UNIT - 11

ELECTROSTATICS

SUMMARY
1.

Electric Charge : Just as masses of two particles are responsible for the gravitational force,
charges are responsible for the electric force. Electric charge is an intrinsic property of a particle.
Charges are of two types : (1) Positive charges (2) Nagative charges.
The force acting between two like charges is repulsive and two unlike charges it is attractive
between .

2.

Quantization of Electric Charge : The magnitude of all charges found in nature are an integral
multiple of a fundamental charge. Q ne, where e is the fundamental unit of charge.

3.

Conservation of Electric Charge : Irrespective of any process taking place, the algebraic sum
of electric charges in an electrically isolated system always remains constant.

4.

Coulomb's Law : The electric force between two stationary point charges is directly proportional to the product of their charges and inversely proportional to the square of the distance
between them.
Fk

q1 q 2
1 q1 q 2

2
r
40 r 2

If q1 q 2 0 then there is a repulsion between the two charges and for q 2 q 2 0 , there is a attraction between the charges.
5.

Equation for Force using Columbs Law, when two charges are placed in a medium having
dielectric constant k.
(1)

The electric force F experienced by a test charge (q0) due to a source charge (q) when
both are
placed in a medium having dielectric constant k and separated by a distance r, is given by :
P

1 q1 q 2
r
40 kr 2

(q o)
O (q)

Here r is the unit vector directed from q to q0.

1
q1 q 2
r
40
k r2

(2)

The equation of coulomb's force may be written as follows : F

(3)

If the source charge and test charge are separated by a number of medium of thickness

d1 , d 2 , d 3 ........ having dielectric constants k1 , k 2 , k 3 ........ respectively, then the

electric force

1
4 0

on charge q0 due to a charge q is given by

qq 0

k1 d

2
1

k2 d

2
2

k3 d

2
3

r OR F

1
4 0

qq 0

k i d i2

In this equation ki is dielectric constant of medium which spreads through the distance di
along the line joining q and q0.
2

For example, see the figure below :

Here, the space between the charges q and q0 is filled with medium (1, 2, 3). The thickness of
medium 1 is d1 and its dielectric consant is k1 Similarly the thickness of medium 2 and 3 is d2 and
d3 of medium 3 and their dielectric constants are k2 and k3 respectively.
6.

Conditions for Equilibrium in Various Cases :

Suppose three charges q1, q2 and q are situated on a straight line as shown below :

If q1 and q2 are like charges and q is of unlike charge then,

(1)

Force on q1 F1

q1
q1
q
2

2
40 r1 r2
r1

(2)

Force on q2 F2

q2
q1
q
2

2
40 r1 r2
r2

(3)

Force on q = F

1 q1 q 2
2

40 r12
r2

Now, from above equations, it is clear that various equilibrium conditions can be as follows :
(a)

Condition for F1 to be zero is,

q
q2
q
r12

r12 r1 r2
q 2 r1 r2 2

Condition for F2 to be zero is,

q
q1
q
r2

2
2
q1 r1 r2 2
r2
r1 r2

Condition for F to be zero is,

q
r
q1 q 2
2 1 12
2
r2
r2
r1
r2

(b)

(c)

If q1 , q 2 and q are of same type charges in nature, then,

(1) Charge q will be in equilibrium, if

F
(2)

q1
q2
q1
r12
q q1 q 2

r12
r22
q2
r22
40 r12
r22

Charges q1 and q2 will not be in equilibrium.

3

7.

Electric Field Intensity : The electric force acting on a unit positive charges at a given point in
an electric field of a system of charges is called the electric field or the intensity of electric field

E at that point.
E

F
q

The SI unit of E is

N
or Vm 1 .
C

If r1 , r2 ,............rn are the position vectors of the charges q1 , q 2 ,..........q n respectively, then the
resultant electric field at a point of position vector r is,
n

Ek

j1

8.

qj
3

r r
j

r rj

Electric Dipole : A system of two equal and opposite charge, separated by a finite distance is
called electric dipole.

Electric dipole moment p q 2a

9.

10.

The direction of p is from the negative electric charge to the positive electric charge.
Electric field of a dipole on the axis of the dipole at point z = z

2kp
E z 3 p^ for z a
z
Electric field of a dipole on the equator of the dipole at point y = y

kp
E y 3 p^ for y a
y
The torque acting on the dipole place in an uniform the electric field at an angle ,

p E , | | p E sin
11.

Electric Flux : Electric flux associated with surface of area A , placed in the uniform electric
field.

E A EA cos where, is the angle between E and A ,

Nm 2
or V.m.
C
Gauss's Law : The total electric flux associated with the closed surface,

Its SI unit is
12.

q
E
d
a

S
0 where, q is the net charge enclosed by the surface.

13.

Electric field due to an infinitely long straight charged wire,

E

1
r, where, r is the perpendicular distance from the charged wire.
2 0 r

14.

Electric field due to bending of charged rod,

15.

Electric field due to uniformly charged thin spherical shell,

(1)

Electric field inside the shell E 0

(2)

Electric field at a distance r from the centre outside the shell,

Ek

16.

q
R2

where, R = radius of spherical shell.

r 2 0 r 2

Electric field due to a uniformly charged density sphere of radius R,

(1)

Q
Electric field inside the region of the sphere, E 4
0

r
R3

r
3 0

(2)

17.

Electric field outside the sphere, Er

Q r
R3

40 r 2 3r 2 0

where, Q is the total charge inside the sphere.

The information about the work done to take an electric charge from one point to the other in a
given electric field, obtained from the quantities called electric potential and electric potential
energy.
B

18.

E dr

is the line-integral of electric field between point A and B and it shows the work done by

the electric field in taking a unit positive charge from A and B. Moreover, it does not depend on
the path and E dr 0 .
19.

"The work required to be done against the electric field to bring a unit positive charge from
infinite distance to the given point in the electric field, is called the electric potential (V) at that
point".
P

Electric potential at point P is Vp E dr

It unit is

20.

J
Joule
volt. Symbolically V
C
coulomb

Its dimensional formula is M1 L2 T 3 A 1

Absolute value of electric potential has no importance but only the change in it is important.
"The work required to be done against the electric field to bring a given change (q) from infinite
distance to the given point in the electric field is called the electric potential energy of that
electric charge at that point."
P

U p q E dr qVp

The absolute value of electric potential energy has no importance, only the change in it is important.
21.
22.

Electric potential at point P, lying at a distance r from a point charge q is Vp kq

r
The electric potential at a point at distance r from an electric dipole is

vr

1 p
, ( For r > > 2a)
40 r 2

Potential on its axis is V

23.

1 p
, Potential on its equator is V 0
40 r 2

Electric potential at a point r due to a system of point charge q1 , q 2 ,.........q n situated at position
n

at position r1 , r2 ,.........rn is V

i 1

kq i
r ri
6

The electric potential at point r , due to a continuous charge distribution is

1
4 0

V r

volume

r d '
r ri

The electric potential due to a spherical shell is

V

24.

25.

1
4 0

q
r

For

1
r R and V
4 0

q
R

For

r R

A surface on which electric potential is equal at all points is called an equipotential surface. The
direction of electric field is normal to the equipotential surface.

dV
gives the magnitude of electric field in the direction of dl .
dl
To find E from V, in general, we can use the equation
E

V
V
V
E
i
j
k
y
z
x

The direction of electric field is that in which the rate of decrease of electric potential with
dV
is maximum, and this direction is always normal to the equipotential surface.
dl

distance
26.

The electrostatic potential energy of a system of point charges q1 , q 2 ,..........q n situated at positions

r1 , r2 ,.......rn is
n

i 1
i j

27.
28.

kq i q j
rij

where rij rj ri

The electrostatic potential energy of an electric dipole in an external electric field E, is

U E p Ep cos
When a metallic conductor is placed in an external electric field,
(i)

A stationary charge distribution is induced on the surface of the conductor.

(ii)

The resultant electric field inside the conductor is zero.

(ii)

The net electric charge inside the conductor is zero.

(iv) The electric field at every point on the outer surface of conductor is locally normal to the
surface.
(v)

The electric potential inside the region of conductor is the same every where.

(vi) If there is a cavity in the conductor then, even when the conductor is placed in an external
electric field, the resultant electric field inside the conductor and also inside the cavity is
always zero.
This fact is called the electrostatic shielding.

When electric charge is placed on the metallic conductor :

(i) The electric field inside the conductor is zero everywhere.
(ii) The charge is distributed only on the outer surface of the conductor.

(iii) The electric field on the surface is locally normal, and is equal to E n .
0

29.

(iv) If a charge is placed inside the cavity in the conductor, the electric field in the conductor
remains zero.
"A device formed by two conductors seprated from each other is called a capacitor." Its capacitance is C

Q
coulomb
constant. The unit of C is
which is also called farad.
V
volt

1 F 10 6 F. pF 10 12 F
30.

The effective capacitance in series connection is C then,

1
1
1
1

..........
C C1 C 2 C 3

The effective capacitance in parallel connection is C then,

C C1 C 2 C 3 .........
31.

The capacitance of the parallel plate capacitor is C

32.

The energy stored in the capacitor is U

stored per unit volume

33.

0A
.
d

Q 2 CV 2 VQ
and the energy density = energy

2C
2
2

1
0 E 2 , where E electric field.
2

When a dielectric is placed in an external electric field E 0 , polarisation of dielectric occurs due
to electrical induction. The electric field produced by these induced charges is in the opposite
direction to the direction of external electric field. Hence the resultant electric field E, inside the
dielectric is less than the external electric field E 0 .
The dipole moment produced per uint volume is called the intensity of polarisation or in short
polarisation
P n b .

Since P E , P 0 xe E xe is called the electric susceptibility of the dielectric medium.

is called the relative

0
permittivity of that medium and it is also called the dielectric constant K.

xe is called the permittivitty of the dielectric medium.


i.e. r K
0
K 1 xe , E

E0
. Thus in the dielectric the electric field reduces to the K th part.
K

D 0 E P is called the electric displacement. Gauss Law in the presence of dielectric is

written as
34.

D ds q , where q is only the net free charge.

when there is air (or vacuum) between the plates of a parallel plate capacitor, the capacitance is
0A
. On placing a medium of dielectric constant K, the capacitance is C' CK. Thus the
d
capacitance becomes K times, due to the presence of the dielectric.
C

35.

With the help of Van-De-Graf generator a potential differance of a few nillion volt can be
established.

10

CONCEPT MAP

MCQ
For the answer of the following questions choose the correct alternative from among the
given ones.
1.

When a Piece of Polythene is rubbed with wool, a charge of 2 10 7 is developed on

polythene. The mass transferred to polythene is ..... kg.
(A) 11.38 10 19

2.

Q Q
,
3 3

(B) 3.15

(C) 6.25

(D) 1.66

(B)

Q Q
,
2 2

(C)

Q 3Q
,
4 4

(D)

Q 4Q
,
5 5

(B) 100

(C) 99

(D) 89
q

(B) 0.75

(C) 0.25

(D) 0.5

Two small conducting sphere of equal radius have charges + 1c and 2c respectively and
placed at a distance d from each other experience force F1. If they are brought in contact and
separated to the same distance, they experience force F2. The ratio of F1 to F2 is ..........
(A) 8 : 1

9.

(D) 2.16 10 11

Given that q1 + q2 = q if the between q1 and q2 is maximum, q1 ...............

(A) 1

8.

(C) 1.25 10 11

Two point charges repel each other with a force of 100 N. One of the charges is increased
by 10% and other is reduced by 10%. The new force of repulsion at the same distance would
be ........ N.
(A) 121

7.

(B) 1.19 10 12

A charge Q is divided into two parts and then they are placed at a fixed distance. The force
between the two charges is always maximum when the charges are .........
(A)

6.

(D) 4.9 106

(C) 3.6 104

(B) 5.4 106

The rate of alpha partical falls on neutral spheare is 1012 per second. The time in which
sphere gets charged by 2c is ......... sec.
(A) 2.25

5.

(D) 9.63 10 19

A copper sphere of mass 2 gm contains about 2 1022 atoms. The charge on the nucleus of
each atom is 29e. The fraction of electrons removed.
(A) 2 10 10

4.

(C) 2.25 10 19

The protonic charge in 100 gm of water is .......... c

(A) 4.8 105

3.

(B) 5.69 1019

(B) 1 : 2

(C) 1 : 8

(D) 2 : 1

Three charges, each of value Q, are placed at the vertex of an equilateral triangle. A fourth
charge q is placed at the centre of the triangle. If the charges remains stationery then,
q = ...............
(A)

Q
2

(B)

Q
3

(C)
11

Q
2

(D)

Q
3

10. Tw o small charged spheres repal each other w i th a f orce 2 10 3 N . The charge on one sphere
is twice that of the other. When these two spheares displaced 10 cm further apart the force
is 5 10 4 N , then the charges on both the spheres are ........
(A) 1.6 10 19C, 3.2 10 19C

(B) 3.4 10 19C, 11.56 10 19C

(C) 33.33 10 19C, 66.66 10 19C

(D) 2.1 10 19C, 4.41 10 19 C

11. Three charges q1, + q2 and q3 are placed

as shown in figure. The x component of
the force on q1 is proportional to .........
(A)
(C)

q2 q3

sin
b2 a 2

(B)

q2 q3
+ sin
b2 a 2

(D)

q3

q2 q3

cos
b2 a 2

b
q1

q2 q3
+
cos
b2 a 2

1
+q2

12. Two equal negative charges q are fixed at points (o, a) and (o, a). A positive charge Q is
released from rest at the point (2a, o) on the X - axis. The charge Q will ..........
(A) move to the origin and remain at rest there
(B) execute simple harmonic motion about the origin
(C) move to infinity
(D) execute oscillations but not simple harmonic motion
13. Four charges, each equal to Q, are placed at the corners of a square and a charge +q is
placed at its centre. If the system is in equilibrium, the value of q is .........
(A)

Q
1 2 2
4

(C)

Q
1 2 2
2

(B)

(D)

Q
1 2 2
4

Q
1 2 2
2

q
(0, a)

14. For the system shown in figure, if the

resultant force on q is zero, then

a

Q = ...............
(A) 2 2Q
(C) 2 3Q

(B) 2 2Q

(D) 3 2Q

12

FA

FA

15. Two point positive charges q each are placed at (a, o) and (a, o). A third positive charge qo is
placed at (o, y). For which value of y the force at qo is maximum .........
(A) a

(B) 2a

(C)

a
2

(D)

a
3

16. Two identical charged spheres suspended from a common point by two massless strings of
length l are initially a distance d (d << l ) apart because of their mutual repulsion. The charge
begins to leak from both the spheres at a constant rate. As a result the spheres approach each
other with a velocity . Then function of distance x between them
becomes ...........
(A) v x

(D) v x 2

(C) v x 1

(B) v x 2

17. Three identical spheres each having a charge q and radius R, are kept in such a way that
each touches the other two spheares. The magnitude of the electric force on any sphere
due to other two is ...........
2

R 1
5q
1
(B)
(A)

2 4 0 4 R
8 0

2
3

q
R

1
3q
(C)
4 0 4 R

1
(D)
8 0

3
2

q
R

18. Two equal negative charges q are fixed at points (o, a) and (o, a) on the Y axis. A
positive charge q is released from rest at the point x (x < < a) on the X-axis, then the
frequency of motion is .........
(A)

q2
0 ma 3

(B)

2q2
4 0 ma3

(C)

4q 2
2 0 ma 3

(D)

q2
2 0 ma 3

19. Two identical balls having like charges and placed at a certain distance apart repel each
other with a certain force. They are brought in contact and then moved apart to a distance
equal to half their initial separation. The force of repulsion between them increases 4.5
times in comparison with the initial value. The ratio of the initial charges of the balls is
........
(A) 4 : 1

(B) 6 : 1

(C) 3 : 1

(D) 2 : 1

20. A point charge q is situated at a distance r from one end of a thin conducting rod of length
L having a charge Q (uniformly distributed along its length). The magnitude of electric
force between the two, is ...............
2kqQ

(A) r(r + L)

kqQ

kqQ

(B) r(r + L)

(C) r(r L)

kQ

(D) r(r + L)

21. Two point charges of +16c and 9c are placed 8 cm apart in air. ............... distance of
a point from 9c charge at which the resultant electric field is zero.
(A) 24 cm

(B) 9 cm

(C) 16 cm
13

(D) 35 cm

22. Point charges 4c and 2c are placed at the vertices P and Q of a right angle triangle PQR
respectively. Q is the right angle, PR = 2 10 2 m and QR = 10 2 m . The magnitude and
direction of the resultant electric field at c is .........
(A) 4.28 109 NC1 , 450

(B) 2.38 108 NC1 , 40.90

(C) 1.73104 NC 1 , 34.7 0

(D) 4.9 1010 NC1 , 34.7 0

23. An inclined plane making an angle of 30o with the horizontal is placed in an uniform
electric field E = 100 Vm1. A particle of mass 1 kg and charge 0.01 c is allowed to slide
down from rest from a height of 1m. If the coefficient of friction is 0.2 the time taken by
the particle to reach the bottom is .......... sec.
(A) 2.337

(B) 4.337

(C) 5

(D) 1.337

24. A small sphere whose mass is 0.1 gm carries a charge of 3 10 10C and is tieup to one end
of a silk fibre 5 cm long. The other end of the fibre is attached to a large vertical conducting
plate which has a surface charge of 25 10 6Cm 2 , on each side. When system is freely
hanging the angle fibre makes with vertical is ...............
(A) 41.80

(B) 450

(C) 40.80

(D) 45.80

25. A Semicircular rod is charged uniformly with a total charge Q coulomb. The electric field
intensity at the centre of curvature is .......
(A)

2KQ
r 2

(B)

3KQ
r 2

(C)

KQ
r 2

(D)

26. The electron is projected from a distance d and with

initial velocity 0 parallel to a uniformly charged flat
conducting plate as shown in figure. It strikes the plate
after travelling a distance l along the direction. The surface charge density of conducting plate is equal to
(A)

2d 0 m0
el

(B)

d 0 m20
el

(C)

d 0 m0
el

4KQ
r 2

v0
X

----l----Y

(D)

2d 0 m20
el 2

27. Two point masses m each carrying charge q and +q are attached to the ends of a massless
rigid non-conducting rod of length l. The arrangement is placed in a uniform electric field
E such that the rod makes a small angle 50 with the field direction. The minimum time
needed by the rod to align itself along the field is ........
(A) t =

2ml
3qE

(B) t =

ml
2 2qE

(C) t =

14

ml
qE

(D) t = 2

ml
E

28. Two uniformaly charged spherical conductors A and B having radius 1mm and 2mm are
separated by a distance of 5 cm. If the spheres are connected by a conducting wire then in
equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of
spheres A and B is .........
(A) 4 : 1
29. Let P(r) =

(B) 1 : 2

(C) 2 : 1

(D) 1 : 4

Q
r be the charge density distribution for a solid sphere of radius R and total
R 4

charge Q. For a point P inside the sphere at distance r1 from the centre of the sphere the
magnitude of electric field is
2

Q
(A) 4 r 2
0 1

30.

Qr1
Qr1
(C)
(B)
4
4 0 R
3 0 R 4
Two point charges q1 2c and q 2 1c are placed at

(B) tan 1

(C) tan 3

(D) tan 2

P(a, b)

q1

distance b = 1cm and a = 2 cm from the origin on the y

and x axes as shown in figure. The electric field vector
at point P (a, b) will subtend an angle with the X - axis
given by,
(A) tan 4

(D) 0

b
a

q2

31. A simple pendulum consists of a small sphere of mass m suspended by a thread of length
l. The sphere carries a positive charge q. The pendulum is placed in a uniform electric
field of strength E directed Vertically upwards. If the electrostatic force acting on the
sphere is less than gravitational force the period of pendulum is
l
(A) T = 2
qE
g m

1
2

l
(B) T = 2
g

1
2

32. Consider a system of three charges q/3, q/3 and 2a/3

placed at points A, B and C respectively as shown in the
figure. It the radius of the circle is R and CAB = 600
then the electric field at centre 0 is ........
q
(A) 8 R 2
0
q

(C) 6 R 2
0

l 2
ml 2
T
=
2

(D)
(C) T = 2
qE
qE

g + m

q2
(B) 54 R 2
0

B
C
600
A

(D) 0

15

33. In Millikans oil drop experiment an oil drop carrying a charge Q is held stationary by a p.d.
2400 v between the plates. To keep a drop of half the radius stationary the potential difference had to be made 600 v. What is the charge on the second drop ?
(A)

3Q
2

(B)

Q
4

(C) Q

(D)

Q
2

34. Equal charges q are placed at the vertices A and B of an equilateral triangle ABC of side a.
The magnitude of electric field at the point c is .........
(A)

Kq
a2

(B)

3Kq
a2

(C)

2Kq
a2

(D) 2 t a 2
0

35. An electric dipole is placed along the x-axis at the origin o. A point P is at a distance of 20
cm from this origin such that OP makes an angle

with the x-axis. If the electric field at

3

P makes an angle with the x-axis, the value of would be ...........

(A)

tan 1
(B)
3
3
2

(C)

2
3

1
(D) tan

36. A particle having a charge of 1.6 10 19 C enters between the plates of a parallel plate
capaciter. The initial velocity of the particle is parallel to the plates. A potential difference
of 300v is applied to the capacitor plates. If the length of the capacitor plates is 10cm and
they are separated by 2cm, Calculate the greatest initial velocity for which the particle
will not be able to come out of the plates. The mass of the particle is 12 10 24 kg .
(A) 10

m
s

(B) 10

m
s

(C) 10

m
s

(D) 10

m
s

37. A charged particle of mass 1 kg and charge 2c is thrown from a horizontal ground at an
angle = 45o with speed 20m/s. In space a horizontal electric field E = 2 107 V/m exist.
The range on horizontal ground of the projectile thrown is ............... .
(A) 100 m

(B) 50 m

(C) 200 m

(D) 0 m

38. If electron in ground state of H-atom is assumed in rest then dipole moment of electron
proton system of H-atom is ............... .
0

Orbit radius of H atom in ground state is 0.56 A .

(A) 0.253 10 29 cm (B) 0.848 10 29 cm

(C) 0.305 10 29 cm

(D) 1.205 10 28 cm

39. At what angle a point P must be located from dipole axis so that the electric field
intensity at the point is perpendicular to the dipole axis ?
(A) 530 to 540

(B) 500 to 510

(C) 450 to 460

16

(D) 520 to 530

40. A n el ectri c di pol e i s pl aced at an angl e of 60 o with an electric field of intensity 105 NC1.
It experiences a torque equal to 8 3Nm . If the dipole length is 2cm then the charge on the
dipole is ........... c.
(A) 8 103

(B) 8.54 10 4

(C) 8 10 3

(D) 0.85 10 6

41. An electric dipole coincides on z axis and its mid point is on origin of the cartesian

co-ordinate system. The electric field at an axial point at a distance z from origin is E(z)

and electric field at an equatorial point at a distance y from origin is E (y)

E (z)

(y = z > > a) = ...............

E ( y)

(A) 1

(B) 2

(C) 4

(D) 3

42. An oil drop of 12 excess electrons is held stationary under a constant electric field of
2.55 104 Vm 1 . If the density of the oil is 1.26 gm/cm3 then the radius of the drop is

.......... m.
(A) 9.81 10 7

(B) 9.29 10 7

(C) 9.38 10 8

(D) 9.34 10 8

43. A Charge q is placed at the centre of the open end of cylindrical vessel. The flux of the
electric field through the surface of the vessel is ...........
q

(A)
0

2q

(B) 2
0

(C)
0

(D) Zero

44. The inward and outward electric flux for a closed surface in units of Nm2/C are respectively 8 103 and 4 103 . Then the total charge inside the surface is ........... c.
(A)

4 103
0

(C) 4 103

(B) 4 103

(D) 4 103 0

45. A sphere of radius R has a uniform distribution of electric charge in its volume. At a
distance x from its centre, (for x < R), the electric field is directly proportional to ..........
(A) x
(B) x1
(C) x2
(D) x2
46. The electric flux for gaussian surface A that enclose the chrged particles in free space is
.............
(given q1 = 14nc, q2 = 78.85 nc, q3 = 56nc)
(A) 104 Nm2/C

3
2
4
2
(C) 6.2 10 Nm /C (D) 6.3 10 Nm /C

(B) 103 Nm2/C

17

47. A hollow cylinder has a charge q coulomb within it. If is the electric flux in units of voltmeter associated with the curved surface B, the flux linked with the plane surface A in units
of volt-meter will be .............

1 q
(A) 2
0

(C)

q
(B) 2
0
q

(D)
0

48. An infinitly long thin straight wire has uniform linear charge density of

1
c/m . Then, the
3

magnitude of the electric intiensity at a point 18 cm away is .......... NC1.

(A) 0.66 1011

(C) 0.33 1011

(B) 1.32 1011

(D) 3 1011

49. Two points are at distances a and b (a < b) from a long string of charge per unit length .
The potential difference between the points in proportional to .............
b2

ln
(B) a 2

b
(A) ln
a

(C)

ln
2 0
a

b
(D) 2 ln a

0

50. A long string with a charge of per unit length passes through an imaginary cube of edge
l. The maximum possible flux of the electric field through the cube will be ...........

(A)

l
3
0

l
(B)
0

(C)

l
2
0

6 l 2
(D)
0

51. Two Points P and Q are maintained at the Potentials of 10 v and 4 v, respectively. The
work done in moving 100 electrons from P to Q is ..............
(A) 2.24 1016 J

(B) 9.60 10 17 J

(C) 2.24 10 16 J

(D) 9.60 10 17 J

52. The electric Potential V at any Point o (x, y, z all in metres) in space is given by V = 4x2
volt. The electric field at the point (1m, 0.2m) in volt/metre is ......
(A) 8, along negative x - axis

(B) 8, along positives x - axis

(C) 16, along negative x - axis

(D) 16, along positives x - axis

53. Charges of +

10
10 9 C are placed at each of the four corners of a square of side 8cm. The
3

potential at the intersection of the diagonals is ....

(A) 150 2 Volt

(B) 900 2 Volt

(C) 1500 2 Volt

18

(D) 900 2 2 Volt

54. Three charges 2q, q, q are located at the vertices of an equilateral triangle. At the centre
of the triangle.
(A) The Field is Zero but Potential is non - zero
(B) The Field is non - Zero but Potential is zero
(C) Both field and Potential are Zero
(D) Both field and Potential are non- Zero
55. In the electric field of a point charge q, a
certain charge is carried from point A to B, C,
D and E. Then the work done ....

(A) Is least along the Path AB

(B) Is least along the Path AD

+q
B

(C) Is Zero along all the Path AB, AC, and

E
C

(D) Is least along AE

56. Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge
densities , and respectively. If VA, VB and VC denote the Potentials of the three
shells, then for c = a + b, we have
(A) VC = VB = VA

(B) Vc = VB VA

(C) Vc VB VA

(D) Vc VA VB

57. The electric Potential at a point P (x, y, z) is given by V = x2y xz3 + 4 The electric field

E at that point is ..........

xz 2
(A) i (2xy + z 3 ) + j x 2 + k3

(B) i 2xy + j (x 2 + y 2 ) + k (3xy y 2 )

(C) i z 3 + j xyz + k z 2

z2 x
(D) i (2xy z 3 ) + j xy 2 + k3

58. Three particles, each having a charge of 10c are placed at the corners of an equilateral
triangle of side 10 cm. The electrostatic potential energy of the system is

1
= 9 109 N.m 2 /c 2 .
Given
4 o

(A) 100 J

(B) 27 J

(C) Zero

(D) Infinite

59. Four equal charges Q are placed at the four corners of a square of each side is a. Work
done in removing a charge - Q from its centre to infinity is ...
(A) 0

2Q2
(B)
0 a

2Q 2
(C)
4 0 a

19

Q2
(D) 2 a
0

60. Two charged spheres of radii R1 and R2 having equal surface charge density. The ratio of
their potential is ...
R2
(A) R
1

R2
(B)
R1

R1
(C)
R2

R1

(D) R
2

61. Two equal charges q are placed at a distance of 2a and a third charge -2q is placed at the
midpoint. The potential energy of the system is ....
9q 2
(A)
8 0 a

q2
(B)
8 0 a

7q 2
(C)
8 0 a

6q 2
(D)
8 0 a

62. Two point charges 100c and 5c are placed at points A and B respectively with AB = 40
cm. The work done by external force in displacing the charge 5c from B to C where BC
= 30 cm, angle ABC =
(A) 9 J

9
2 2
and 4 9 10 Nm /c .
2
0

(B)

9
J
25

(C)

81
J
20

9
4

(D) J

63. The electric potential V is given as a function of distance x (metre) by V = (5x2 + 10x 9)
volt. Value of electric field at x = 1 is .....
(A) 20

v
m

(B) 6

v
m

(C) 11

v
m

(D) 23

v
m

64. A sphere of radius 1cm has potential of 8000 v, then energy density near its surface
will be ...
5
(A) 64 10

J
m3

(B) 2.83

J
m3

3
(C) 8 10

J
m3

(D) 32

J
m3

65. If a charged spherical conductor of radius 10cm has potential v at a point distant 5 cm
from its centre, then the potential at a point distant 15cm from the centre will be .....
3
2
V
(C) 3V
(D) V
2
3
Electric charges of +10c, 5c, 3c and 8c are placed at the corners of a square of side

(A)
66.

1
V
3

(B)

2m the potential at the centre of the square is ......

(A) 1.8 V

(B) 1.8 105V

(C) 1.8 106 V

(D) 1.8 10 4V

67. Two positive point charges of 12c and 8c are 10 cm apart each other. The work done in
bringing them 4cm closer is .....
(A) 5.8 J

(B) 13eV

(C) 5.8eV

20

(D) 13 J

68. The displacement of a charge Q in the electric field E = e1 i + e 2 j + e3 k is r = ai + bj .

The work done is .....

e12 + e 2 2

a + b

(A) Q e1 + e2 a 2 + b 2

(B) Q

(C) Q ae1 + be 2

(D) Q ae1 + be 2

69. If an electron moves from rest from a point at which potential is 50 volt to another point
at which potential is 70 volt, then its kinetic energy in the final state will be .....
(A) 1 N

(C) 3.2 10 10 J

(B) 3.2 10 18 J

(D) 1 dyne

70. Three charges Q, + q and + q are placed at the verticles

of a right-angled triangle as shown. The net electrostatic
energy of the configuration is zero if Q is equal to .....

(A) 2q

(B) 1 + 2
2q

(C) + q

(D) 2 + 2
+q
+q
a
71. Two electric charges 12c and 6c are placed 20cm apart in air. There will be a point P
on the line joining these charges and outside the region between them, at which the electric potential is zero. The distance of P from 6c charge is ........
(A) 0.20 m

(B) 0.10 m

(C) 0.25 m

72. In the rectangle, shown below, the two corners have

charges q1 = 5c and q 2 = +2.0c . The work done in
moving

charge

3c

from

to

q1

(B) 2.8 J

is

1
= 1010 Nm 2 /c 2 .
take
4 0

(A) 5.5 J

(D) 0.15 m

(C) 3.5 J

------ 15 cm ------q2

(D) 4.5 J

73. 4 Points charges each +q is placed on the circumference of a circle of diameter 2d in such
a way that they form a square. The potential at the centre is ......
(A) 0

(B)

4d
q

(C)

q
4d

(D)

4q
d

74. Three identical charges each of 2c are placed at the vertices of a triangle ABC as shown
in the figure. If AB + AC = 12 cm and AB . AC = 32cm2, the potential energy of the charge
at A is .....
(A) 1.53 J

(B) 5.31 J

(C) 1.35 J

21

(D) 3.15 J

75. A ball of mass 1 gm and charge 108 c moves from a point A, where the potential is 600 volt
to the point B where the potential is zero. Velocity of the ball of the point B is 20cm/s. The
velocity of the ball at the point A will be .....
(A) 16.8

m
s

(B) 22.8

cm
s

(C) 228

cm
s

(D) 168

m
s

76. Three charges Q, +q and +q are placed at the vertices of an

equilateral triangle of side l as shown in the figure. It the
net electrostatic energy of the system is zero, then Q is equal
(A) q

(B) +q

(C) Zero

(D)

q
2

+q

+q

77. Electric potential at any point is V = 5x + 3y + 15z , then the magnitude of the electric
field is ..... N/C.
(B) 4 2

(A) 3 2

(C) 7

(D) 5 2

78. A small conducting sphere of radius r is lying concentrically inside a bigger hollow conducting sphere of radius R. The bigger and smaller sphere are charged with Q and q (Q >
q) and are insulated from each other. The potential difference between the sphers will be
......
1

(A) 4 r R (B) 4 r R

0
0

(C) 4 R + r

(D) 4 R r

79. If 3 charges are placed at the vertices of equilateral triangle of charge q each. What is the
net potential energy, if the side of equilateral triangle is l cm.
1 3q 2
(A)
4 0 l

1 2q 2
(B)
4 0 l

1 q2
(C)
4 0 l

1 4q 2
(D)
4 0 l

80. If identical charges (q) are placed at each corner of a cube of side b, then electric potential energy of charge (+q) which is placed at centre of the cube will be .....
(A)

4q 2
3 0 b

8 2q 2
(B)
4 0 b

8 2q 2
(C)
0 b

4 2q 2
(D)
4 0 b

81. A simple pendulum of period T has a metal bob which is negatively charged. If it is
allowed to ascillate above a positively charged metal plate, its period will ........
(A) Remains equal to T

(B) Less than T

(C) Infinite

(D) Greater than T

22

82. A charged particale of mass m and charge q is released from rest in a uniform electric field
E. Neglecting the effect of gravity, the kinetic energy of the charged particale after t
second is ......
(A)

Eq 2 m
2t 2

(B)

E 2q 2 t 2
2m

(C)

2E 2 t 2
qm

(D)

Eqm
t

83. A thin spherical conducting shell of radius R has a charge q. Another charge Q is placed at
the centre of the shell. The electrostatic potential at a point p a distance

R
from the centre
2

of the shell is .....

(q + Q) 2

(A) 4 R
0

2Q

2q

2Q

(B) 4 R 4 R
0
0

2Q

(C) 4 R 4 R (D) 4 R
0
0
0

84. Two point charges q and +q are located at points (o, o, a) and (o, o, a) respectively. The
potential at a point (o, o, z) where z > a is ......
2qa
q
(A) 4 z 2 a 2 (B) 4 a
0
0

(C)

2qa

qa
4 0 z 2

(D) 4 z 2 a 2

85. Point charges q1 = 2c and q 2 = 1c are kept at points x = 0 and x = 6 respectively..

Electrical potential will be zero at points .....
(A) x = 2, x = 2

(B) x = 1, x = 5

(C) x = 4, x = 12

(D) x = 2, x = 9

86. Two thin wire rings each having a radius R are placed at a distance d apart with their axes
coinciding. The charges on the two rings are +q and q. The potential difference between
the centres of the two rings is ....
1

R

R 2 + d 2
1

Q
(C) 4
0

87. Tw o charges q 1 and q2 are placed 30cm apart, as shown

in the figure. A third charge q3 is moved along the arc of
a circle of radius 40 cm from C to D. The change in the
potential energy of the system is
(A) 8q2

q3
K , where k is .....
4 0

(B) 8q1

(C) 6q2

23

1

R

R 2 + d 2
1

QR

(D) 4 d 2
0

q3

C
40 cm

(A) 0

Q
(B) 2
0

q2 B
q1

30 cm

(D) 6q1

q3 = 3 10-6C

88. Figure shows a triangular array of three point

charges. The electric potencial v of these
source charges at the midpoint P of the base
1

0.3m

of the triangle is
9 109 Nm 2 /c 2
4

-6

(A) 55 KV
(C) 49 KV

q1 = 1 10 C

(B) 63 KV
(D) 45 KV.

| 0.2 m | | 0.2 m | q2 = -2 10-6C

R

89. Charges +q and q are placed at point A and B

respectively which are a distance 2L apart, C is the
midpoint between A and B. The work done in
moving a charge +Q along the semicircle CRD
is .......
A

qQ

(A) 2 L
0

qQ

qQ

(B) 6 L
0

(C) 6 L
0

qQ

(D) 4 L
0

90. N identical drops of mercury are charged simultaneously to 10 volt. when combined to
form one large drop, the potential is found to be 40 volt, the value of N is ......
(A)4

(B)6

(C) 8

(D) 10

91. Tw o paral l el pl ate ai r capaci tors have thei r pl ate areas 100 and 500 cm 2 respectively. If
they have the same charge and potential and the distance between the plates of the first
capacitor is 9.5 mm, what is the distance between the plates of the second capacitor ?
(A) 0.25 cm

(B) 0.50 cm

(C) 0.75 cm

(D) 1 cm

92. The effective capacitances of two capacitors are 3F and 16F , when they are connected
in series and parallel respectively. The capacitance of each capacitor is
(A) 2F, 14F

(B) 4F, 12F

(C) 6F, 8F

(D) 10F, 6F

93. An electrical technician requires a capacitance of 2F in a circuit across a potential difference of 1KV. A large number of 1F capacitors are available to him, each of which can
withstand a potential difference of not than 400 V. suggest a possible arrangement that
requires a minimum number of capacitors.
(A) 2 rows with 2 capacitors

(B) 4 rows with 2 capacitors

(C) 3 rows with 4 capacitors

(D) 6 rows with 3 capacitors

94. Two spherical conductors of radii r1 and r2 are at potentials V1 and V2 respectively, then
what will be the common potential when the conductors are brought in contant ?
(A)

r1 v1 + r2 v 2
r1 + r2

(B)

r1 v1 + r2 v 2
r1 r2

(C)

24

r1 v1 r2 v 2
r1 + r2

(D) None of these

95. A 5F capacitor is charged by a 220 V supply. It is then disconnected from the supply and is
connected to another uncharged 2.5F capacitor. How much electrostatic energy of the
first capacitor is lost in the form of heat and electromagnetic radiation ?
(A) 0.02 J

(B) 0.121 J

(C) 0.04 J

96. Find the equivalent capacitance of the

system across the terminals A and B. All
the capacitors have equal capacitances.
(A) 2C
(C) 3C

(D) 0.081 J
C

A
C

(B) 4C
(D) 5C

4
times its original value if a dielectric
3

97. Capacitance of a parallel plate capacitor becomes

slab of thickness t = d/2 is inserted between the plates (d is the separation between the
plates). The dielectric constant of the slab is
(A) 8

(B) 4

(C) 6

(D) 2

98. The plates of a parallel capacitor are charged up to 100 V. If 2 mm thick plate is inserted
between the plates, then to maintain the same potential difference, the distance between
the capacitor plates is increased by 1.6mm the dielectric constant of the plate is
(A) 5

(B) 4

(C) 1.25

(D) 2.5

99. A parallel plate air capacitor has a capacitance 18F . If the distance between the plates is
tripled and a dielectric medium is introduced, the capacitance becomes 72F . The dielectric constant of the medium is
(A) 4

(B) 12

(C) 9

(D) 2

100. Taking earth to be a metallic spheres, its capacity will approximately be

(A) 6.4 106 F

(B) 700 F

(C) 711 F

(D) 700 pF

101. A parallel plate capacitor has the space between its plates filled by two slabs of thickness
d
each and dialectric constant K1 and K2. If d is the plate separation of the capacitor, then
2

capacity of the capacitor is ...............

(A)

2d 0 K1 + K 2

A K1K 2

(B)

2A 0
d

(C)

2A 0 K1 + K 2

d K1K 2

(D)

2A 0
K1 + K 2
d

25

K1K 2

K1 + K 2

1F

102. For the circuit shown in figure the charge on

4F capacitor is
(A) 20c

(B) 40c

(C) 30c

(D) 54c

4F

3F

5F
+

10V

103. The capacitors of capacitance 4F, 6F and 12F are connected first in series and then in
parallel. What is the ratio of equivalent capacitance in the two cases ?
(A) 2 : 3

(B) 11 : 1

(C) 1 : 11

(D) 1 : 3

104. Large number of capactors of rating 10F/200V V are available. The minimum number of
capacitors required to design a 10F/700V capacitor is
(A) 16

(B) 8

(C) 4

(D)7

105. A variable condenser is permanently connected to a 100 V battery. If capacitor is changed

from 2F to 10F . then energy changes is equal to
(A) 2 10 2 J

(B) 2.5 10 2 J

(C) 6.5 10 2 J

(D) 4 10 2 J

106. Two positive point charges of 12c and 8c are placed 10 cm apart in air. The work done
to bring them 4 cm closer is
(A) Zero

(B) 4.8 J

(C) 3.5 J

(D) 5.8 J

107. 1000 similar electrified rain drops merge together into one drop so that their total charge
remains unchanged. How is the electric energy affected ?
(A) 100 times

(B) 200 times

(C) 400 times

(D) 102 times

108. There are 10 condensers each of capacity 5F . The ratio between maximum and minimum capacities obtained from these condensers will be
(A) 40 : 1

(B) 25 : 5

(C) 60 : 3

(D) 100 : 1

109. A parallel plate capacitor is made by stocking n equally spaced plates connected alternately. If the capacitance between any two plates is x, then the total capacitance is,
(A) nx

(B) nx2

(C)

110. For the circuit shown figure, which of

the following statements is true ?

n
x

(D) (n 1)x

v1=30v

S3
v2=20v

C1=2pf

C2=3pf

S1

(A) With S1closed V1 = 15V, V2 = 20V

(B) With S3 closedV1 = V2 = 20V
(C) With S1 and S3 closed V1 = V2 = 0
(D) With S1and S3closed V1 = 30V, V2 = 20V
26

S2

111. Two identical metal plates are given positive charges Q1 and Q2 (< Q1) respectively. If they
are now brought close to gether to form a parallel plate capacitor with capacitance C, the
potential difference between them is
(A)

(Q1 Q 2 )
2c

(B)

(Q1 Q 2 )
c

(C)

(Q1 Q 2 )
2c

(Q1 Q 2 )
c

(D)

C3

112. In the circuit arrangement shown in figure, the value

C1

C4

of C1 = C2 = C3 = 30 pF and C4 = 120 pF. If the

combination of capacitors is charged with 140V

C2

DC supply, the potencial differences across the four

capacitors will be respectively

140V

(A) 80, 40, 40 and 20V

(B) 20, 40, 40 and 80V

(C) 35, 35, 35 and 35V

(D) 80, 20, 20 and 20V

113. In the arrangement of capacitors shown

B

in figure, each capacitor is of 9F , then

the equivalent capacitance between the
points A and B is
(A) 18F

C1

A
C2

C3

(B) 9F
C4

(C) 15F

(D) 4.5F

114. The electric potencial V at any point x, y, z (all in metre) in space is given by V = 4x2 volt.
The electric field at the point (1m, 0, 2m) in Vm1 is
(A) + 8i

(B) 8i

(C) 16i

(D) + 16i

115. Two air capacitors A = 1 F , B = 4 F are connected in series with 35 V source. When a
medium of dielectric constant K = 3 is introduced between the plates of A, change on the
capacitor changes by
(A) 16 c

(B) 32 c

(C) 28 c

(D) 60 c

116. A parallel plate capacitor with air between the plates has a capacitance of 9 pF. The
separation between its plates is d. The space between the plates is now filled with two
dielectrics. One of the dielectric constant K1 = 3 and thickness d/3 while the other one has
dielectric constant K2 = 6 and thickness 2d/3. Capacitance of the capacitor is now
(A) 1.8 pF

(B) 20.25 pF

(C) 40.5 pF
27

(D) 45 pF

117. A thin spherical shell of radius R has change Q spread uniformly over its surface. Which of
the following graphs, figure most closely represents the electric field E (r) produced by the
shell in the range 0 r < , where r is the distance from the centre of the shell.

(A)

(B)
r

(C)

(D)
R

118. A parallel plate condenser with dielectric of constant K between the plates has a capacity C
and is charged to potential V volt. The dielectric slab is slowly removed from between the
plates and reinserted. The network done by the system in this process is
(A) Zero

(B)

1
(K 1)cv 2
2

2
(D) cv

(C) (K 1)cv2

(K 1)
K

119. Charges are placed on the vertices of a square as shown. Let E be the electric field and V
the potential at the centre. If the charges on A and B are interchanged with those on D and
C respectively then
q
q

(A) E Change V remains unchanged

(B) E remains unchanged , V changes

(C) Both E and V change

(D) E and V remain unchanged

-q

-q

120. The potencial at a point x (measured in m ) due to some charges situated on the x-axis is
20

given by V(x) = x 2 4 Volt . The electric field at x = 5m is given by

(A) 53 Vm1 and in positive x - direction
1
(B) 10
9 Vm and in positive x - direction
1
(C) 10
9 Vm and in positive x - direction

(D) 53 Vm1 and in positive x - direction

28

121. A battery is used to charge a parallel plate capacitor till the potential difference between the
plates becomes equal to the electromotive force of the battery. The ratio of the energy
stored in the capacitor and work done by the battery will be
(A)

1
2

(B)

2
1

(C) 1

(D)

1
4

122. Two spherical conductors A and B of radii 1mm and 2mm are separated by a distance of
5mm and are uniformly charged. If the spheres are connected by a conducting wire then
in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of
sphere of A and B is
(A) 1 : 2

(B) 2 : 1

(C) 4 : 1
1
2
3
4
5

123. The following arrangement consists of five

identical metal plates marked 1, 2, 3, 4 and 5
parallel to each other. Area of each plate is A
and separation between the successive plates
is d. The capacitance between P and Q is
(A) 5

A 0
d

(B)

7 A 0
3 d

(D) 1 : 4

(C)

5 A 0
3 d

p
q

(D)

4 A 0
3 d

124. A parrallel plate capacitor of capacitance 5F and plate separation 6 cm is connected to a

1 V battery and charged. A dielectric of dielectric constant 4 and thickness 4 cm is introduced between the plates of the capacitor. The additional charge that flows into the capacitor from the battery is
(A) 2c
(B) 5c
(C) 3c
(D) 10c
125. For circuit the equivalent capacitance between
points P and Q is
(A) 6 C
(B) 4 C
3
(C) C
2

6
(D) C
11

126. Four identical capacitors are connected in series with a 10 V battery as shown in the
figure. Potentials at A and B are
(A) 10 V, 0 V
(B) 5 V, 5V
(C) 7.5 V, 2.5 V
(D) 7.5 V, 2.5 V
127. 64 identical drops of mercury are charged simultaneously to the same potential of 10 volt.
Assuming the drops to be spherical, if all the charged drops are made to combine to form
one large drop, then its potential will be
(A) 100 V
(B) 320 V
(C) 640 V
(D) 160 V
128. Two metal plate form a parallel plate capacitor. The distance between the plates is d. A
metal sheet of thickness d/2 and of the same area is introduced between the plates. What
is the ratio of the capacitance in the two cases ?
(A) 4 : 1
(B) 3 : 1
(C) 2 : 1
(D) 5 : 1
29

129. The circular plates A and B of a parrallel plate air capacitor have a diameter of 0.1 m and are
2 10 3 m apart. The plates C and D of a similar capacitor have a diameter of 0.12 m and
are 3 10 3 m apart. Plate A is earthed. Plates B and D are connected together. Plate C is
connected to the positive pole of a 120 V battery whose negative is earthed, The energy
stored in the system is
(A) 0.1224J

(B) 0.2224J

(C) 0.4224J

130. Two parallel conducting plates of area A = 2.5m2 each

are placed 6 mm apart and are both earthed. A third
plate, identical with the first two, is placed at a distance of 2 mm from one of the earthed plates and is
given a charged of 1 C. The potencial of the central
plate is
(A) 6 107 V

(D) 0.3224J
1

2mm

4mm

(D) 4 107 V

(C) 2 107 V

(B) 3 107 V

131. What is the energy stored in the capacitor between terminals A

and B of the network shown in the figure ? (Capacitance of each
capacitor C = 1F )
(A)Zero

(B) 50 J

(C) 12.5 J

(D) 25 J

10v
C

C
C

C
C

132. Two identical capacitors 1 and 2 are connected in series to a battery as shown in figure.
Capacitor 2 contains a dielectric slab of constant K. Q1 and Q2 are the charges stored in 1
and 2. Now, the dielectric slab is removed and the corresponding charges are Q1 and Q2.
Then
2

(A)

1
1

Q
K +1
=
Q1
K

Q21 K + 1
=
(C)
Q2
2K

(B)

1
1
1
1

Q
K
=
Q
2

Q21 K + 1
=
(D)
Q2
K

+ E

133. A parallel plate capacitor has plate of area A and separation d. It is charged to a potential
difference Vo. The charging battery is disconnected and the plates are pulled apart to three
times the initial separation. The work required to separate the plates is
2
(A) A 0 V0

(B)

A 0 V0 2
2d

(C)

A 0 V0 2
3d

(D)

A 0 V0 2
4d

134. Two identical capacitors have the same capacitance C. one of them is charged to a potential
V1 and the other to V2. The negative ends of the capacitors are connected together. When
the positive ends are also connected, the decrease in energy of the combined system is
(A)

1
c v12 v 2 2
4

(B)

1
c v12 + v 2 2
4

(C)
30

1
2
c v1 v 2
4

(D)

1
2
c v1 + v 2
4

135. A parallel plate air capacitor has a capacitance C. When it is half filled with a dielectric of
dielectric constant 5, the percentage increase in the capacitance will be
(A) 200 %

(B) 33.3 %

(C) 400 %

(D) 66.6 %

136. A network of six identical capacitors, each of value C is made as shown in figure. Equivalent capacitance between points A and B is
C
(A)
4

(C)

4C
3

3C
(B)
4

(D) 3 C

137. The capacities of three capacitors are in the ratio 1 : 2 : 3. Their equivalent capacity when
connected in parallel is

60
F more then that when they are connected in series. The
11

individual capacitors are of capacities in F

(A) 4, 6, 7

(B) 1, 2, 3

(C) 1, 3, 6

(D) 2, 3, 4

138. In the given arrangement of capacitors equivalent

capacitance between points M and N is

(A)

5
c
4

4
(C) c
3

(B)

C
C

4
c
5

C
M

N
C
C

3
(D) c
4

139. An electric circuit requires a total capacitance of 2F across a potencial of 1000 V. Large
number of 1F capacitances are available each of which would breakdown if the potential is more then 350 V. How many capacitances are required to make the circuit ?
(A) 24

(B) 12

(C) 20

(D) 18

140. Read the assertion and reason carefully to mark the correct option out of the options given
below :
(a)

If both assertion and reason are true and the reason is the correct explanation of the
assertion.

(b)

If both assertion and reason are true but reason is not the correct explanation of the
assertion.

(c)

If assertion is true but reason is false.

(d)

If the assertion and reason both are false.

(e)

If assertion is false but reason is true.

31

1.

Assertion : The coulomb force is the dominating force in the universe.

Reason

2.

: The coulomb force is weaker than the gravitational force.

Assertion : If three capacitors of capacitance C1 < C2 < C3 are connected in parallel then
their equivalent capacitance Cp > C3
1

Reason
3.

: The surface density of charge on the plate remains constant or unchanged.

: Electric field at a point superimpose to give one resultant electric field.

Assertion : If a proton and an electron are placed in the same uniform electric field.
They experience different acceleration.
Reason

9.

: Capacity of the capacitor does not depend upon the nature of the material.

Assertion : Electric lines of force cross each other.

Reason

8.

: Because electrons have negative charge

Assertion : A parallel plate capacitor is connected across battery through a key. A dielectric slab of constant K is introduced between the plates. The energy which
is stored becomes K times.
Reason

7.

: In a hollow shherical shield, the electric field inside it is zero at every point.

Assertion : If the distance between parallel plates of a capacitor is halved and dielectric
constant is made three times, then the capacitance becomes 6 times.
Reason

6.

Assertion : Electrons move away from a low potential to high potential region.
Reason

5.

Assertion : A metalic shield in form of a hollow shell may be built to block an electric
field.
Reason

4.

: C C C C
p
1
2
3

: Electric force on a test charge is independent of its mass.

Assertion : Dielectric breakdown occrus under the influence of an intense light beam.
Reason

: Electromagnetic radiations exert pressure.

10. Assertion : When charges are shared between any two bodies, no charge is really lost,
but some loss of energy does occur.
Reason

: Some energy disappeares in the form of heat, sparking etc.

32

KEY NOTES
1(A)

17(C)

33(D)

49(D)

65(D)

81(B)

97(D)

113(C)

129(A)

2(B)

18(A)

34(C)

50(A)

66(B)

82(B)

98(A)

114(B)

130(A)

3(D)

19(D)

35(A)

51(A)

67(D)

83(C)

99(B)

115(C)

131(C)

4(C)

20(B)

36(A)

52(A)

68(C)

84(D)

100(B)

116(C)

132(C)

5(B)

21(A)

37(C)

53(C)

69(B)

85(C)

101(B)

117(B)

133(A)

6(C)

22(B)

38(B)

54(B)

70(D)

86(B)

102(B)

118(A)

134(C)

7(D)

23(D)

39(D)

55(C)

71(A)

87(A)

103(C)

119(A)

135(D)

8(A)

24(C)

40(C)

56(D)

72(B)

88(D)

104(A)

120(B)

136(C)

9(B)

25(A)

41(B)

57(A)

73(D)

89(B)

105(D)

121(A)

137(B)

10(C)

26(D)

42(A)

58(B)

74(C)

90(C)

106(D)

122(B)

138(A)

11(C)

27(B)

43(D)

59(B)

75(B)

91(A)

107(A)

123(C)

139(D)

12(D)

28(C)

44(D)

60(D)

76(D)

92(C)

108(D)

124(B)

13(B)

29(B)

45(A)

61(C)

77(C)

93(D)

109(D)

125(D)

14(A)

30(D)

46(B)

62(D)

78(B)

94(A)

110(D)

126(C)

15(C)

31(A)

47(A)

63(A)

79(A)

95(C)

111(D)

127(D)

16(B)

32(C)

48(C)

64(B)

80(A)

96(A)

112(A)

128(C)

140 :

33

1(D)

2(C)

3(A)

4(A)

5(B)

6(C)

7(E)

8(B)

9(B)

10(B)

(9)

2
a sin 60
Distance OA =
3

2
3
. a.
3
2

= a

O
q
F2
A

F
F1

The force on the Charge at A due to those at B and C have magnitude F = k

The Resultant of theses force is
F1 2 F cos 30
F1 = 2

kQ 2 3

a2 2
3KQ 2
q2

F2

3KQq

The force on the charge Q at A due to Charge q at o is, F2 =

a2
Now for equilibrium of the Charges, F1 F2 Now Calculate q.
(10) Let q and 2q be the Charges and r the distance between them.
Then 2 103
20
So,
=
5

2 kq 2
2 kq 2
4

5
10
and
( r 0.1) 2
r2

br 0.1g

r2

r 0.1
r 0.1 m .
r2

2=

Now, Substitating the Value of r So obtained

2 10
q2

2q 2
= 9 10
(0.1)2
9

107
10 14
q

3
9

Now find out q and 2q.

kq1q2
along axis
b2
kq q
Force on -q1 due to q3 is F13 12 3 at negative direction of yaxis.
a
x component of force on -q, is Fx = F12 F13 sin

(11) Force on -q1 due to q2 is F12 =

= Fq1

LM q
Nb

2
2

i.e = Fx

q3
sin
a2

OP
Q

q2 q3
sin
b2 a 2

35

Q2
a2

(12) Force exerted by charges -q at A and B on

Charge Q are F1 amd F2 which are equal and
have a magnitude F KQq
2
r

The resultant of these equal forces equally

inclined with the X-axis is along the -X direction to wards the origin.
so, F '2 F 2 F 2 2F 2 cos = 2 F 2 (1 cos )
since F

1 1
1
, F is also Proportional to 2 ,
2
r
r

Hence charge Q will move towards the origin and because of its inertia it will
overshoot the origin o. Thus charge Q will oscillate about o but its motion is not
simple harmonic.
a
2

(13) OA OC r
F1 F2

KQ 2
a2

F3

KQ 2
2a 2

F4

2KQq
a2

The resultant of F1 & F2 is F 2 F1 3

KQ 2
a2

F and F3 act along AP So, F 1 F F3 find.

Now for equilibrium F 1 F4 .
From this find out q.
(14) Net attraction force on q due to Q = repulsion force due to q
2 FA F 1 from find out q.
(15)

F1

kq0 q
kq q
F2 2 0 2
2
2
a y a y

F1 F2

By symmetry, the x components of force will

cancel each other while along y axis will add up
The resultant force on + q is
F 2 F1 cos

2kqq0
y
.
2
2
a y
a2 y2

Now, Force on charge q0 will be maximum, when

32 y (2y)
1
2kq0 q 2

3
2
2 5
(a y 2 ) 2 (a y ) 2
1
3y2
Now find out y.

0
3
2
2 5
2
2 2
a

y
a y
2

h c

36

dF
=0
dy

(16) T cos = mg and T sin = F

F
mg

tan

x
q2
2
2 x

q 2 x3

q2 x

dq 3 1 2 dx
x
dt 2
dt

V x

12

dq

dt Constant

(17) FAB

1 92

2 (along BA )
4 4 R

FAC

1 92
2 (along CA )
4 4 R

FAB FAC F

F 1 F 2 F 2 2 F 2 cos 60

Now find out F 1 .

kq 2
kq 2

(18) Force on q is F
( a x ) 2 (a x ) 2

LM
N

2
ma = F kq (a x ) 2 (a x ) 2
2

q x
ma 3

OP
Q

Now compare with a = 2x and find out frequenly.

(19) Suppose the balls having charges Q1 and Q2 respectively..
Initially,....... F =

kQ1Q2
r2

It is given that F 1 4. 5 F

K Q1 Q2
r2

bQ Q g
1

= 4.5

Q1 Q2
r2

= 4.5 Q1Q2 Now solve it, and find

37

Q1

Q2 .

(20) Consider a small element of the rod of length dx, at a distance x from the point
charge q.
The force between q and charge element will be,
kqdQ
Q
But dQ = dx ,
2
x
L
kqQ dx
dF
L x2

dF =

r L

kqQ
dF
L

r +L

1
dx
x2

Now solve it.

(21)

k . q1
kq
22 then find x
2
( x 0. 08)
x

(22) E p
EQ

kq p
( PQ )

NC1

NC1

kqQ
(QR)

in PQR, cos
2

QR 1
= 60
PR 2

E p EQ 2E p EQ cos 600 and

tan

Q sin
p EQ cos

find out E and .

(23) From the fig, Net force F acting
along the inclined plance ...(i)
F = mg sin - qE cos - f
ma = mg sin - q E cos
So, ma = mg sin qE cos
- (mg cos + q E sin )
from this, find out a.
Now, d vot 1 at 2 use this equation and calculate t.
2

(24) From the fig Tsin qE

Tcos mg

E
o

Tcos

q
mg

Now calculate .
38

(25) Let be the charge Per unit length so, charge on Portion PQ ...
k rd
r

= Intensity at o is dE =
dE

k d
r

Total intensity E =

dE

and

total cahrge on the rod, Q = r

Now find out E.
(26) Here E =

and t l / vo

Along y axis vo = 0,

a=

F
eE / M
M

1
2

So, d vot at 2
Now Put the values
(27) qE l sin
qEl

The moment of inertia of the rod is

FlI
I mG J
H 2K

F lI
mG J
H 2K

Now, = I =

ml 2
2

Calculate and compale with 2 then

qE
ml

T
So, T = 2 and rod will become Paralled to E in a time t = Now calculate.
4

(28) After Connection V1 V2 ,

KQ1 KQ 2
Q
r

1 = 2
r1
r2
Q 2 r1

KQ1
E1
r12
Q1 r22
=
=

The ratio of electric fields

E 2 KQ 2
r12 Q 2
r22

Now Calculate

39

(29) Consider a Spherical Shell of thickness dx and radius x.

The area of this Spherical shell = 4 x 2 dx

LM Qx OP4 x dx 4Q x dx
R
N R Q
2

The Charge enclosed in a Sphere of

r1

r
4Q
4Q x 4
Q
radius r1 is = 4 x 3dx = 4 = 4 r14
R 0
R 4 0 R

LM
MM
N

Q 4
r
4 1
1
R
.
=
2
4
r1

OP
PP
Q

Now find out E.

(30) E1 =

Kq
Kq1
and E2 2 2
2
b
a

Now, tan =

E2 q2 a2

E1 q1 b 2

(31) Net acceleration

So, T

Now, Put the values.

g1 g

gE
m

l
Now Put the Value of g ' .
g'

(32) Net electric field due to both charges

So. electric field of O is E

q
will get cancelled.
3

q2
= 6 R 2

R2

(33) In balance condition

QE mg Q

V 4 3
r g
d 3

r3
Now find out Q2
V

(34) Use equation, E E 2 E B 2 2 E A cos 60

1
,tan tan 3 tan 1 3
2
3
2

1
So, tan 3 2
3

(35)

40

(36)

1
1 qE x
d at 2

2
2 m v

qE
V0 x
2md
2

Now find out vo.

(37) Time of flight is t F

Where ax

2voy
g

1
2

Now range R Vox tF ax t 2 F

qE
m

Now, Calculate range.

(38) P e ro Calculate P..
tan
, Shown in fig 90
(39) As tan

tan( 90 )

tan
1
tan

tan
2
2
1
tan ( 2) 52 to 53
(40) PE sin = q(2q)E sin
cot

tan
2

tan 2 2

Now find out q.

(2a ) E sin
(41) Theory related quesition.
(42) As the drop is stationary, weight of drop = froce due to electric field.
q

4
r 3 g = neE
3

So, r 3

neE
now find out r..
4 g

(43) Theory related question.

(44) =

Q enclosed
Q enclosed f 0 (8 103 4 103 ) 0
0

Now find Q.
(45) Applysing gauss law
E .4 x 2

q v 4 3
x = E x

(46) Applying gauss law

(47) total = A B C
So, 2

q
0

q
Assume b = and A = C = 1

1
2

41

(48)

q
E . da
E

q
2 rl

(49) E

vb

va

E.2 rl

dv
dr

dv

E
dv

q
0

Now find out E.

0 r

0 r

dv

2 r
dr

1
dr
r

Now calculate.
(50) maximum length of string =
maximan enclosed charge =

3l
3 l

(51) (A) W = 100e (-4-10) = -1400ev

= -1400(-1.6 10-19) J = 2.24 10-16 J
(52) (A) The electric Potential V ( x , y , z ) 4 x 2 Volt
dv
dv
dv
Now E i j k
dy
dz
dx
dv
dv
dv
0
= 8x , dy 0 and
dx
dz

Hence E = 8xi , So at Point (1m,0,2m)

E = 8i Volt/metre or 8 along negative x-axis

Now

(53) (c) Potential at the centre o, V 4 1

q
4

Where Q = 10 3 109 C and a = 8cm = 8 10 2 m

9
So = 4 9 10

10
109
3

8 102
= 1500 2 Volt
2

(54) Obviously, from charge configuration, at the

centre electric field is non - zero. Potential
at the centre due to 2q charge V2q q and
r

Potential due to q Charge V q q

(r = distance of centre Point)

Total Potential V V2q V q V q = 0

42

(55) ABCDE is an equipotential surface, on equipotential surface no work is done in

shifing a chrge from one place to another.

(56) VA (a b c )

IJ
K

FG
H

a2
b c
b

VB

2
2
VC = a c b c C
on Putting C = a +b VA = VC VB

dv
2 xy z 3
dx
dv
Ey
x2
dy

(57) E x

Ez

dv
3xz 2
dz

E E xi E y j C z k xy z 3 i x 2 j 3xz 2 k

(58) (B) For Pair of Charge

LM
MN

OP
PQ

LM
MN

1
10 10 6 10 10 6
10 106 10 106

U= 4
+
10
10
100
100

OP
PQ +

LM10 10 10 10
MN 10100
6

OP
PQ

3 9 109 100 102 100

=
= 27 J
10

(59) (B) Potential at Centre o of the square Vo = 4

4

a
2

Work done in shifting (-Q) Charge from Centre to infinity

W Q V V0 QV0

Q 2
Q 2

a
4 a

(60) (D) Let Q1 , and Q2 are the Charges on Sphere of radii R1 and R2 respectively
ch arg e
Area
According to given Problem, 1 2

Surface Charge density

Q

1
2
= 4 R 4 R
2
2

2
Q1
R1
Q = R 2 .....(1)
2
2

43

In Case of a charged sphere, vs = 4

R

1 Q1
1 Q2
V1 = 4 R , V2 = 4 R

FRI
= G J
HR K

V1 Q1 R2
V R Q
2
1
2

Rz

1
= Q R
2
1

R2 R1

.....(using (i) )
R1 R2

7q 2
1
( q)( 2q )
1 ( 2q)( q)
1 ( q )( q)

(61) Usystem =
=
8 o a
4
q
4
a
4 2a

(62) Work done indisplacing charge of 5lic from B to C is

W 5 109 (Vc Vb ) where
VB

9 109 100 106 9

106 v
0. 4
4

VC

9 109 100 106 9

106 v
0.5
5

So W 5 106
(63)

FG 9 10
H5

IJ
K

9
9
106
J
4
4

dv d

5x 2 10 x 9 10x 10

dx
dx

E (x ) 10 20

v
m

FG IJ
HK

v
(64) Energy density ue = 1 2 E 2 1 2 8.86 10 12
r

= 2.83 J / m3

(65) Potenti al i nsi de the Sphere w i l l be sam e as that on i ts Surf ace i .e. v = V surface
=

q
volt
10

Vout =

q
volt
15

vout 2

v
3

2
Vout V
3

(66) Length of each side of square is

2m
2
1m
2

so distance of its centre from each cornet is

Potential at the centre
V 9 109

LM10 10
N 1

5 106 3 106 8 106

1
1
1

V 1.8 105 V
44

OP
Q

LM 1 1 OP
Nr r Q
L 1
8 10 M
N 4 10

(67) W Uf U 1 9 109 Q1Q2

6
9
= W 9 10 12 10

= 12. 96 10 J 13 J

(68) By using W = Q E . r

1
10 10 2

OP
Q

W Q e1i e2 j e3 k . ai bj Q e1a e2b

6
18
(69) K.E. = q0 (VA VB ) 1.6 (70 50 ) 10 J

2
(70) Net electrostatic energy U KQq Kq KQq 0

a 2

Kq
Q
Qq

a
2

Now find out Q.

(71) Point P will lie near the Charge which is smaller in magnitude i.e. -6lic Hence
Potential at P.
V

1 (12 6 )
(6 6 )

x
4 (0.2 x)

x 0. 2m
(72) Calculate as MCQ 67.
(73) Calculate as MCQ 66.
(74) (C) AB+AC = 12 cm
= AB . AC = 32 cm2

.......(i)

= AB AC ( AB AC ) 2 4 AB . AC
= AB AC 4
From equation (i) and (ii)
AB = 8 cm; AC = 4cm
Potential energy at Point A
VA

1
q1 q2

AB AC

V A 1. 35 J

2
2
(75) Use the equation 1 2 m V1 V2 = QV

45

(76) Potential energy of the system

kQq kq 2 kqQ

0
l
l
l

KQ
(Q q Q ) 0
l

(77)

Ex

q
2

dv
(5) also find E an E
y
z
dx

Enet =

E x E y Ez

(5) 2 ( 3) 2 15

(78) Van - d - glaph generater principal

(79) U

Unet

LM
N

1 Q1Q2 Q2 Q3 Q1Q3

r1
r2
r3
4

OP
Q

1 q2
3

.
=
40 l

(80) Length of the diagonal of a cube having each side b is 3 b. So distance of centre
3b
.
2

of cube from each vertex is

Hence Potential energy of the given system of charge is

1 ( q)(q)

=
U = 8 4
3b
0
2

4q 2
3 b

(81) When a negatively charged Pendylum oscillates overa Positively charged Plate
then effective Value of 9 increases so, according to T 2 decreases
g

(82) When charge q is released in uniform electric field E then its acceleration
qE

a = m (is constant) so its motion will be uniformly accelerated motion and itss
Velocity after time is given by
2

V at

qE
1 qq
q 2 E 2t 2
t = K = 1 mv2

2
m
2 m
2m

(83) Electric Potential at P

V

KQ
R
2

Kq
Q
q

R 4 R 4 R

46

(84) Potential at P due to (+q) charge

V1

q
.
0 ( z a )

Potential at P due to (-q) Charge

1
q
.
4 ( z a)

= V2

Total Potential at P due (AB) electric dipole V V1 V2

Now calculate
(85) (C) Potential will be zero at two Points .....

LM
MN

1 106
1 2 10 6
At internal Point(M) = 4 ( 6 l )
l

h OP 0
PQ

l2

So distance of M from origin; x 6 2 4 At exteriot Point (N)

1 2 6 (1 6 )

l'
4 (6 l )
l'

So distance of N from origin x 6 6 12

(86) Potential at the centre of rings are
VO 1

k .q
k (q )

,
R
R2 d 2

VO 2

k ( q)
kq

R
R2 d 2

1
1
VO 1 VO 2 2kq
R2 d 2
R

q 1
1

R2 d 2
2 R

(87) (A) Change in Potential energy (u) = uf - ud

Now calculate
(88) Theory base Question
(89) Potential at C, VC = 0
Potential difference VD -VC =

2 kq
3 L

W Q (VD VC ) put the values

(90) V N

V 40 N

10

N 3 4 N 2 64 N 8
(91) C1 C2
A1
A
A
2 d 2 2 d1 Now find d .
1
A1
d1
d2

47

(92) Here Cs 3l1 F and C p 16 l1 F

So, C1 C2 16 11

Now in Parallel connection C p C1 C2

CC

CC

1 2
1 2
in series connection C5 C C So, = C C .....(2)
1
2
1
2

g b

or C1C2 Now, C1 C2 2 = C1 C2 2 4C , C2
C1 C2 8 ........(3)
Adding the question (1) and (3) we have
C1 C2 + C1 C2 16+8

gb

or

a F & C2 C1 F

(93) Suppose that the techinician makes a combination use of N Capacitors and
connects them in m rows, each row having m Capacitors Then N=mn
Capacitance of each capacitor = 1 l1 F required Capacitance of the combination
C = 2 l1 F
Voltage rating of each < apalitor = 400V
required Voltage rating of the combination = 103 V
When capacitars are connected in series P.d. a cross their Plates get added. for
n capacitors
Voltage ...to 400 nv
400n 103

103
2.5
400

or n 3
1

1 1 1

The total Capucitae C 1 1 1 3

1

C'

1
3

The total Capacitanae of m rous C mc ' OR m

(94) Common Potential V

V

C

C '

C1V1 C2V2 4 r1v1 4 r2 v2

C1 C2
4 r1 4 r2

r1v1 r2 v2
r1 r2

1
2

2
(95) U 1 C1V1 0.121 J

Total charge on the two Capacitors q C1V1 C2V2 11 104 C

C C1V2 5l1 F 2. 5l1 F 7. 5l1 F 7. 5 106 F

9 440

V
C
3
1
U 2 CV 2 0. 081 J Now, energy lost = U 1 U 2 find it.
2

48

(96) Apply wheatstone bridge law.

A
4
A
1
with dielectlic slab C
Now C = C
(d t t / k )
3
d

(97) Cair

Fd t t I
H kK

4 A
3 d

4t

4(q / 2)

= K = 4t d 4(d / 2 d ) = 2
(98) As P.d. remains the same, Capacity must remain the same,
1

x = t 1
k

x = 1.5 mm

t= 2mm

Now find out k.

A
k A
72
18 C
Now, find out K.
3 d
d
R
(100) C = 4 R . Put the Values of R&K.
k

(99) Co

(101) C1

k1 0 A 2k1 0 A

d
d
2
1

2 k2 d
2

Now, C C C
3
1
2
(102) Apply lawa of series & Parallel conection of Capacitor
C2

(103) C C C C
5
1
2
3
Cs
C p C1 C2 C3 Now fiud out C
p

(104) Number of Capacitors to be connected in series

V

voltage rat int g required 700

3. 5
voltage rat int g required 200

i . e 4.
Ceq

10
2.5r1 F
4
Capacityrequired

10

4
Number of rows required = Capacityof each row
2.5
Total number of Capacitor 4 4 = 16
1
2

1
2

2
2
(105) U1 C1V & U 2 C2V U U 1 U 2

49

(106) Work done = U 2 U 1

q1q2
4

1 1
r r Now Calculate.
2 1
4

3
2
(107) Volume of big drop = 1000 volume of small drop R 1000 l
3
3
Now find out initial energy

1000q
q2
U1 1000
then final energy U 2
2C
2C1

U2

then U
1

R = 10r so, C1 10C

(108) minimum capacity is Cs (Series Connection) & maximum Capaciy is C P (Parallel
Cp

Connection) Now C Calculate

s
(109) Theory base question
(110) With S1 & S3 Closed , the Capacitors C1 & C2 are in series arrangenent. So
C
3
V11
1
1
2 &V2 V2 V1 V2 30 20 50V Now simplify..
1
C1 2
V2

1
2
1
1
(111) E 2 2 2 A 2 A Now Simplify..

(112) C23 30 30 60 F Now,, C C C C

1
23
4
120
pf Total charge Q =CV
7
Q
Q
Q
V1 , V2 V3 V23
&V4
C1
C23
C4

(113) The arrangement can be redrawn as

shown in figule Now find out.

(114) V = 4x2 E =
1

dv
= 8x
dr

Now Put the value of x.

(115) C C C and q C5V

5
1
2
(116) C

A
9 PF
d
1

C1

3k1 0 A
d

and

Now C C C
3
4
2
50

C2

3k 2 0 A
2

(117) Knowledge base question.

(118) Knowledge base question.
(119) Knowledge base question.
(120) Use equation E

dV
dx

(121) W QV ( CV )V CV 2 and

1
U
CV 2 Now find
2
w

(122) When Spheres are connected by a conducting wire their Potentials become equal.
C1 r1 1 q1 C1V C1 1
= =
=
=
=
C2 r2 2 q 2 C2 V C 2 2

Kq1
E
r2
Now, 1 1 Now find out rativ..
E 2 Kq 2
r22

(123)

(124) Q = CV = 5c
1
= C

F tI
d t
H kK

A / d
t tk
1
d

F
GG
H

I
JJ
K

Now Put the value.

(125) Knowledge base question.

(126)

q q q q
10
c c c c

or

10

2.5V
C 4

Now VA 0 = 7.5 V A 7.5V

Again V N VB ..... O VB 2.5 VB 25V
64q

64 q

(127) V = 4 R = 4 (4 r )

C
1
(128) C

F 1I
d t 1
H kK

Use this equation

51

6
1
(129) C1 d 4 and C2
5
1

Now C
(130) C =

C1C2
C1 C2

3 A
2 d

and V

Q
C

(131) Use wheatstons bridge equation Ceq C and Q CV

Charge on Capacitor between the terminals

Q CV
2
= Enegy stored in capacitor =
A and B is
2
2
2C

(132) Theory base question.

(133) Work done = Final energy - initial energy =
1
2

2
2
(134) U i C V1 V2

and

V=

Q2 Q2

2C 1 2C

q1 + q2 V1 + V2
=
c1 + c2
2

1
( 2C )V 2 Now find U iU f
2
A
A
C2
(135) C1 d 10
d 2
Uf

C5

5C
3

Percentage increase in Capacitance =

(136) Use Series and Parallel Connection law.

(137) Theory base question.
(138) Theory base question.
(139) n =

1000
= 2.8 = 3
350

1
m
CS = F = F
3
3
m
F = 2F
3
m=6
total no = mn = 3 6 = 18

52

C5 C
100%
C