7 3 Electric Fields MCQ QP-merged (1)-pages-4

Prévia do material em texto

8	/	10
13.	 Initial	energy	stored	in	 	capacitor,
Charge	on	5	mF	capacitor	
The	two	capacitors	attain	a	common	potential	V	when	they	are	connected	together.
Final	energy	of	the	combination,
Electrostatic	energy	lost	in	the	process	of	attaining	the	steady	state
14.	 i.	 Parallel	plate	capacitor	consists	of	two	thin	conducting	plates	each	of	area	A	held
parallel	to	each	other	at	a	suitable	distance	d.	One	of	the	plates	is	insulated	and
other	is	earthed.	Say,	there	is	vacuum	or	air	between	the	plates.	Structure	of	a
parallel	plate	capacitor	is	shown	below.
Suppose,	the	plate	X	is	given	a	charge	of	+q	coulomb.	By	induction,	-q	coulomb	of
charge	is	produced	on	the	inner	surface	of	the	plate	Y	and	+q	coulomb	on	the
outer	surface.	Since,	the	plate	Y	is	connected	to	the	earth,	hence	the	relatively
weak	charge	+q	residing	far	away	i.e.	on	the	outer	surface	flows	to	the	earth.	Thus,
the	plates	X	and	Y	have	equal	and	opposite	charges	+q	and	-q	respectively
Suppose,	the	surface	density	of	charge	on	each	plate	is	 ,	We	know	that	the
intensity	of	electric	field	at	a	point	between	two	plane	parallel	sheets	of	equal	and
opposite	charges	is	=	 	 	[ 	are	electric	field
intensities	in	between	the	two	plates	due	to	charges	+q	and	-q	on	the	two	plates	of
the	capacitor	respectively],	where	 	is	the	permittivity	of	free	space.	The
intensity	of	electric	field	between	the	plates	will	be	given	by,	
9	/	10
The	charge	on	each	plate	is	q	and	the	area	of	each	plate	is	A.	Thus,
............(i)
Now,	let	the	potential	difference	between	the	two	plates	be	V	volt.	Then,	the
electric	field	between	the	plates	is	given	by
.....(ii)
Substituting	the	value	of	E	from	equation	(i)	into	equation	(ii),	we	get
Now	capacitance	of	the	parallel	plate	capacitor	is
Where,	 	is	the	permittivity	of	vacuum	or	air.
ii.	 Surface	charge	density	of	a	spherically	charged	body	is	given	by
After	connecting	both	the	conductors,	their	potentials	will	become	equal.
	[	For	a	spherically	charged	conductor	with	charge	q	potential	is
given	by,	 ]
15.	 i.	 a.	 When	a	conductor	is	placed	in	an	external	electric	field,	the	free	charges
present	inside	the	conductor	redistribute	themselves	in	such	a	manner	that	the
electric	field	due	to	induced	charges	opposes	the	external	field	within	the
conductor.	This	happens	until	a	static	situation	is	achieved,	i.e.	when	the	two
fields	cancels	each	other,	then	the	net	electrostatic	field	in	the	conductor
becomes	zero.
b.	 Dielectrics	are	non-conducting	substances.	i.e.	they	have	no	charge	carriers.
Thus,	in	a	dielectric,	free	movement	of	charges	is	not	possible.	When	a
dielectric	is	placed	in	an	external	electric	field,	the	molecules	are	re-oriented
and	thus	induces	a	net	dipole	moment	in	the	dielectric.	This	produces	an
electric	field.	The	diagram	clearly	shows	that	the	net	electric	field	in	case	of	a
conductor	becomes	zero,	whereas	in	case	of	a	dielectric	net	electric	field
intensity	becomes	non	zero.
10	/	10
However,	the	opposing	field	is	so	induced	that	does	not	exactly	cancel	the
external	field.	It	only	reduces	it.	And	the	resultant	electric	field	reduces	by
some	value.
Both	polar	and	non-polar	dielectric	develop	net	dipole	moment	in	the	presence
of	an	external	field.	The	dipole	moment	per	unit	volume	of	the	substance	is
called	polarisation	and	is	denoted	by	P	for	linear	isotropic	dielectrics.	
,	 	is	the	susceptibility.
ii.	 a.	 At	point	C,	inside	the	shell.	The	electric	field	inside	a	spherical	shell	is	zero.
Thus,	the	force	experienced	by	the	charge	Q/2	kept	at	the	centre	C	of	the	shell
will	also	be	zero.
)
At	point	'A',	magnitude	of	the	force	experienced	by	charge	+2Q	there,	IFA=	2Q	×
	(since	3Q/2	is	the	net	charge	of	the	shell)
	,	direction	of	this	force	is	away	from	shell
b.	 Electric	flux	through	the	shell,	 	×	magnitude	of	the	net	charge	enclosed
by	the	shell.	(In	this	case	there	is	no	effect	of	the	charge	which	lies	above	the
shell)
ALLEN 1
no
de
06
\B
0B
0-
BA
\K
ot
a\
JE
E 
M
ai
n\
Je
e 
M
ai
n-
20
19
_S
ub
je
ct
 To
pi
c P
D
F 
W
ith
 S
ol
ut
io
n\
Ph
ys
ics
\E
ng
lis
h\
5-
El
ec
tro
st
at
ics
E
Electrostatics
ELECTROSTATICS
1. Two point charges q1( 10 mC) and q2(–25 mC)
are placed on the x-axis at x = l m and x = 4
m respectively. The electric field (in V/m) at
a point y = 3 m on y-axis is,
-é ù= ´ê úpeë û
9 2 2
0
1
take 9 10 Nm C
4
(1) - + ´ 2ˆ ˆ( 63i 27j) 10
(2) - ´ 2ˆ ˆ(81i 81j) 10
(3) - ´ 2ˆ ˆ(63i 27j) 10
(4) 2ˆ ˆ( 81i 81j) 10- + ´
2. Charge is distributed within a sphere of radius
R with a volume charge density -r = 2r / a
2
A
(r) e
r
,
where A and a are constants. If Q is the total
charge of this charge distribution, the radius
R is :
(1) 
æ ö-ç ÷
pè ø
a Q
log 1
2 2 aA
(2) 
æ ö-ç ÷
pè ø
Q
a log 1
2 aA
(3)
æ ö
ç ÷
ç - ÷
pè ø
1
a log
Q
1
2 aA
(4) 
æ ö
ç ÷
ç - ÷
pè ø
a 1
log
Q2 1
2 aA
3. Three charges +Q, q, + Q are placed
respectively, at distance, 0, d/2 and d from the
origin, on the x-axis. If the net force
experienced by + Q, placed at x = 0, Ls zero,
then value of q is :
(1) +Q/2 (2) –Q/2
(3) –Q/4 (4) +Q/4
4. For a uniformly charged ring of radius R, the
electric field on its axis has the largest
magnitude at a distance h from its centre. Then
value of h is :
(1) 
R
5 (2) R
(3) 
R
2 (4) R 2
5. Charges –q and +q located at A and B,
respectively, constitute an electric dipole.
Distance AB = 2a, O is the mid point of the
dipole and OP is perpendicular to AB.
A charge Q is placed at P where OP = y and
y >> 2a. The charge Q experiences and
electrostatic force F. If Q is now moved along
the equatorial line to P' such that OP'= y
3
æ ö
ç ÷
è ø
,
the force on Q will be close to :
y
2a
3
æ ö>>ç ÷è ø
A –q +q
B
Q P'
O
P
(1) 
F
3
(2) 3F (3) 9F (4) 27F
6. Four equal point charges Q each are placed in
the xy plane at (0, 2), (4, 2), (4, –2) and
(0, –2). The work required to put a fifth charge
Q at the origin of the coordinate system will
be :
(1) 
2
0
Q
2 2pe (2) 
2
0
Q 1
1
4 5
æ ö+ç ÷pe è ø
(3) 
2
0
Q 1
1
4 3
æ ö+ç ÷pe è ø
(4) 
2
0
Q
4pe
ALL
EN
2 ALLEN
no
de
06
\B
0B
0-
BA
\K
ot
a\
JE
E 
M
ai
n\
Je
e 
M
ai
n-
20
19
_S
ub
je
ct
 To
pi
c P
D
F 
W
ith
 S
ol
ut
io
n\
Ph
ys
ics
\E
ng
lis
h\
5-
El
ec
tro
st
at
ics
E
Electrostatics
7. A charge Q is distributed over three concentric
spherical shells of radii a, b, c (a(1) 
ˆ ˆi j(q )
2
+
l (2) 
ˆ ˆj i3q
2
-
l
(3) ˆ3q j- l (4) ˆ2q jl
ALL
EN
ALLEN 3
no
de
06
\B
0B
0-
BA
\K
ot
a\
JE
E 
M
ai
n\
Je
e 
M
ai
n-
20
19
_S
ub
je
ct
 To
pi
c P
D
F 
W
ith
 S
ol
ut
io
n\
Ph
ys
ics
\E
ng
lis
h\
5-
El
ec
tro
st
at
ics
E
Electrostatics
13. There is a uniform spherically symmetric
surface charge density at a distance R0 from
the origin. The charge distribution is initially
at rest and starts expanding because of mutual
repulsion. The figure that represents best the
speed V(R(t)) of the distribution as a function
of its instantaneous radius R (t) is :
(1)
R(t)R0
V0
V(R(t))
(2) 
R(t)R0
V(R(t))
(3)
R(t)R0
V(R(t))
(4) 
R(t)R0
V(R(t))
14. An electric dipole is formed by two equal and
opposite charges q with separation d. The
charges have same mass m. It is kept in a
uniform electric field E. If it is slightly rotated
from its equilibrium orientation, then its angular
frequency w is :-
(1) 
qE
2md
(2) 
qE
2
md
(3) 
2qE
md
 (4) 
qE
md
15. A positive point charge is released from rest at
a distance r0 from a positive line charge with
uniform density. The speed (v) of the point
charge, as a function of instantaneous distance
r from line charge, is proportional to :-
r0
(1) 0r / rv e+µ
(2) 
0
r
v n
r
æ ö
µ ç ÷
è ø
l
(3) 
0
r
v
r
æ ö
µ ç ÷
è ø
(4) 
0
r
v n
r
æ ö
µ ç ÷
è ø
l
16. The electric field in a region is given by
( ) ˆE Ax B i= +
r
, where E is in NC–1 and x is in
metres. The values of constants are
A = 20 SI unit and B = 10 SI unit. If the
potential at x = 1 is V1 and that at x = –5 is V2,
then V1 – V2 is :-
(1) –48 V
(2) –520 V
(3) 180 V
(4) 320 V
17. The bob of a simple pendulum has mass 2g
and a charge of 5.0 µC. It is at rest in a uniform
horizontal electric field of intensity 2000 V/m.
At equilibrium, the angle that the pendulum
makes with the vertical is : (take g = 10 m/s2)
(1) tan–1(5.0)
(2) tan–1(2.0)
(3) tan–1(0.5)
(4) tan–1(0.2)
ALL
EN
4 ALLEN
no
de
06
\B
0B
0-
BA
\K
ot
a\
JE
E 
M
ai
n\
Je
e 
M
ai
n-
20
19
_S
ub
je
ct
 To
pi
c P
D
F 
W
ith
 S
ol
ut
io
n\
Ph
ys
ics
\E
ng
lis
h\
5-
El
ec
tro
st
at
ics
E
Electrostatics
18. A solid conducting sphere, having a charge
Q, is surrounded by an uncharged 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. If the shell is now given a
charge of –4 Q, the new potential difference
between the same two surfaces is :
(1) V (2) 2V
(3) –2V (4) 4V
19. Four point charges –q, +q, +q and –q are placed
on y-axis at y = –2d, y = –d, y = +d and
y = +2d, respectively. The magnitude of the
electric field E at a point on the x-axis at
x = D, with D >> d, will behave as :-
(1) E µ 
1
D
(2) E µ 3
1
D
(3) E µ 2
1
D
(4) E µ 4
1
D
20. A system of three charges are placed as shown
in the figure :
+q d –q Q
D
If D >> d, the potential energy of the system
is best given by :
(1) 
2
2
0
1 q qQd–
4 d 2D
é ù
-ê úpe ë û
(2) 
2
2
0
1 q qQd
4 d D
é ù
+ +ê úpe ë û
(3) 
2
2
0
1 q 2qQd–
4 d D
é ù
+ê úpe ë û
(4) 
2
2
0
1 q qQd– –
4 d D
é ù
ê úpe ë û
21. A simple pendulum of length L is placed
between the plates of a parallel plate capacitor
having electric field E, as shown in figure. Its
bob has mass m and charge q. The time period
of the pendulum is given by :
++++++++++++
L
m
q
E
(1) p
æ ö+ ç ÷
è ø
2
2
L
2
qE
g
m
(2) p
æ ö+ç ÷
è ø
L
2
qE
g
m
(3) p
æ ö-ç ÷
è ø
L
2
qE
g
m
(4) p
-
2 2
2
2
L
2
q E
g
m
22. In free space, a particle A of charge 1 mC is
held fixed at a point P. Another particle B of
the same charge and mass 4 mg is kept at a
distance of 1 mm from P. if B is released, then
its velocity at a distance of 9 mm from P is :
-é ù
= ´ê úpeë û
9 2 2
0
1
Take 9 10 Nm C
4
(1) 2.0 × 103 m/s (2) 3.0 × 104 m/s
(3) 1.5 × 102 m/s (4) 1.0 m/s
23. A uniformly charged ring of radius 3a and total
charge q is placed in xy-plane centred at origin.
A point charge q is moving towards the ring
along the z-axis and has speed u at z = 4a. The
minimum value of u such that it crosses the
origin is :
(1)
æ ö
ç ÷peè ø
1/22
0
2 1 q
m 15 4 a
(2) 
æ ö
ç ÷peè ø
1/22
0
2 2 q
m 15 4 a
(3)
æ ö
ç ÷peè ø
1/22
0
2 4 q
m 15 4 a
(4) 
æ ö
ç ÷peè ø
1/22
0
2 1 q
m 5 4 a
ALL
EN