A block having mass `'m'` and charge `q` is resting on a frictionless plane at distance `L` from the wall as shown in fig.Discuss the motion of the block when a uniform electric field `E` is applied horizontally towards the wall assuming that collision of the block with the wall is perfectly elastic.

Explanation

Acceleration of the block
`a = (qE)/(m)`
Time taken by the block to reach at wall
`d = (1)/(2) a t^(2)`
`t = sqrt((2d)/(a)) = sqrt((2d)/(qE//m)) = sqrt((2md)/(qE))`
After completely elastic collision , the speed of the block is reversed and then it moves under retardation and comes to rest at `O`. Again it is accelerated towards the wall and so on. In fact it is executing oscillatory motion of the time period
`T = 2t = 2sqrt((2md)/(qE))`
As force `qE` is constant , the motion of block is not simple harmonic.