Only one option correct

1. Two identical conducting spheres, having charges of opposite sign, attract each other with a force of

0.108N when separated by 0.5m . The spheres are connected by a conducting wire, which is then

removed, and thereafter, they repel each other with a force of 0.036 N . The initial charges on the

spheres are

(a) 6 65 10 15 10C and C (b)

6 61.0 10 3.0 10C and C

(c) 6 62.0 10 6.0 10C and C (d)

6 60.5 10 1.5 10C and C

2. Two identical point charges are placed at a separation of l . P is a point on the line joining the charges,

at a distance x from any one charge. The field at P is E is plotted against x for values of x from close

to zero to slightly less than l . Which of the following best represents the resulting curve?

(a) (b)

(c) (d)

3. Six charges are placed at the corner of a regular hexagon as shown. If an electron

is placed at its centre O, force on it will be:

(a) Zero (b) Along OF (c) Along OC (d) None of these

4. For equal positive charges are fixed at the vertices of a square of side L. Z-axis is

perpendicular to the plane of the square. The point 0Z is the point where the diagonals of the square

intersect each other. The plot of electric field due to the four charges, as one moves on the z-axis.

(a) (b)

(c) (d)

EXERCISE # 1

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 2

5. The charge per unit length of the four quadrant of the ring is 2 , 2 , and

respectively. The electric field at the centre is

(a) 0

ˆ2

iR

(b)

0

ˆ2

jR

(c)

0

2 ˆ4

iR

(d) None

6. The direction of E at point P due to uniformly charged finite rod will be

(a) at angle 30from x axis (b) 45

from x axis

(c) 60from x axis (d) none of these

7. Two equal negative charges are fixed at the points 0,a and 0, a on the y-

axis. A positive charge Q is released from rest at the points 2 ,0a on the x-axis. The charge Q will

(a) execute simple harmonic motion about the origin

(b) move to the origin and remain at rest

(c) move to infinity

(d) execute oscillatory but not simple harmonic motion

8. If the electric potential of the inner metal sphere is 10volt & that of the outer shell is

5 volt, then the potential at the centre will be:

(a) 10volt (b) 5volt (c) 15volt (d) 0

9. Three concentric metallic spherical shell A,B and C or radii ,a band c a b c have surface

charge densities , and respectively. The potential of shell A is:

(a) 0 a b c (b) 0 a b c

(c) 0 b a c (d) none

10. A charged particles having some mass is resting in equilibrium at a height H above the centre of a

uniformly charged non-conducting horizontal ring of radius R . The force of gravity acts downwards.

The equilibrium of the particle will be stable

(a) for all values of H (b) only if 2

RH

(c) only if 2

RH (d) only if

2

RH

11. An infinite non conducting sheet of charges has a surface charges density of 7 210 C m

. The

separation between two equipotential surfaces near the sheet whose potential differ by 5V is

(a) 0.88cm (b) 0.88mm (c) 0.88m (d) 75 10 m

12. A bullet of mass m and charge q is fired towards a solid uniformly charged

sphere of radius R and total charge q . If it strikes the surface of sphere with

speed u , find the minimum speed u so that it can penetrate through the sphere.

(Neglect all resistance forces or friction acting on bullet except electrostatics

forces)

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 3

(a)

02

q

mR (b)

04

q

mR (c)

08

q

mR (d)

0

3

4

q

mR

13. In space, a horizontal Electric Field E mg q exist as shown in figure

and a mass m attached at the end of a light rod. If mass m is released from

the position shown in figure find the angular velocity of the rod when it

passes through the bottom most position

(a) g

l (b)

2g

l (c)

3g

l (d)

5g

l

14. The diagram shows a small bead of mass m carrying charge q . The bead can

freely move on the smooth fixed ring placed on a smooth horizontal plane.

In the same plane a charge Q has also been fixed as shown. The potential

at the point P due to Q is V . The velocity with which the bead should

projected from the point P so that it can complete a circle should be greater

than

(a) 6qV

m (b)

qV

m (c)

3qV

m (d) none

15. A unit positive point charge of mass m is projected with a velocity V inside the

tunnel as shown. The tunnel has been made inside a uniformly charged non

conducting sphere. The minimum velocity with which the point charge should be

projected such it can it reach the opposite end of the tunnel, is equal to

(a) 1 2

2

04R m (b) 1 2

2

024R m

(c) 1 2

2

06R m (d) zero because the initial and the final points are at same potential

16. A conducting sphere of radius a has charge Q on it. It is enclosed by a neutral conducting concentric

spherical shell having inner radius 2a and outer radius 3a . Find electrostatic energy of system.

(a)

25

12

kQ

a (b)

211

12

kQ

a (c)

2

2

kQ

a (d) none

17. A charged particle of charge Q is held fixed and another charged particle of mass m and charge q (of

the same sign) is released from a distance r . The impulse of the force exerted by the external agent

on the fixed charge by the time distance between Q and q becomes 2r is

(a) 04

Qq

mr (b)

04

Qqm

r (c)

0

Qqm

r (d)

02

Qqm

r

18. In a regular polygon of n sides, each corner is at a distance r from the centre. Identical charges are

placed at 1n corners. At the centre, the intensity is E and the potential is V . The ratio V E has

magnitude

(a) r n (b) 1r n (c) 1n r (d) 1r n n

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 4

19. The equation of an equipotential line in an electric field is 2y x , then the electric field strength

vector at 1,2 may be

(a) ˆ ˆ4 3i j (b) ˆ ˆ4 8i j (c) ˆ ˆ8 4i j (d) ˆ ˆ8 4i j

20. Uniform electric field of magnitude 100V m in space is directed along the line 3y x . Find the

potential difference between point 3,1 & 1,3A B

(a) 100V (b) 200 2V (c) 200V (d) 0

21. A wheel having mass mhas charges q and q on diametrically opposite points.

It remains in equilibrium on a rough inclined plane in the presence of uniform

vertical electric field E

(a) mg

q (b)

2

mg

q (c)

tan

2

mg

q

(d) none

22. Figure shows the electric field lines around an electric dipole. Which of the

arrows best represents the electric field at point P ?

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

23. Two short electric dipole are placed as shown. The energy of electric interaction

between these dipoles will be

(a) 1 2

3

2 coskPP

r

(b) 1 2

3

2 coskPP

r

(c) 1 2

3

2 sinkPP

r

(d) 1 2

3

4 coskPP

r

24. 4 charges are placed each a distance ‘a’ from origin. The dipole moment of

configuration is

(a) ˆ2qaj (b) ˆ3qaj (c) ˆ ˆ2aq i j (d) none

25. Both questions (a) and (b) refer to the system of charges as shown in the figure.

A spherical shell with an inner radius ‘a’ and an outer radius ‘b’ is made of

conducting material. A point charge Q is placed at the centre of the spherical

shell and a total charge q is placed on the shell.

(A) Charge q is distributed on the surfaces as

(a) Q on the inner surface, q on outer surface

(b) Q on the inner surface, q Q on the outer surface

(c) Q on the inner surface, q Q on the outer surface

(d) The charge q is spread uniformly between the inner and outer surface

(B) Assume that the electrostatic potential is zero at an infinite distance from the spherical shell. The

electrostatic potential at a distance R a R b from the centre of the shell is

(a) 0 (b) k Q

a (c)

Q qK

R

(d)

Q qK

b

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 5

(where 0

1

4K

)

26. A positive charge q is placed in a spherical cavity made in a positively charged sphere. The centres of

sphere and cavity are displaced by a small distance l . Force on charge q is:

(a) in the direction parallel to vector l

(b) in radial direction

(c) in a direction which depends on the magnitude of charge density in sphere

(d) direction cannot be determined

27. A conducting sphere of radius r has a charge. Then

(a) The charge is uniformly distributed over its surface, if there is an external electric field

(b) Distribution of charge over its surface will be non uniform if no external electrical field exist in

space .

(c) Electric field strength inside the sphere will be equal to zero only when no external electric field

exists

(d) Potential at every point of the sphere must be same

28. The figure shows a non conducting ring which has positive and negative charge

non uniformly distributed on it such that the total charge is zero. Which of the

following statements is true?

(a) The potential at all the points on the axis will be zero.

(b) The electric field at all the points on the axis will be zero.

(c) The direction of electric field at all points on the axis will be along the axis

(d) If the ring is placed inside a uniform external electric field then net torque

and force acting on the ring would be zero.

29 A point charge Q is located at the centre of a hollow spherical conductor of inner radius R1 and outer

radius R2, the conductor being uncharged initially. The potential at the inner surface will be

(a) 1 2

1 1KQ

R R

(b)

1 2

1 1KQ

R R

(c)

2 1

1 1KQ

R R

(d) none of these

30. A dipole of 2 C charges each consists of the positive charge at the point P (1,-1) and the negative

charge is placed at the point Q(-1,1). The work done in displacing a charge of 1 C from point

A(-3, -3) to B (4, 4) is

(a) 191.6 10 J (b) 193.2 10 J (c) zero (d) 4.8 eV

31. A and B are two concentric spheres if A is given a charge Q while B is earthed as shown in figure,

then

(a) the charge densities of A and B are same (b) the field inside and outside A is zero

(c) the field between A and B is not zero (d) the field inside and outside B is zero.

32. The maximum electric field intensity on the axis of uniformly charged ring of charge q and radius R

will be

(a) 2

0

1

4 3 3

q

R (b)

2

0

1 2

4 3

q

R (c)

20

1 2

4 3 3

q

R (d)

20

1 3

4 2 2

q

R

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 6

33. Consider the situation as shown in the adjacent figure. The

work done in taking a point charge from P to A is WA. from P

to B is BW and from P to C is WC. Therefore,

(a) A B CW W W (b) A B CW W W

(c) A B CW W W (d) A B CW W W

34. A charge Q is fixed at a distance d in front of an infinite metal plate. The lines of force are

represented by

35 A thin metallic shell contains charge Q on it. A point charge q is placed at

the centre of the shell and another charge q1 is placed outside it as shown in

the adjacent figure. All charges are positive. The force on the charge at the

centre is

(a) towards left (b) towards right

(c) upward (d) zero

36. If charges q/2 and 2q are placed at the centre of face and at the corner of a cube, then the total flux

through the cube will be

(a) 02

q

(b)

0

q

(c)

06

q

(d)

08

q

37. Three charge Q, +q and +q are placed at the vertical of a right – angled

isosceles triangle as shown in the adjacent figure. The net electrostatic energy

of the configuration will be zero if Q is equal to

(a) 1 2

q

(b)

2

2 2

q

(c) -2q (d) +q

38. Find the charge on an iron particle of mass 2.24 mg, if 0.02% of electrons are removed from it

(a) -0.01996 C (b) 0.01996 C

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 7

(c) 0.02 C (d) 2.0 C

39. A thick shell with inner radius R and outer radius 3R has a uniform charge

density C/m3. It has a spherical cavity of radius R as shown in the figure.

The electric field at the centre of the cavity is

(a) zero (b) 02 /R

(c) 03 / 4R (d) 07 /12R

40. A Gaussian surface in the figure is shown by dotted line. The electric field

on the surface will be

(a) due to q1 and q2 only (b) due to q2 only

(c) zero (d) due to all

41. Two concentric spherical shell of radii R and r have similar charges with equal surface density

. The electric potential at their common centre is

(a) 0/ (d) 0

R r

(c)

0

R r

(d) None of the above

42. Two connected charges of +q and –q are at a fixed distance AB apart in a

non-uniform electric field whose lines of force are shown in the figure. The

resultant effect on the two charges is

(a) a torque in the plane of the paper and no resultant force.

(b) a resultant force in the plane of the paper and no torque.

(c) a torque normal to the plane of the paper and no resultant force.

(d) a torque normal to the plane of the paper and a resultant force in the plane

of the paper.

43. A ring of radius R carries a charge +q. A test charge –q0 is released on its axis at a distance 3R

from its centre. How much kinetic energy will be acquired by the test charge when it reaches the

centre of the ring?

(a) 0

0

1

4

qq

R (b) 0

0

1

4 2

qq

R

(c) 0

0

1

4 3

qq

R

(d) 0

0

1

4 3

qq

R

44. A charge Q is distributed over two concentric hollow spheres of radii r and R (R > r) such that their

surface densities are equal. Find the potential at the common centre. (Given 0

1

4k

)

(a) kQ

R r (b)

2 2

kQ R r

R r

(c)

kQ

r (d)

kQ

R

45. A uniform electric field exists is x – y plane. The potential of points A(2m, 2m), B(–2m, 2m) and

C(2m, 4m) are 4V, 16V and 12V respectively. The electric field is

(a) ˆ ˆ(4 5 )V

i jm

(b) ˆ ˆ(3 4 )V

i jm

(c) ˆ ˆ(3 4 ) V

i jm

(d) ˆ ˆ(3 4 )V

i jm

46. A point charge q = 50 C is located in the x – y plane at the point of position vector 0ˆ ˆ2 3 r i j

What is the electric field at the point of position vector ˆ ˆ8 5 r i j ?

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 8

(a) 1200V

m (b) 24 10

V

m (c) 900

V

m (d) 4500

V

m

47. An infinite, uniformly charged sheet with surface charge density cuts through a

spherical Gaussian surface of radius R at a distance x from its centre, as shown in

the figure. The electric flux through the Gaussian surface is

(a) 2

0

R (b)

2 2

0

2 ( )

R x (c)

2

0

( )

R x (d)

2 2

0

( )

R x

48. A very long uniformly charged circular cylinder (radius R) has a surface charge

density . A very long uniformly charged line charge (linear charge density ) is

placed along the cylinder axis. If electric field intensity vector outside the cylinder is

zero, then :

(a) = R (b) = –R (c) = RR (d) = –2R

49. In a certian region of space, the potential is given by V = k[2x2 – y2 + z2]. The electric field at the

point (1, 1, 1) has magnitude

(a) 6k (b) 2 6k (c) 2 3k (d) 4 3k

50. 1 C charge is uniformly distributed on a spherical shell given by equation x2 + y2 + z2 = 25. What

will be intensity of electric field at a point (1, 1, 2)?

(a) 5 N/C (b) 45 N/C (c) 5 3

/2

N C (d) Zero

one or more than one option correct

1. Four charges of 1 ,2 ,3C C C and 6 C are placed one at each corner of the square of side 1m.

The square lies in the x y plane with its centre at the origin

(a) The electric potential is zero at the origin

(b) The electric potential is zero everywhere along the x axis only of the sides of the square are

parallel to x and y axis

(c) The electric potential is zero everywhere along the z axis for any orientation of the square in

the x y plane.

(d) The electric potential is not zero along the z-axis except at the origin.

2. Two fixed charges 4Q (positive) and Q (negative) are located at A and B, the distance AB being 3m

(a) The point P where the resultant field due to both is zero is on AB outside AB.

(b) The point P where the resultant field due to both is zero is on AB inside AB.

(c) If a positive charge is placed at P and displaced slightly along AB it will execute oscillations.

(d) If a negative charge is placed at P and displaced slightly along AB it will execute oscillations

EXERCISE # 2

R

x

y

x

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 9

3. Two identical charges +Q are kept fixed some distance apart. A small particle P with charge q is placed

midway between them. If P is given a small displacement , it will undergo simple harmonic motion

if

(a) q is positive and is along the line joining the charges

(b) q is positive and is perpendicular to the line joining the charges.

(c) q is negative and is perpendicular to the joining the charges

(d) q is negative and is along the line joining the charges.

4. Three point charges ,4Q Q and 16Q are placed on a straight line 9cm long. Charges are placed in

such a way that the system has minimum potential energy. Then

(a) 4 Q ans 16 Q must be at the ends and Q at a distance of 3 cm from the 16 Q

(b) 4 Q and 16 Q must be at the ends and Q at a distance of 6 cm from the 16 Q.

(c) Electric field at the position of Q is zero

(d) Electric field at the position of Q is 04

Q

5. Two infinite sheets of uniform charge density and are parallel to each other as shown in the

figure. Electric field at the

(a) points to the left or to the right of the sheets is zero

(b) midpoint between the sheets is zero

(c) midpoint of the sheets is 0 and is directed towards right.

(d) midpoint of the sheet is 02 and is directed towards right

6. A circular ring carries a uniformly distributed positive charge. The electric field (E) and potential (V)

varies with distance (r) from the centre of the ring along its axis is

(a) (b)

(c) (d)

7. A charged cork of mass m suspended by a light string is placed in uniform electric

field of strength 5 1ˆ ˆ 10 E i j NC as shown in the figure. If in equilibrium

position tension in the string is

2

1 3

mg

then angle ' ' with the vertical is

(a) 60 (b) 30

(c) 45 (d) 18

8. An electric dipole moment ˆ ˆ2.0 3.0 P i j Cm is placed in a uniform electric field

5 1ˆˆ3.0 2.0 10E i k N C

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 10

(a) The torque that E exerts on P is ˆˆ ˆ0.6 0.4 0.9i j k Nm

(b) The potential energy of the dipole is 0.6 J

(c) The potential energy of the dipole is 0.6 J

(d) If the dipole is rotated in the electric field, the maximum potential energy of the dipole is 1.3 J

9. Which of the following is true for the figure showing electric lines of force? (E is

electrical field, V is potential)

(a) A BE E (b)

B AE E (c) A BV V (d)

B AV V

10. Three points charges are placed at the corners of an equilateral triangle of side Las shown in the figure.

(a) The potential at the centroid of the triangle is zero

(b) The electric field at the centroid of the triangle is zero

(c) The dipole moment of the system is 2 qL

(d) The dipole moment of the system is 3 qL

11. An electric dipole is placed at the centre of a sphere. Mark the correct

answer

(a) the flux of the electric field through the sphere is zero

(b) the electric field is zero at every point of the sphere.

(c) the electric potential is zero everywhere on the sphere.

(d) the electric potential is zero on a circle on the surface.

12. A conducting sphere A of radius a, with charge Q, is placed concentrically inside a conducting shell B

of radius b. B is earthed. C is the common centre of the A and B

(a) The field at a distance r from C , where a r b is 2

0

1

4

Q

r

(b) The potential at a distance r from C , where a r b , is 0

1

4

Q

r

(c) The potential difference between A and B is 0

1 1 1

4Q

a b

(d) The potential at a distance r from C , where 0

1 1 1,4

a r b Qr b

13. Three concentric spherical shells have radius ,2r r and 3r and 1 2,Q Q and 3Q

are final charges respectively. Innermost and outermost shells are already

earthed as shown in figure. Choose the correct statements.

(a) 1 3 2Q Q Q (b) 21

4

QQ

(c) 3

1

3Q

Q (d) 3

2

1

3

Q

Q

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 11

14. Two thin conducting shells of radii R and 3R are shown in the figure. The outer shell

carries a charge Q and the inner shell is neutral. The inner shell is earthed with the

help of a switch S.

(a) With the switch S open, the potential of the inner sphere is equal to that of the outer

(b) When the switch S is closed, the potential of the inner sphere becomes zero.

(c) With the switch S closed, the charge attained by the inner sphere is 3Q

(d) By closing the switch the capacitance of the system increases.

15. X and Y are large, parallel conducting plates closed to each other. Each face has an

area A. X is given a charge Q. Y is without any charge. Points A,B and C are as

shown in figure.

(a) The field at B is 02

Q

A

(b) The field at B is 0

Q

A

(c) The field at A,B and C are of the same magnitude

(d) The field at A and C are of the same magnitude, but in opposite directions

16. Plates A and B constitute an isolated, charged parallel-plate capacitor. The inner

surfaces (I and IV) of A and B have charges +Q and –Q respectively. A third plate

C with charge +Q is now introduced midway between A and B. Which of the

following statements is/are correct?

(a) The surfaces I and II will have equal and opposite charges

(b) The surfaces III and IV will have equal and opposite charges

(c) The charge on surface III will be greater than Q. (d) The potential difference between A and C will be equal to the potential difference between C and B.

17. Two identical positive point charge each of value Q are fixed at the point (a,0) and (-a, 0) on the x-

axis. A particle of mass m and carrying charge –q is released from rest from the point P(0, b) on the

y-axis. Let V0 be the velocity of the particle when it passes through the origin O and it covers

distance OP before coming to rest momentarily.

(a)

1/ 2

0

0

QqV

ma (b) 'OP OP

(c) motion of particle is oscillatory (d) motion of particle is SHM

18. An electric dipole is placed in uniform electric field as shown in the

figure. The dipole is rotated through a small angle about its centre and

released. Select the correct statement(s)

(a) The motion of dipole is oscillatory but no SHM.

(b) The motion of dipole is SHM.

(c) The motion of dipole is neither oscillatory nor SHM.

(d) The motion of dipole is oscillatory.

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 12

19. Figure shows three concentric conducting thin spherical shells A, B and C of

radii a, b, and c. The shells A and C are given charge q and –q,

respectively, and shell B is earthed. Then,

(a) The charge q will be there at outer surface of A

(b) the charge bq

c

will be there at inner surface of C

(c) the charge –q will be at inner surface of B

(d) the charge –q (1-b/c) will be there at outer surface of C

20. Two conducting plates A and B are placed parallel to each other, A is given a charge Q1 and B a

charge Q2. Then

(a) the charge on the outer plate A is 1 2

2

Q Q (b) the charge on the outer plate B is 1 2

2

Q Q

(c) the charge on inner plate A is 1 2

2

Q Q (d) the charge on inner plate B is 1 2

2

Q Q

21. A point charge q is placed at origin. Let , and A B CE E E be the electric field at three points

A(1, 2, 3), B (1, 1, -1) and C (2, 2, 2) due to charge q. Then

(a) A BE E (b) ||A CE E (c) 4B CE E (d) 8B CE E

22. S is a solid neutral conducting sphere. A point charge q of 1 × 10–6C is placed at point

A. C is the centre of sphere and AB is a tangent. BC = 3m and AB = 4m :

(a) The electric potential of the conductor is 1.8 kV

(b) The electric potential of the conductor is 2.25 kV

(c) The electric potential at B due to induced charges on the sphere is –0.45 kV.

(d) The electric potential at B due to induced charges on the sphere is 0.45 kV.

23. Two concentric shells have radii R and 2R, charges qA and q

B and potential 2V and

3

2

V respectively.

Now shell B is earthed and let charges on them become qA

and qB. Then :

(a) 1

2A

B

q

q (b) 1

A

B

q

q

(c) Potential of A after earthing becomes 3

2

V

(d) Potential difference between A and B after earthing becomes 2

V

24. A Gaussian surface :

(a) Must not pass through any discrete charge

(b) Must pass through any material medium whether conducting or non-conducting

(c) May pass through a continuous charge distribution

(d) May pass through a region where no material medium is present.

25. Select the correct statements :

(a) If a point charge is placed off-centre inside an electrically neutral spherical metal shell then induced

charge on its inner surface is uniformly distributed

C

S

A B

AB

S C H O L A R S E M P I R E / P H Y S I C S / P R A V I N P A N D E Y P a g e 13

(b) If a point charge is placed off-centre inside an electrically neutral, isolated spherical metal shell, then

induced charge on its outer surface is uniformly distributed.

(c) A non-metal shell of uniform charge attracts or repels a charge particle that is outside the shell as if

all the shell’s charge were concentrated at the centre of the shell

(d) If a charged particle is located inside a non-metal shell of uniform charge, there is no electrostatic

force on the particle due to the shell

Passage 1

In a certain region, uniform electric field exist as 0ˆE = E j . Proton and electron are projected from

origin at t = 0 with certain velocities along the +ve x-axis direction. Due to the electric field, they experience force and so they move in the x-y plane along different trajectory 1. The path followed by the particles will be (a) Parabola (b) Circular (c) Hyperbola (d) Spiral 2. If they have same initial kinetic energy then for the same displacement along x-direction, deflection is : (a) More for proton (b) More for electron (c) Equal for both (d) Independent of kinetic energy 3. If they have same initial velocity then for same x-axis displacement, deflection is (a) More for proton (b) More for electron (c) Equal for both (d) Independent of kinetic energy

Passage 2 A point charge +Q having mass m is fixed on horizontal smooth surface. Another point charge having magnitude +2Q & mass 2m is projected horizontal towards the charge +Q from far distance with velocity V0. 4. Force applied by floor on the fixed charge in horizontal direction, when distance between charges becomes ‘d’ :

(a) 2

2

2KQ

d (b)

2

2

KQ

d (c) Zero (d) None

5. The impulse acting on the system of particle (Q + 2Q) in the time interval when distance between them becomes ‘d’ :

(a) 2

2

0 0

2KQ2m V V

md

(b) 2mV0

(c) 2

2

0

2KQ2m V

md

(d) None

6. Minimum distance of approach is

(a) 2

2

0

2KQ

mV (b)

2

2

0

KQ

mV (c)

2

2

0

4KQ

mV (d) None

7. Acceleration of particle 2Q when it is closed to fixed particle Q is

EXERCISE # 3

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(a) Zero (b) 4

0

2

mV

2KQ (c)

4

0

2

mV

4KQ (d) None

8. If particle +Q is free to move, then what will be the closest distance between the particles?

(a) Zero (b) 2

2

0

6KQ

mV (c)

2

2

0

3KQ

mV (d) None

Passage 3 A point charge q is located at a distance r from the centre O of an uncharged conducting spherical layer whose inside and outside radii are equal to R1 and R2, respectively. It is given r < R1. Assume zero potential at infinity. 9. The potential at point O is

(a) Zero (b) 0 1 2

q 1 1 1

4πε r R R

(c) 0 1

q 1 1

4π r R

(d) Can not be determined

10. The electric field intensity at point O is

(a)Zero (b) 2 2 2

0 1 2

q 1 1 1- +

4πε r R R

(c)2 2

0 1

q 1 1

4πε r R

(d) Can not be determined

11. The electric potential of the conductor is

(a) Zero (b) 0 1 2

q 1 1 2

4πε r R R

(c) 0 2

q

4 R (d) Can not be determined

Passage 4 A thin homogeneous stick of mass m and length L may rotate in the vertical plane around a horizontal axle pivoted at one end of the stick. A small ball of mass m and charge Q is attached to the opposite end of this

stick. The whole system is positioned in a constant horizontal electric field of magnitude mg

E2Q

. The stick

is held horizontally at the beginning.

12. What is the acceleration of the small ball at the instance of releasing the stick?

(a) 3g

2 (b)

3g

4 (c)

9g

8 (d) None of these

13. What is the speed of ball when rod becomes vertical :

(a)

3gL

2 (b) 2gL (c)

3gL

4 (d)

2

3

gL

14. Magnitude of acceleration of ball when it swings through the vertical position?

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(a) 3 5 g

2 (b)

3 17 g

8 (c)

3 2 g

4 (d) 10

2

g

Matching Type Problems

1. Two spherical shells are as shown in figure. Suppose r is the distance of a point from their common centre. Then,

Column-I Column-II (a) Electric field for r < R1 (p) Is constant for q2 and vary for q1 (b) Electric potential for r < R1 (q) is zero for q2 and vary for q1 (c) Electric potential for R1< r < R2 (r) is constant (d) Electric field for R1 < r < R2 (s) is zero 2. A neutral spherical conductor A has two spherical cavities B and C. Two point charges qB and qC are placed at centers of cavities B and C, respectively. Another point charge q is fixed at a large distance r from the centre of sphere. In Column I, information about force experienced by the particle is given while in Column II the details of the forces. Match the entries of Column I with the entries of Colum II.

Column-I Column-II a) Force on qB (p) Zero b) Force on qC (q) Non-zero

c) Force on q (r) B C

2

0

(q q )q

4πε r

d) Force on conductor (s) Rightward

3. Column I gives a situation in which two dipoles of dipole moment ˆpi and ˆ3 pj are placed at origin. A circle

of radius R with centre at origin is drawn as shown in Fig. Column II gives coordinates of certain positions on the circle. Match the statements in Column I with the statements in Column II.

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Column-I Column-II

(a) The coordinate(s) or point on circle

where potential is maximum (p) R 3R

,2 2

(b) The coordinate(s) of point on circle

where potential is zero (q) R 3R

,2 2

(c) The coordinate(s) of point on circle

where magnitude of electric field

Intensity is 3

0

1 4p

4πε R (r)

3R R,

2 2

(d) The coordinate(s) of point on circle

where magnitude of electric field

Intensity is 3

0

1 2p

4πε R (s)

3R -R,

2 2

4. In the fig. shown, the conductor is uncharged and a charge q is placed inside a spherical cavity at a distance ‘a’ from its centre c.

Column-I Column-II (a) Electric field due to induced charges On the inner surface of cavity at point P (p) Zero (b) Electric potential due to charges on the Inner surface of cavity and q at P (q) non-zero (c) Electric field due to induced charges On the outer surface of conductor and q at c (r) value can be stated with the given data

(d) Electric potential due to induced

Charges on the inner surface of cavity at c (s) value cannot be stated from the given data

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5. A spherical metallic conductor has a spherical cavity. A positive point charge is placed inside cavity at its centre. Another positive point charge is placed outside (near) the conductor. The conductor is initially electrically neutral Column-I (Cause) Column-II (Effect)

(a) When outside charge is shifted to

other position (p)Distribution of charge on inner surface of cavity changes

(b) When inside charge is shifted to

other position within cavity (q)Distribution of charge on outer surface of conductor changes

(c) When magnitude of charge inside cavity

is increased (r)Electric potential at centre of conductor due to charges present on outer surface of conductor changes

(d) When conductor is earthed (s)Force on charge inside cavity changes

1. A spherical Gaussian surface surrounds a point charge q. What happens to its total flux if the

charge is moved to another location inside the surface?

2. If a proton is released from rest in a uniform electric field, does the electric potential increase or

decrease? What about its electrostatic potential energy?

3. A charge situated at a certain distance from an electric dipole (small), in the end – on position,

experience a force F. Find the force acting on the same charge due to same dipole if its distance

from the centre of dipole is doubled.

4. For the electrostatic charge system shown in this figure.

(a) find the net force on the electric dipole if 1 2 3 .q q q q

(b) find the electrostatic energy of the system

5. Point charge +q and –q are kept alternately at the corners of a cube of side

‘a’ as shown in the figure. Write an expression for the work done in

removing all the charges far away from each other.

6. Positive charge Q is uniformly distributed throughout the volume of a dielectric sphere of radius R. A point

mass having charge +q and mass m is fired towards the centre of

the sphere with velocity v from a point A at distance r (r > R)

from the centre of the sphere. Find the minimum velocity v so

that it can penetrate R/2 distance inside the sphere. (neglect any

resistance other than electric interaction. Charge on the

small mass remains constant throughout the motion.)

EXERCISE # 4

- q

- q

+q

- q +q

- q

+ q

+q

a

p

R

r

2RR

2

Rrp

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7. A solid spherical region, having concentric a spherical cavity whose diameter ‘R’ is equal to the radius of the

spherical region, has a total change ‘Q’. Find the electric field and potential at a point P as shown.

8. The length of each side of a cubical closed surface is l. If charge q is situated on one of the

vertices of the cube, then find the flux passing through shaded face of the cube.

9. A point charge Q is located on the axis of a disc of radius R at a distance a from the

plane of the disc. If one fourth (1/4th) of the flux from the charge

passes through the disc, then find the relation between a & R.

10. A charge Q is uniformly distributed over a rod of length l. Consider a hypothetical cube of edge l with the centre

of the cube at one end of the rod. Find the minimum and maximum possible flux of the electric field through

the entire surface of the cube

11. An infinite dielectric sheet having charge density has a hole of radius R in

it. An electron is released on the axis of the hole at a distance 3 R from the

centre. What will be the velocity when it crosses the plane of sheet. (e = charge

on electron and m = mass of electron)

12. A rigid insulated wire frame in the form of a right angled triangle ABC ,

is set in a vertical plane as shown in the figure. Two beads of equal

masses m each and carrying charges q1 and q

2 are connected by a cord of

length l and can slide without friction on the wires. Considering the case

when the beads are stationary determine. :

(a) the angle

(b) the tension in the cord

(c) If the chord is now cut what are the value of the charges for which the beads continues to remain stationary?

13. A thin charged ring of radius R , charge Q and an infinitely long uniformly charged

wire, charge density , oriented along the axis of the ring with one of its ends

coinciding with the centre of the ring, form a system. Find the force of interaction

between the ring and wire.

14. Two free charges + q & + 4 q are placed at a distance l apart. Find the magnitude, sign and location of a third

charge which makes the system in equilibrium.

15. Positive charge Q is distributed uniformly over a circular ring of radius R. A particle having a mass m and a

negative charge q, is placed on its axis at a distance x from the centre. Find the force on the particle. Assuming

x < < R, find the time period of oscillations of the particle if it is released from there.

16. Two identically charged spheres are suspended by strings of equal length. The string make an angle of 30° with

each other when suspended in air. If they are suspended in a liquid of density 0.8 gm/cc, the angle remains the

same. What is the dielectric constant of the liquid? The density of the material of the sphere is 1.6 gm/cc.

A q 2 q 1

Q

P 30

o 60

o

B C

R

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17. A particle A having a charge of 1.0x10-6C is held fixed on a horizontal table. A second charged particle of mass

80 g stays in equilibrium on the table at a distance of 10cm from the first charge. The coefficient of friction

between the table and this second particle is = 0.1. Find the range within which the charge on the second

particle may lie.

18. Two similar & equally charged identical metal sphere A & B repel each other with a force 2x10-5 N. A third

identical, uncharged sphere C is touched with A & then placed at the midpoint between A & B. What is net

electric force on C?

19. Two point charges + q & - q are separated by the distance 2 l. Find the flux of the

electric field strength vector across a circle of radius R as shown in the figure.

20. A spherical shell of radius R1 with a uniform charge q has a point charge q

0 at its centre. Find the

work performed by the electric forces during the shell expansion from radius R1 to radius R

2

21. Three concentric conducting spherical shells of radii R, 2R and 3R carry charges Q, –2Q and 3Q

respectively.

(a) Find the electric potential at r = R and at r = 3R, where r is the radial distance from the centre.

(b) Find the electric field at r = (5/2)R

(c) Find the electrostatic energy stored in the system

22. A block having mass m = 4kg and charge q = 50 C is connected

to a spring having a force constant k = 100 N/m. The block lies on

a frictionless horizontal track and a uniform electric field E = 5 ×

105 V/m acts on the system as shown in fig. The block is released

from rest when the spring is un stretched (at x = 0). (i) By what

maximum amount does the spring expand? (ii) What is the

equilibrium position of the block? (iii) Show that the block’s motion is simple harmonic and

determine the amplitude and time period of the motion

23. The bob of a pendulum has mass m = 1 kg and charge q = 40 C. Length of

pendulum is L = 0.9 m. The point of suspension also has the same charge 40 C.

What the minimum speed u should be imparted to the bob so that it can complete

vertical circle? [Take g =10 m/s2]

24. Charge q and cq

b are placed at (b, 0) and

2

, 0

c

b. Find the locus of points in x

– y plane, having zero potential. What is its shape?

l

-qR

+q

l

q

u

mq

KE

mq

0x

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25. A solid sphere having uniform volume charge density and radius R is shown in fig. A spherical

cavity of radius R/2 hollowed out. Find the potential difference between the centre of sphere O and centre of

cavity O1. (As shown in figure)