A ball having charge `q` and mass `m` is suspended from a string of length `L` between two parallel plates where a vertical electric field `E` is established . Find the time period of simple pendulum if electric field is directed (a) downward and (b) upward.

Explanation

For simple pendulum,
Time - period `T = 2 pi sqrt((L)/(a))`
where `a` : effective acceleration.
`a = ("net external force on the ball" )/("mass of the ball")`
(a) `a = (mg + qE)/(m) = g + (gE)/(m)`
`T = 2 pi sqrt((L)/(g +(qE)/(m))`
(b) `a = (mg - qE)/(m) = g - (qE)/(m)`
`T = 2 pi sqrt((L)/(g - (qE)/(m))`