Electrostatics - Time

8/11/2019 Electrostatics - Time

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T.l.M.E.

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cf

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Education

PvL

L d'

TEST

in

PIIY$CS

Ref

:

RTP62l2l4

SECTION

A

Integer

Answer

TYPe

Questiilns

I

'4:

Mark

the

con€ct

answer

to

friese

;;;;;

in

ttre

data

column

Provided'

No

negativema*ing

4x4={6

t.

Three

posiNe

point

charses

q'2:ltl

1.jli-3

r've'wrr"-

F-'

rtices

of

an

equilateral

are

Placed

at

the

vg

-r-.r- ^r

rha

ffi"fi;

;id;

".

rhe .n'asliY::.-:t,i1"

figure

0n radian)

uli'r$.v

vr

'mced

bY

a

charge

is

F'

ma:<imum

force

exPene

-

r

--.-L^

,aF

Time

:90

min'

Marks:105

3.

A

solid

non-conduding

spherc

Tlo

a

-'

.

unibrmly

distributed

cfiarge'

Find

the

ralio

of

the

elecfosbtic

energy

stored

in

tre

feld

outside

the

sPhere

to

thatinside

the

sphere'

1"

Gertain

quantity

of

positive

cfiarge

is

no*untficrmly

distibuted

over

a

thin

ring

of

raoius

f,

rnetre

as

per

linear

drarge

density

r,

=

6r)"in[".*1)

c

m-1'

wriere

0

is

as

per

Find

the

work

done

6n

rr'J)

by

the

field

forces

in

disptacing

a

point

drarge

ot

I

nC

fiom

the

cenfie

of

the

ring

to

infinitY'

SEC'TION

B

Single

Correst

Answer

TYPe

Quetions

5

'

19:

This

sec{ion

contains

15

;;;

with

only

one

conect

arsrrer'

iiark

JifV

o*

choice

on

the

oillR

sheets'

Marking

iol

n"n

one

answer

will

be

deemed

as

an

inconect

rcsponse

and

ONE

mark

will

be

deduc@d.

15x3=4S

5.

?-

-

- -

-

-

-

+-et

- -

-'-

--

-

-

-

Q+-o-

--

-

-

oP2

Force

on

a

short

dipole

of

moment

[]

due

to

a

short

dipole

of

moment

I

is

OireaeO

bnards

(a) up

(b)

dotrn

(c)

left

(d)

right

iuil'*"""r

poini

charse

q

q

T?:s|l.-f:l

i;ilS'.iii.ttacea

at

the

cenfioid

of

the

tdangte

;;;*

work

equai

,,

ffi'

Find

x'

2.

I

I

t

I

Figure

shows

an

infinite

line

of

uniform

charge

""T

"

o"*

cFrarge

at

psint

P'

Nor

the

point

charge

is

given

a

velocitY

vo'

Gase

(i)

lf

vo

is

direcled

perpendicular

to

the

plane

of

ffi;*

point

charge

reaches

point

P

again

aftertime

h.

Case (ii)

lf

vo

is

on

the

plane

of

paper

and

directed

i"d""i,*"r

to

ine

infinite

line'

of

charge'

the

;;ilil"*

reacies

point

P

again

after

reaching

a

maximum

Oistance

r

from

the

wire'

lf

*

=

**,

find

r

in

cm'

(Here

e

is

the

base

of

./e

natural

log?nftm)



A unibrm

infinite

line

of

charge,

an

equilateral

tiangle

of

side

1

m

and

a

point

p

are

all

ophnar.

The

work

done

in

moving

a

test

charge

from

P

to

any

of

the

three rrerticee-of

the

triangle

is

same.

Norr

a

uniformly

drarged

dng

is

ptaid

oplanar.

The

rrcrk

done

in

movin

the

test

cfiarge

bad<

to

p

is

same

inespeAtve

of

the

vertex

it

is

morred

fiom.

Then,

thE

distance

of

the

cenfiedthe

ring

to the

line

of cfrarge

is

(in

m)

o,#

o+

G,+

tg

D1e

to

a

point

drarge

located

somerrvhere

on

ry

plane,

the

potentials

at

p

and

e are

1

V

and

2

V

respectively.

Also,

the

diredions

of

electric

field

at

&ese

poinb

arc

at right

angles

to

eadr

other.

Then

ff

PQ

=

Jdm,

the

potential

at

midpoint

of

PQ

is

ralfv

tcl

-lv

J6

or

f,v

(d) none of the

abore

10.

The

elec{rostatic

fietcl

in

ry

plane

is

given

E=ry2i+g2j

ff,"

typical

representation

lines

of

force

in

the

ftrst

quadrant

of

ry

plane

is

(a)

.,

e

by

of

v

7.

&

@:

+z

ABcDEF

is

a

regutar

hexagon

on

*yiqn"

nm

1..:"'

/

{

f

,

B

parallelto

x

axis.

Due

to

a

uniform

E

in

me

x

region,

Vo

=

Vr

(V:

potential);

Also,

positive

work

.. F _,

-

needs

to

be

done

by

extemal

"g"rit

t"

,"""'"

11'

E

at

a

point

due

to

a

short

dipole makes

an

negalive

lest

cfrarge

ftom

A

to

e.

rn"n,

ntli

ansle

$

rad

wittr

its

dipole

msnent

The

acute

among

the

follorving

coutd

be

E?

(a)

eo

(i+60

(b)

Eo

(i_6i)

rcra

ei+r6i)

fiff-,f

::: i'*

o

Eo

(-i-.6il

(c)

tan-1;l;

(d)

cot-r#

9.

The.etedrostatic

field

in

ry

plane

is

given

by

12.

_

v'30v

ve15V

E=ft2v'i*vtrr)

,u

c,,

a,'rin

#;;:

il

fl K.--l

F]

work

done

by

extemal

agent

in

moving

a

test ,,{

4w

3

$F

Lr"^

foc

;iryffi+l

x

10i c

rirom

(0'0)

to

tril

i'

r'i

-=L

(a)

+1

,:-';'

v

\""

:

+

*-'

-5

O)

-*

S"witches

sr,

Sz

and

Ss

are

ctosed

ii

tr,ut

oro"r.

(").3

.,-3

:#ffi:;"+i.1',ili,ffiT,1H3's,;rnJq

(a)

108

(b)

10s

(c)

15

(d)

21

Triumphant

t".tft,fr"

Tel:040"278981%/115

Fax

: ffr2784?3f4

cnrll

, inroot*a"ao.ai--.#;.;;,

*,,*.qre4education.com

.*t"62t2t*2



13.

The apptied

F.d

E is

(a)

4.75

(b)

s.2s

(c)

5.25

(d)

6.2s

14.

The

rt/ork

done

by

a

battery

in

cfrarging

two

identicat

capacitors

in

parailetis

ttre

sar;

i"

U,"

uork

done

by

it in

cfrarging

them

in

series

but

ater

inserting

different

dielecftics

in

nem.

Hor

many

of

the

following

values

can

be

the

higher

of

the

two

dieledric

constants?

2.5,3.25,3.75

(a)

None

(b)

ene

(c)

Two

(d)

three

(a)

oi

is

unibrm,

o6

is

unibrm

(b)

oi is

uRihrm,

oo

is

non_unibrm

(c)

q

is

non-unibrm,

oo

is

unibrm

(d)

q

is

non-unibrm,

oo

is

nonuniform.

18.

A

is

a

solid

conducting

spftere

of

radius

R.

B

is

a

hollon

conducting

sphere

of

inner

Edius

r

and

outer

radiue

R.

A

canies

+q

dnrge

and

B

has

nil

charge.

A

and

B

are

far

***oC

*om

eactt

other.

Now

they

are

inGr

connected

Oy

a

long

wire.

Then

the

surface

cfiarge

Oenstty

*

n"

inner

surface

of B

is

(o)+

(d)

none

of

thse

R

;f,I

t-

E

volt

(a)

Zero

o#

i3

voll

{5"

A

hollow

conducting

sphere

witfr.

no

charge

loyor

a

pointdtarge

located

otr_centre

hde

hollovv.

lf

c

and

o0 represent

the

induced

surface

durge

densiti*

on

the

inner

and

outer

surh;s

respedively

of

the

hollow

sphere,

then

19.

ABC

is

an

equitaterat

triangle

with

its

ptane

perpendicular

to

an

infinite

plane

of

unibrm

charge

densrty

o

and

base

dc p""iel

t

*,"

plane.

Wor{<

done

in

modng

a

unit test

,f,urg"

along

each

of

trro

sides

AB

orAC

of

tre

Gngb

is

equalto

W.

The

side

of

the

tiangte

ls

equatto

€,;*

*,;+

'

The

time

constants

of

the

ttro

cirurits

ere

sagne

and

thesoules

are

ideaL

Ttlen

fr

n

F)

;

{n,

*

@,t

1.2

(d)2

A

large condueting

phte is

given

a

cfiarye

+q

and

kept

normal

to

a

uniform

fieH

E

"nJ

tn"n

earthed.

SECTION

C

Reasoning

Type

This

sedon

contalns

+

reasodig

typc

quetions

numbercd

Z0

b

23.

Each

guasffon

eonlins

ff*

P-liflg"noicee

(a),

(b),

(e|

and

tcl,

i,rrii*rri"r,

ONLY

oitE

is

conecr

oNE

mark

wiii

G

cJu*t"o

foreach

wxtng

answer.

{a}

STATE*IENT.I

is

Tnre,

STATEffiENT.2

is

True;

STATEIIdENT.Z

le

a

coneet

explanaiion

fioTSTATEMENT-i.

(bl

STATEITTENT-|

is

True,

STATEilEHT-Z

is

True;

STATEiIEI{T.A

ig

NOT

u

**"t

explanation

for

STATEffi

ENT-i.

(c)

STATEMENT.I

Is

True,

STATEtrEI{T-Z

is

False

The

efrarge

frat

flows

to

earh

is

{a)

zero

(b)

non-zero,

less

than

g

(c)

q

(d)

morethan

q.

(c)

z",E5U

6

{d}

sTATErrrEr{T-l

True

20.

STATEIiENT_

I

(q

4wqo

{3o

Is

False,

S?ATEFJEE {T-E

is

4x3={?

q>

+q

il

il

il

Ll--,

:

+

7.

lf

L

is

a

closed path

in

a region

containing

a

point

charge,

hen

uork

oone

in

taking

a

;J

&;;"

along

any

part

of

the

path

L

enn&

Oe'zero.

.

and

STATEMENT-2

JE.

A,

=0

tur

a

dosed path,

wfiere

E

is

the

eledrostatic

field.

&farao

lx'[l$:ffi

d

:040-2789&94D5

Far

:

g$-2?842334

cmait

:

websitc:rvrrw.time4education.com

RIP62U14t|



21-

STATENf,ENT-

t

ln a

region

of

etec{rostatic

field two

points

lying

on

two

different

lines of

force

cannot

be

equipotential

and

STATEMENT-2

Tangent

at a

point

on

a

line

of

force

(along

with

the anow

direction)

gives

the

direction

of

E

at

that

point

22. STATEMENT.-1

Afterfully

drarging

a

capacitor,

if a

dielectric

slab

is

introduced

Case

(D

with the battery

disconnected

Case'(i)

wtth

the

battery conneded,

then,

the

gain

in

electrostatic

energy,

stored

in the

capacitor

in case

(i)

is more

than

the

loss

of the

same

in

case

(t)

and

STATEMENT-2

ln case

O

the energy

for the

work

done

when

the

dielectric

is

moved

in,

is taken

trom

the

initially

stored

energy

white

in

case

(ii)

the

energy

is

drawn

from the baftery.

23.

STATEMENT-I

ln

a region

of

eledrostatic

field

caused

by

an

infinite

plane

of

charge,

if a test

charge

is moved

with

the same @nstant

and

uniform

speed

via

any

path

and

fiom

any

point

to

any

point,

the

instantaneous

power

is same

for

all

paths

for all

points

and at

all

instants of

motion.

and

STATEMENT.2

Forplaneof

charge,

E

andtherefore

F

issame

at all

Points.

Section

D

Multiple

Gorrect

Choice

TYPe

Queetions

24

-

28= This

section

contains

5

quesiions.

Each

question

may

have

ONE

or

MORE corect

answ€Gt.

ln

order

to

secute

marks

for

a

given

question,

ALL

conect

choiceq

and

OlrlLY

the

conect

choices

must

be

chosen.

No

negative

marking.

5x3=15

1-..

,-

24.

ln the

set

up shown,

a

dielectric slab

of dielectric

constant

K

and

having

dimensions

exactly

fitting

the interspace

between

the

plates

is

introduced

to

a distance'a'within

the

interspace.

Then:

The force

experidnced

by the

dielectric

is

independentof

the distance

moved

in

The force

experienced

by the

dielec{dc

is

propodional

to

'a'

i.e.,

the

distrance

moved

in

lf

the

inside

surface of the

plates

is smooth

and

the

plates

are rigidly

fixed, the

dielectric

will execute

periodic(non-SHM)

oscillations.

period

of

oscillations

is

proportional

to

Jt-a

Three

metal

plates,

all

identical,

are

placed

as

shown.

Plate

B canies

a charge

+Q

while A and

C

are uncharged.

Subsequently

switches

Sr and

S2 are

closed.

Then

closing

Sr

and

Sz)

inside

surface

ota

is

-$

lnitially

cfrarge

on

outside surface

of

C

is

+

9

Wren

switches

are

closed

charge

on

inside

t

surface

of

A

is

-i

A

When

switches

are

closed

ctrarge

on

inside

surface

ofA

and

c

are-

9

2

(a)

(b)

(c)

(d)

25.

B

l;*.i

Sz

I

I

=

fiarge on

-'-LJ

_

=

nitially

(before

a)

(b)

(c)

(o

etry

Comple'q

Secunderabad

-

500

003'

Tcl

: 04&2?898194/95

Far ? 04f-.7I./847334

ut"it

i

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