V(x) at a general

point

on the

x-axis

and sketch the

function

V(x)

on

the whole

x-axis.

(c)

Ifa

particle

ofcharge

+4

starts

from

rest at the the

centre

ofthe

circle,

show

by a

short quantitative

enr

that

the.

particle eventually

crosses the

circte.

Find its

speed

when

it

does so"

(f 991 :4+2+2 _Marks)

67. (a)

A

charge

of

p

coulomb is uniformly

distributed

over

a

spherical voiume

of

radius R

metre. Obtain

an expression

for

the

energy

of

the

system.

(b)

What

will

be the

corresponding

expression

for

the

(8)

210 earth against

the

gravitational

pull

amongst its

constituent

Particles?

Assume

the

earth

to

be a sphere

of uniform

mass

density.

Calcuiate this

energy,

given the

product

of

the

mass

and

the

radius

of

the earth

to

be

2.5 x 1031

kg.

m.

(c)

If

the

same charge

of

Q

coulomb as

in

part

(a) above

is

given

to

a

spherical conductor

ofthe

same

radius

R,

what

will

be energy

of

the system? {,1992'' 10 Marks)

68.

TWo

paraltel

plate

capacitors

I

and

B

have

the

same

separation

d:

8.85 x

lOa m

between the plates'

The

plate

area

of

A

and

respectively.

A

slab

pennittivity)

K

:

9

exactly

fill

the

sPace

B

are 0.04

m2 and A.02

mz

of

dielectric constant (relative

has

dimensions such

that

it

can between the Plates of, caPacitor B.

tto o

_(u)

0i ':

(")

(i)

The

dielectric

slab

is

placed inside

I

as

shown

in

'

figure

(a).

I

is then charged to a potential

differlnle

of

liO

V. Calculate

the

capacitance

o'f

A

and the

energy stored

in it'

(ii)

The battery is

disconnected and then the

dielectric

slab

is moved

ftom

A. Find

the workdone

by

the

external agency

in

removing

the

slab from

A'

(iii)The

same

dieiectric

slab

is now

placed inside

8'

filling

it

completely' The

two

capacitots

A

and

B

are then connected as shown in figure

(c)'

Calculate

the energy stored

in tne

sY$ef,

sg

-

z2+g*zMarks)

69. A eircular ring of

radius R

with unifonn

positive

charge

density l.

per

unit

length

is

located inthe

y-z plane

with

its

centre

at the

origin

O. A

particle

of

mass

m

and

positive

charge

q is

prbjected

from the

point

P(n6

0,

CI) on

the positive x-axis directly towards O'

with

an

initial

speed

v" Find the

smallest (non-zero)

value

of

the

speed

v

such

that the particle

does not

return

to

P. (1993 - 4 Marks)

-j-

-T-Two

square

metal plates

of

side

1

m

are

kept

0'01

m

apaft

like

a

parallel

plate

capacitor

in air in

such

a way

that one

oftheir

edges is

perpendicular to

oil

surface

in

70.

-l lT- J E E C h a P te rw i s e

Sorufions

tank

fitled with

an insulating

oil.

The

plates

are connected

to

a battery

of emf

500 V. The plates are then

lowered

vertically

into

the

oil

at a speed

of

0'001'ms-l'

Calcuiate the current

drawn from

the

battery during

the process.

(Dielectric

constant

of

oil

=11,

.

ee

=

g.g5

x

10-12

c2N-h-t)

(1994 - 6 Marks)

A

71.

K2,

respectively.

Find the

capacitance

of

the resulting

capacitor. (1996 - 2 Marks)

72. Two isoiated

metallic solid

spheres

of

radii

Rand2R

are charged such

that

both ofthese

have

same charge

density

o.

The

spheres are

located

far

away

from

each

other, and

connected

by

a

thin

conducting

wire'

Find

the

new

charge

density on the

bigger

sphere'

(1996 - 3 Marks)

73. Two

capacitors

I and

ZVF _r

_tc

B

with

capacities 3 PF

and2pr

u."

"r,ureJ

,*?$f" __rr$t

to a

Potential

diflerence

of

100

V

and

180

V

respectively" The plates

of

the

capacitors are connected as

shown

in

the figure

with

one

wire

from

each capacitor free. The upper

plate

of

I

is

positive

and

that of

B is negative.

An

uncharged

2 pF

capacitor

with

lead

wires

falls

on

the free

ends to

complete the

circuit.

Calculate

(i)

the

final

charge

on the

threecapacitors

and

(ii)

the amount

of

electrostatic energy stored

in

the

system before and after the

completion

ofthe circuit'

(1997 - 5 Marks)

74. A

conducting

sphere 51

of

radius

r

is

attached

to

an

insulating

hunOt".

Another

conducting-

tlh."t:

l:

.?f

radius rR is mounted on an

insulating

stand' Sr is

initially

uncharged,

;,

t;;i;;;

"

charge Q,

brought into

contact

with

sr,

and

removed.

,S1

is

recharged such

that the

charge

on

it

is

again _Q;and

it

is again

brought into

contact

with

52 and

removed.

This

procedure

is

repeated

n

times.

(a)

Find the electrostatic energy

of

52 after

n

such

contacts

with

51.

(b)

What,is

the

limiting

value of this

energy as n

-+ q?

(1998 - 8 Marks)

(9)

75. A

non-Conducting disc

ofradius

a and

uniform positive

surface charge

density

o

is placed

on

the

ground,

with

its axis

vertical.

A

particle

of mass ze and positive charge

q is

dropped, along

the

axis

of

the disc,

from

a

height

H

with

zero

initial

velocity. The particle

has

qlm

=

4esglo.

(a)

Find

the

value of

F/

if

the

particle

just

reaches the disc.

(b)

Sketch

the potential enerry

of

the particle

as

a

function

of

its

height and

find its

equilibrium

position.

(1999

-

t0

Marks)

76. Fourpoints

charye

+

8 pC,

_-

I

pC,

_-

I

pC,

and+

8

pC

arefixedattt

re pornts

_{-{t r, -{t}

ffi

E

,{2

E

.

m

uno

*{T

m

respectively

on

the

y-axis.

A particle

of

mass

6 x l0+

kg

and charge

+

0.I

pC

moves along the

x-direction. Its

speed at

x

:

+

o

is

vs.

Find the

least

value

of

vs

for which

the

particle is

at the origin.

Find

also the

kinetic

energy of the

particle

at the

origin.

Assume

that

space

is gravity

free.

6;u",,

I

:9

x

loe Nm2/C2.

.

4ne6

77,

Charyes

_lO

and

-q

are

located

at

the comers

of

a cube

of

side

o

us*4

shown

in the

figure. Find

the

workdone

to

separate

the

charges

to infinite

distance.

_-a

Q002 - 10 Marks)

A

charge

_{+Q is fixed at the origin}

_of

_the

_co-ordinate

system

while

a

small electric dipole

of

dipole moment

p

pointing

away

from

the

charge

along

the

x-axis

is set

free

from

a

point far

away

from

the origin.

(a)

Calculate the

kinetic

energy

of

the

dipole

when

it

reaches

to

a

point

(d,0).

(b)

Calculate the force on the charge +

p

at this moment.

(2003 - 4 Marks) TWo

uniformly

charged

plane

sheets

S,

and

^g2

having

charge densities

o1

and

oz

(or

>

o)

are

placed

at

a

distance

d

parallel

to

each other.

A

charge _?ois

moved

along

a

line of

length a(a <

d)

at an angle

+5otuittt

ttre

normalJo

,S1.

Calculate

the workdone by the

electric

field.

(2004 - 2 Marks)

A

conducting

liquid

bubble

of

radius

a and thickness

r

(t << a) is charged to

potential

V.lf

the bubble collapses

78.

79.

80.

to

a

droplet,

find

the

potential

on

the

droplet.

Instructions

:

The

_following

question-

contains

statement-l

(assertion)

and

_{statement-2 (reason). Of}

these statements,'

_{mark correct choice}

if

(a)

Statements-l and

2 are true and

statement-2,

is

a

correct

explanation

_for

statemenl-

I

(b)

Statements-I and

2 are true

and'statement-2

is not

.n correct

explanation

_for

statement-I

(c)

Statement-| is true,

statement-2

is

_false

(d)

Siatement-[

is

_false,

statement-2

is

true.

81. Statement

-

I

: For

practical

purposes, the ea,rth is used as a

reference atzero potential

in

electrical circuits:

Statement

-

2 : The electrical potential

of

a sphere

of

radius

R

with

charge

p

uniformly distributed on

the

a

surface is given

bV

q",

_{R' '}

_lzoot;

0

(2005 - 2 Marks)

The nuclear

charge

(Ze)

is

non-

o(?

uniformly

_{istributed

_within

_u

.l

nucleus

of,ruOiu,

n.

ifr-

;";t;

d

density

p(r)

_[charge

per

unit

volume] is

dependent

only

on the

radial

distance

r

from

the centre

of

the

nircleus

as shown

in

figure.

The

electric

field

is

only

along the

radial

direction.

82.

The

electric

field

at

r

= R

is

(a)

independent

of

a ,

(b)

directlyproportionalloa

(c)

directly

proportional to

a2

(d)

inversely proportional to

d

(200s)

83.

For

a:0,the

value

d(maximum

value of

p as shown

in

the

figure)

is 3Ze

ta)

_o*:

4Ze

c)

tF

(a)

a:

o

(c)

_a:R

R

(b)

a=z

-D L 2l

(d)

o=

3 {2008) 3Ze

(b)

"Rr

_Ze

(d)

3"Rt

(2008)

.84. The

electric

field within

the

nucleus

is

generally

(10)

are constants and

r

is the distance

from

its

centre'

Ifthe

electric

freldatr=

N}is

l/8

times

tlntatr=

R,

findthe

85. A

solid

sphere

of radius

'R has a charge O

dlstrilute$

la

--

its

volume

with

acharge density

P:

d'where

rcand a

value

of

a.

1. #,

6. _-8

2qAY

---v-q'

7' 4*r;V

21.

(d)

2s.

(c)

3s.

(b)

42.

(a), (d) Q2

2. B

3. 180"'

o*l;7V

11.

True

18.

(a)

2s.

(a)

32.

(c)

3e.

(a)

'46.

_(a)

s2.

(d)

5. _-qEa

12.

False

le.

(d)

'26.

(b)

33.

(d)

40.

(b)

53.

(a), (c)

K+2

20.

(d)

27.

(b)

3a.

(a)

41.

(d) False (b) (b) (o) (c) (b) (c) 13.

True

14.

(b)

g. True

10" True

16. (b)

17.

(b)

23. (b)

24.

(c)

30. (c)

31.

(d)

37. (c)

38.

(a)

44.

(b),

(d)

as.

(a)

s0.

(d)

51.

(b), (c) ?

61. '=

62.

8'48 m

)

64.3.16 x

l0-eC 8. 15. 22. 29. 36. 43. 49. 56. 47. (a),(c),

(d)

48.

(b)

5a.

(a),

(c)

ss.

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

(d)

s7.

(a)

58., (a)

(i) 60'

(ii)

_T

*

*,

(iii)

.,6 mg,

mg

(b) qt and gr must have unlike charges for

beads to remain stationary'

'

_Q(R+r)

5e.

No

60. 4m16

63. 2q and

q

are at 3 cm. Field = zero

6s.

(i)

lt"-

_€o

b.d.L(+-r*"1

_eo\D

_,/

,:(ry)

_eo\

(ii)c=a+b

ol

|

_---?-1

_^,94

66. (a)

4a,(5a,0) (b)

4,n0l3a

_-

r i+rJ

(c/

!4nes\Zma)

67. (.a)

ffi

_G)

t

2OnenR

392

1r*,1.5

x,1o32J

(r)

tfo

68. (i)

2 x,lOa

_R

1"21

x

lO-s

l

(iD 4'84

x

10r'J

(iiD

l'l

x

l0r

J

.^

_tr'

_d(K,-

f

:f

'Al-i .

_K)

n*

_Kz

73. (i)

90

x

10{

C, 210

x

10{

C, 150

x

l0{

C,

74

(a)

i

_"

#"

[+{t

-

(#)1[

$)

#

,r'tnw;

r _-lB

*.

t

_L#l

sl.

(b) Q2

70.

4.425

x

104

A. (ii)

4.74

x

l0-2 J, 1.8

x

10-2J 5o

72:

-e

rpQ

73. (a)

4r*;7

76.3ms-r,3x104J

79. 85.

7s.

(a)

_T

(r)

n6

|

2nO"

(b)

_4"%''F'

83. (b)

8a.

(c)

6s

6e'

lz%m

82.

(a)

(11)

1.

Plates

I

and2 form aparallel plate condenser. Plate

I

is connected to

*ve

terminal while plate

2 is

connecied to negative terminal.

c/

canacitv 1-

=

10"

d

.'.

Charge on plate

t

=

*

fulr,

dl

.:.

chargeonplate

4=

_-2"orA

y

d

2.

3.

Plate 4 is connected to

_-

ve terminal. The plate 4 forms two

condensers / capacitors, the one with 3 and the other with 5.

....(ii)

The magnitude of electric field is greatest at the point where the lines offorce are crowded most, being close to each other. At.B, the separation between

l0

V and 20 V lines is the least,

as is clear from the figure.

Hence the electric field is greatest at B.

The

two balls

hang

in

gravity-free

space

in

state

of

weightlessness in the satellite. There is only electrostatic force

of repulsion between them. The balls

will

be repelled

till

the two strings are at l80o The tension in each string

will

be equal to the electrostatic force between charges.

Angle between strings

=

l80o

I

Q"Q

' -

4ltto

_OA'

I

or

lensronl/

l=

-

4ttto

..q -. | -

g.-r \-/g.-r

1 800

^

K--'--T'tF-t4

-4,

^.

4r

4. The total charge remains conserved.

Initially the battery is connected.

llt=cv,

q2= (2 C)V Total charge =

CV+2CV

or

q=3CV....(i)

Finallv O. =

KCV'

Qr=

(2C)

v'

Total charge

:

KCV' +2CV'

g=

_v'c(K+

2)

Q:C

Y'C(K+2)=3CV

or 3V ....(ii) ....(D

V'=

K+2

....(iii)

t0.

%*fu@o

....(i)

.'. Potential difference across the capacitors =

5.

The

field

E

is parallel to X-axis. The point S is (0, 0, 0).

The electrostatic field is a conservative field.

or

(Wpg

+ Wgp+

Wn)

+

llro

= 0

or

Wr,

+

Wrr:

0 ... Work

done:

qE

.SF

wo=

qEi

.(r,

_-rr)

wo=

qEi

'tai +

bjl

lVu=

gEa

..

Wrs=

-Wsp =-qEa

:.'.

Workdoneby

field

alongPQ{S

:

_-

qEa Elechic potential V

=

4x2

Obviously Zdepends only on x, noJ on

_/,

not on z. .'. Intensity of electric

neil:

_{- *}

_'clx

d)

:. E-: --(4x'):

-8x

ctx

.'.

Atpoint

(1,0,2),E"=-B

x

_l:-8

_voltm-r.

7.

Charges

+q

placed

at

I

and

4

exert

equal and opposite

the forces

on

(-g)

placed at centre. Total force = 0.

Similarly total force due to charges at

2 and 5 is zero.

Thus total force due to charges placed at

1,2,4

and 5 is zero.

3I/

K+2

8.

9.

The only unbalanced force is due to (+q) placed at 3.

.'.

Magnitude of force at centre

=

.f- !

_{N lattractionl.}

4ren

Il

False

Electrostatic force

is

conservative

in

nature. Workdone in carrrying a charge between two points does not depend upon path along which the charge is carried.

The statement is false.

rrue

The metallic sphere

rihich

acquires positive charges loses electrons and so it loses mass. The metallic sphere which gains negative charge gains electrons and so

it

gains mass. Their

masses on charging are evidently different.

The statement is true.

True

When a high energy X-ray beam falls on a metal ball, it ejects electrons from the ball. The ball therefore becomes positively

(12)

214

11.

True

When a parallel plate capacitor

is

charged

to

a potential difference Z, a

uniform

elecaric

field E

:

Vld is produced between the plates. Let each

ofthe

proton,

A

and

B,

carry

charge q.

Force on aproton, A or

B:

qE

Since q and

Eare

same for each proton, the forces on them are identical.

12.

False

Field along axis of

ring

_*

E

=

₊

-*ft,-4neo

(R"

+x')"''

-x:

distance from centre

ofring

or

x=2R

_t

e"zn

lR

"

_"-aie4wy

+ 2QR

-

_{4"% sFRs}

2Qq

.'.

Force:

_-

aE:

_'

--4neo 5'l5R'

#

The force is not proportional.to displacement,

The charge particle

wili

not execute simple harmonic motion. The statement is false.

N.B.

If

*

((

R,

the

charged particle

will

execute simple harmonic

motion.

y

13. True

A unit positive charge is placed

at

/

(1, 0).

Line

of

force

is

circular with

radius

=

l.

A

line of force represents the path

in

an electrie

field

along which a

unit positive charge moves.

The _{unit irositive charge}at A is already on the circular line

of

force. It

will

move along the circular line of force. The statement is tnre.

L4.

(b) : Electric poteniial at any point inside a hollow metal sphere is constant. The potential atthe surface is

l0

volt' The potential

at the centre

will

also be

l0

volt.

15. (b):

(a) Eon;r-axis.

E

will

not

have

same

direction along

entire

x-axis. Option

(a)

is

incorrect.

For

_{-dlxAd,thafieldis}

along + x-axis

For

all

otheq Points, E is

along negative x-axis.

(-d,0) (0,0) (a) +q (d,0) E(nn)

+qL-ed,a)

(0, 0) (d,0) 16.

(b)

Electric

field

at

P,

a

point ony-axis is parallel to

x-axis.

It

is

not

along

x-axis itself. It is nearest to correct answer"

(c)

Electric potential at

origin:

zero

No work has to be done in bringing atesl charge from

infinity

to the

origin.

Option (c) is incorrect

(d)

The dipole moment is directed from

_-

q

charge to

+

q charge, along negative direction, ofx-axis.

.'.

Dipole

moment:

_-

2 qd alongx-axis.

The option is incorrect.

Hence option (b) is nearest to correct answer.

(b) : C and 2C arc in parallel to each other.

.'.,

Resultant capacity = (2C +

q

Co:3C

Net potential = 2V

_-

V

V*:

V

1

.'.

Final energy

=

lC

₂

_"',

oU,^\'

:f,ocxv>'

_--1'n''

17.

(b)

:

Acceleration of

electron:

a" Force on

electron

eE

"

Mass of

electron

ffi,,

Similarly, acceleration of proton oo

_{= "E}

'

mp

t.

'.'

S:

ut

i -at'

2 l1

.."

s:

o+

|

a^fi

and

S:

0+'

aJZ

2 "',

2 t','

1"lr

;.

_{iauti torti}

1=0

18. (")'-

J l=a

".

[2)'

=

4"

=

eE

,

mp

=

mt, . t2:(2)t''

\tr

/

ap mc eE ma t,

\mu)

E.dl

=

Potential at the cen-tre of ring.

= I g

(9xloe)x(1.11"1.0-10)

_₂_volt.

4neg

r

(d)

:

Resistor

(R)

and capacitor (C) are connected

in

parallel.

They

are connected across a 1.5

volt

source

of

negligible resistance.

Since

the

capacitor

is directly connected to voltage source and there is

no resistance

in

the path,

0.5 19.