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 downwards. Finds the period of oscillation of the pendulum due to the electrostatic force acting on the sphere, neglecting the effect of the gravitational force.

Explanation

Let the pendulum be be displaced from its equilibrium position A to position B through a small angle ` theta ` and then released. Forces acting on pendulum are (i) force F= qE in vertical downward direction due to the electrical field, and (ii ) the tension `T_0` and hence unbalanced restoring force is qE `sin theta`
if ` theta ` is small then ` sin theta =theta =(arc AB)/(1) `
` therefore ` Restoring force `=-qE theta =(-qE)/(l) (areAB)`
obviously the motion of pendulum is SHM ,whose time period is given as:
`T=2pi sqrt(("inertia factor ")/("spring factor ") )=2pi sqrt((m)/(qE//l))=2pi sqrt((ml)/(qE))`
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