# NCERT Physics Exemplar Solution : Electric Charge & Fields

Q:1. A point positive charge is brought near an isolated conducting sphere (figure). The electric field is best given by

Ans: (a)

Q:2. Figure shows electric field lines in which an electric dipole P is placed as shown. Which of the following statements is correct?

(a) The dipole will not experience any force

(b) The dipole will experience a force towards right

(c) The dipole will experience of force towards left

(d) The dipole will experience a force upwards

Ans: (c)

Q:3. A point charge + q is placed at a distance d from an isolated conducting plane. The field at a point P on the other side of the plane is
(a) Directed perpendicular to the plane and away from the plane

(b) Directed perpendicular to the plane but towards the plane directed radially away from the point charge

(c) Directed radially towards the point charge

Ans: (a)

Q:4. A hemisphere is uniformly charged positively. The electric field at a point on a diameter away from the centre is directed

(a) Perpendicular to the diameter

(b) Parallel to the diameter

(c) At an angle tilted towards the diameter

(d) At an angle tilted away from the diameter

Ans: (a)

Q:5. If $\int_{S} E.dS = 0$ over a surface, then

(a) The electric field inside the surface and on it is zero

(b) The electric field inside the surface is necessarily uniform

(c) The number of flux lines entering the surface must be equal to the number of flux lines leaving it

(d) All charges must necessarily be outside the surface

Ans: (c). (d)

Q:6. The electric field at a point is

(a) Always continuous

(b) Continuous only if there is no charge at that point

(c) Discontinuous only if there is a negative charge at that point

(d) Discontinuous if there is a charge at that point

Ans: (b). (d)

Q:7. If the there were only type of charge in the universe, then

(a) $\oint_s E.dS \ne 0$ on any surface

(b) $\oint_s E.dS = 0$ if the charge is outside the surface

(c) $\oint_s E.dS$ could not be defined

(d) $\oint_s E.dS = \frac{q}{\epsilon_0}$ if charges of magnitude q were inside the surface

Ans: (c). (d)

Q:8. Consider a region inside which there are various type of charges but the total charge is zero. At points outside the region,

(a) The electric field in necessarily zero

(b) The electric field is due to the dipole moment of the charge distribution only

(c) The dominant electric field is $d \propto \frac{1}{r^3}$ , for large r, where r is the distance from a origin in this regions

(d) The work done to move a charged particle along a closed path, away from the region, will be zero

Ans: (c). (d)

Q:9. Refer to the arrangement of charges in figure and a Gaussian surface of radius R with Q at the centre. Then ,

(a) Total flux through the surface of the sphere is $– \frac{Q}{\epsilon_0}$

(b) Field on the surface of the sphere is $– \frac{Q}{4\pi \epsilon_0 R^2 }$

(c) Flux through the surface of sphere due to 5Q is zero

(d) Field on the surface of sphere due to -2Q is same everywhere

Ans: (a). (c)

Q: 10. A positive charge Q is uniformly distributed along a circular ring of radius R.A small test charge q is placed at the centre of the ring figure. Then,

(a) If q > 0 and is displaced away from the centre in the plane of the ring, it will be pushed back towards the centre

(b) If q < 0 and is displaced away from the centre in the plane of the ring, it will be never return to the centre and will continue moving till it hits the ring

(c) If q < 0, it will perform SHM for small displacement along the axis

(d) Q at the centre of the ring is in a unstable equilibrium within the plane of the ring for q > 0

Ans: (a). (b), (c)

Q: 11. Two fixed , identical conducting plates (α and β) , each of surface area S are charged to – Q and q, respectively, where Q > q > 0. A third identical plate (γ) , free to move is located on the other side of the plate with charge q at distance d (figure). the third plate is released and collides with plate β. Assume the collision is elastic and the time of collision is sufficient to redistribute charge amongst β and γ.

(a) Find the electric field acting on the acting on the plate γ before collision.

(b) Find the charges on β and γ after the collision.

(c) Find the velocity of the plate γ after the collision and at a distance d from the plate β

Ans: (a).

Q:12. Two charges – q each are fixed separated by distance 2d. A third charge q of mass m placed at the mid – point is displaced slightly by x(x<<d)perpendicular to the line joining the two fixed charged as shown in figure. show that q will perform simple harmonic oscillation of time period $\displaystyle T = \frac{8 \pi^3 \epsilon_0 m d^3}{q^2}$

Q:13. Total charge – Q is uniformly spread along length of a ring of radius R.A small test charge + q of mass m is kept at the centre of the ring and is given a gentle push along the axis of the ring.

(a) Show that the particle executes simple harmonic oscillation.

(b) Obtain its time period

Q:14. A positively charged particle is released from rest in an uniform electric field. The electric potential energy of the charge
(a) Remains a constant because the electric field is uniform
(b) Increases because the charge moves along the electric field
(c) Decreases because the charge moves along the electric field
(d) Decreases because the charge moves opposite to the electric field

Ans: (c).