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. With what period will the pendulum oscillate if the electrostatic force acting on the sphere is less than the gravitational force? Assume oscillations to be small.

The sphere of mass m has charge q on it. The length of pendulum is l.

 

The electric field E is directed vertically upwards. Now, due to this field, the sphere experiences a force in the upward direction.

 

This force is given as F = qE.

 

Due to this force, the acceleration produced in the upward direction in sphere is

 

a = F/m = qE/m

 

Thus, the net acceleration on the sphere is g - qE/m

 

The time period of simple pendulum is thus given as