A block having mass `'m'` ad carge `q` is resting on a fractionless 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

The situation is shown in fig Electric froces `vec(F)=qvec(E)` will accelerate the block towards the wall producing an acceleration
`a=(F)/(m)=(qE)/(m)L=(1)/(2)at^(2)`
i.e, `t=sqrt((2L)/(a))=sqrt((2mL)/(qE))`

As collision with the wall is perfectly elastic the block will rebound with same speed and as now is motion is opposite to the accelereation ,it will come to rest after travelling same distance `L` in same time `t`.After stopping it will begain accelerated towards the wall and so the block will execute oscillatory motion with "sprain" `L` and time period
`T=2t=sqrt((2mL)/(qE))`
However as the restoring force `f=(=qE)` when the block is moving away from the wall is constance and not proportional to displacement `x` the motion is not simple harmonic.