The simple pendulum of the previous problem is placed in uniform electric field `E`, directed horizontally. Find the angle made by string with vertical in equilibrium and tension in the string . Now the ball is slightly displaced and it exceutes simple harmonic motion, find its time period of oscillation.

Explanation

The ball is in equilibrium under three forces
(a) Weight of ball `mg`
(b) Electric force `qE`
(c ) Tension in the string `T`
`tan theta = (qE)/(mg) rArr theta = tan^(-1) ((qE)/(mg))`
`T = sqrt((mg)^(2) + (qE)^(2))`
For time period :
effective acceleration `a = = sqrt(((mg)^(2) + (qE)^(2))/(m))`
Time period `T' = 2pi sqrt((L)/(a))`
`= 2pi sqrt((L)/([g^(2) + ((qE)/(m))^(2)]^((1)/(2))))`