Test Topic: Electric Charges & Fields

Test Code: PH/ONLINE/15

Maximum Marks: 200 Time: 2 hours
Correct Option = +4 Incorrect Option = -1

1. Charge nC is on Y- axis at y=+3 cm and charge =-6.0 nC is on Y- axis at y=-3 cm

calculate force on a test charge nC placed on X-axis at =4 cm.
a) N b) N c) N d) N
2. The electric intensity outside a charged sphere of radius at a distance is
a) b) c) d)
3. An uniform electric field exists along positive -axis. The work done in moving a charge 0.5 C
through a distance 2 m along a direction making an angle with -axis is 10 J. Then the magnitude
of electric field is
a) b) c) d)
4. 64 small drops of mercury, each of radius and charge coalesce to form a big drop. The ratio of the
surface density of charge of each small drop with that of the big drop is
a) 1 : 64 b) 64 : 1 c) 4 : 1 d) 1 : 4
5. Two point charges are placed at points respectively with The
work done by external force in displacing the charge from where , angle

and
a)
b)

c)

d)
6. An electric dipole is placed at an angle of with an electric field of intensity 105 NC-1. It experiences
a torque equal to Nm. Calculate the charge on the dipole, if the dipole length is 2 cm.
a) b) c) d)
7. A sphere of radius is suspended within a hollow sphere of radius. The inner sphere is
charged to potential 3 and the outer sphere is earthed. The charge on the inner sphere is
a)
b)
c)
d)
8. Two small spheres of masses 𝑀1 and 𝑀2 are suspended by weightless insulating threads of lengths 𝐿1
and 𝐿2 . The spheres carry charges 𝑄1 and 𝑄2 respectively. The spheres are suspended such that they
are in level with one another and the threads are inclined to the vertical at angles of 𝜃1 and 𝜃2 as
shown. Which one of the following conditions is essential, if 𝜃1 = 𝜃2

a) 𝑀1 ≠ 𝑀2 but 𝑄1 = 𝑄2 b) 𝑀1 = 𝑀2 c) 𝑄1 = 𝑄2 d) 𝐿1 = 𝐿2
9. Given that For what ratio will the force between and be maximum?

Sahitya Roy (B. Tech -EE-IIT Kharagpur) 1

 a) 0.25 b) 0.5 c) 1 d) 2
10. Two plates are at potentials and If the separation between the plates be The
electric field between them is
a) b) c) d)
11.
Consider a system of three charges and placed at points A, B and C, respectively, as shown in
the figure. Take to be the centre of the circle of radius R and angle

a) The electric field at point O is directed along the negative axis

b) The Potential energy of the system is zero
c)
The magnitude of the force between the charges at C and B is
d) The potential at point O is
12. There is a uniform electric field of strength along -axis. A body of mass and charge
is projected into the field from origin along the positive -axis with a velocity Its speed
in after is (Neglect gravitation)
a) 10 b) c) d) 20
13. Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of
30° with each other. When suspended in a liquid of density 0.8 gcm−3 , then angle remains the same. If
density of the material of the sphere is 16g cm−3 , the dielectric constant of the liquid is
a) 4 b) 3 c) 2 d) 1
14. The electrostatic potential inside a charged spherical ball is given by where is the
distance from the centre a, b are constants. Then the charge density inside the ball is
a) b) c) d)
15. A thin semi-circular ring of radius 𝑟 has a positive charge 𝑞 distributed uniformly over it. The net field
E at the centre 𝑂 is

𝑞 𝑞
a) 𝐢̂ b) − 𝐣̂
4𝜋 2 𝜀0 𝑟 2 4𝜋 2 𝜀0 𝑟 2
𝑞 𝑞
c) − 2 2 𝐢̂ d) 𝐣̂
2𝜋 𝜀0 𝑟 2𝜋 𝜀0 𝑟 2
2

16. The electric potential is given as a function of distance (metre) by Value

of electric field at is
a) b) c) d)
17. The work done in carrying a charge of from a point to a point in an electric field is The
potential difference is then
a) b) c) d)

Sahitya Roy (B. Tech -EE-IIT Kharagpur) 2

 18. What is not true for equipotential surface for uniform electric field?
a) Equipotential surface is flat
b) Equipotential surface is spherical
c) Electric lines are perpendicular to equipotential surface
d) Work done is zero

19. Four charges equal to are placed at the four corners of a square and a charge is at its centre. If
the system is in equilibrium the value of is
a) b) c) d)
20. The figure shows four situations in which charges as indicated ( 0) are fixed on an axis .In which
situation is there a point to the left of the charges where an electron would be in equilibrium?

a) 1 and 2 b) 2 and 4 c) 3 and 4 d) 1 and 3

21. Two charged spheres of radii and having equal surface charge density. The ratio of their
potential is
a) b) c) d)
22. The electric field due to an electric dipole at a distance from its centre in axial position is . If the
dipole is rotated through an angle of 90° about its perpendicular axis, the electric field at the same
point will be
a) E
b)

c)
d) 2E

Sahitya Roy (B. Tech -EE-IIT Kharagpur) 3

 23. Two identical positive charges are fixed on the -axis at equal distances from the origin . A
negatively charged particle starts on the -axis, at a large distance from , moves along the -axis,
passes through and moves far away from . Its acceleration is taken as positive along its direction
of motion. The best graph between the particle’s acceleration and its -coordinate is represented by

a)

b)

c)

d)

24. Let three be a spherically symmetric charge distribution with charge density varying as
upto is the distance from the origin. The
electric field at a distance from the origin is given by
a) b) c) d)
25. Two equal charges are separated by a distance A third charge placed on a perpendicular bisector at
distance will experience maximum coulomb force when
a) b) c) d)

26. Two unit negative charges are placed on straight line. A positive charge q is placed exactly at the mid-
point between these unit charges. If the system of these three charges is in equilibrium, the value of q
(in C) is
a) 1.0 b) 0.75 c) 0.5 d) 0.25
27.
A solid sphere of radius and volume charge density is enclosed by a hollow sphere of radius
with negative surface charge density , such that the total charge in the system is zero, is a

positive constant and is the distance from the centre of sphere. The ratio is
a) b) c) d)

Sahitya Roy (B. Tech -EE-IIT Kharagpur) 4

 28. If the electric flux entering and leaving an enclosed surface respectively are and , the electric
charge inside the surface will be
a) b) c) d)

29. An electron is released from the bottom plate as shown in the figure The velocity of
the electron when it reaches plate will be nearly equal to

a) b) c) d)

30. There are two equipotential surfaces as shown in figure. The distance between them is The charge
of coulomb taken from the surface the resultant work done will be

a) b) c) d) zero
31. Two equal point charges are fixed at and on the -axis. Another point charge is
placed at the origin. The change in the electrical potential energy of when it is displaced by a small
distance along the -axis, is approximately proportional to
a) b) c) d)
32. Three concentric spherical shells have radii and and have surface charge densities
and respectively. If and denote the potentials of the three shells, then, for
we have
a) b) c) d)

33. A infinite number of charges, each of charge 1 C, are placed on the -axis with co-ordinates 1, 2,
4, 8, . If a charge of 1 C is kept at the origin, then what is the net force acting on 1C charge?
a) 9000 N b) 12000 N c) 24000 N d) 36000 N
34. Two conducting spheres of radii and are separated by a distance of in free space. If
the spheres are charged to same potential of each, the force of repulsion between them is
a) b) c) d)
35. Two conducting sphere of radii r1 and r2 are charged to the same surface charge density. The ratio of
electric field near their surface is
a) / b) / c) / d) 1 : 1

36. Point charge moves from point to point along the path (figure shown) in a uniform
electric field pointing coparallel to the positive direction of the -axis. The coordinates of the points
and are and respectively. The work done by the field in the
above process is given by the expression

Sahitya Roy (B. Tech -EE-IIT Kharagpur) 5

 a) b) c) d)
37. Consider the following statements about electric dipole and select the correct ones
S1 : Electric dipole moment vector is directed from the negative charge to the positive charge
S2 : The electric field of a dipole at a point with position vector depends on as well as the angle
between and
S3 : The electric dipole potential falls off as and not as
S4 : In a uniform electric field, the electric dipole experiences no net forces but a torque
a) S2, S3 and S4 b) S3 and S4 c) S2 and S3 d) All four
38. A hollow charged metal sphere has a radius r. If the potential difference between its surface and a
point at a distance 3r from the centre is V, then electrical intensity at distance 3r from the centre is
a) b) c) d)

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

a) b) c) d)

40. An infinite number of electric charges each equal to (magnitude) are placed along
-axis at and so on. In the setup if the consecutive
charges have opposite sign, then the electric field in at is

a) b) c) d)

41. In the figure, a proton moves a distance in a uniform electric field as shown in the figure. Does the
electric field do a positive or negative work on the proton? Does the electric potential energy of the
proton increase or decrease

a) Negative, increase b) Positive, decrease c) Negative, decrease d) Positive, increase

42. When one electron is taken towards the other electron, then the electric potential energy of the system
a) Decreases b) Increases c) Remains unchanged d) Becomes zero

43. Four electric charges and are placed at the corners of a square of side (see figure).
The electric potential at point midway between the two charges

Sahitya Roy (B. Tech -EE-IIT Kharagpur) 6

 a) Zero
b) c) d)
44. A charged particle is shot towards another charged particle which is fixed, with a speed . It
approaches upto a closest distance and then returns. If is shot with speed2 , the closest distance
of approach would be
a) b) c) d)

45. The figure shows the path of a positively charged particle 1 through a rectangular region of uniform
electric field as shown in the figure. What is the direction of electric field and the direction of particles
2, 3 and 4

a) Top; down, top, down b) Top; down, down, top

c) Down; top, top, down d) Down; top, down, down
46. Two identify long parallel conducting plates having surface charge densities and respectively,
are separated by a small distance. The medium between the plates is vacuum. If is the dielectric
permittivity of vacuum, then the electric field in the region between the plates is
a) b) c) d)

47. Two concentric conducting thin spherical shells and having radii and are charged
to and The electrical field along a line, (passing through the centre) is
a) b) c) d)

48. The electric intensity due to an infinite cylinder of radius and having charge per unit length at a
distance from its axis is
a) Directly proportional to b) Directly proportional to
c) Inversely proportional to d) Inversely proportional to

49. A molecule with a dipole moment is placed in an electric field of strength E. Initially the dipole is
aligned parallel to the field. If the dipole is to be related to be anti-parallel to the field the work
required to be done by an external agency is
a) b) c) d)
50. The force between two charges apart is . If each charge is moved towards the other by
, then the force between them will become
a) b) c) d)

Sahitya Roy (B. Tech -EE-IIT Kharagpur) 7