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

The situation is shown in fig electric force `vecF=qvecE`
will accelerate the block towards the wall producting an acceleration
`a=F/m=(qE)/mL=1/2 at^(2)`
i.e. `t=sqrt((2L)/a)=sqrt((2mL)/(qE))`

As collision with the wall is perfectly elastic, the block will rebounded with same speed and as now is motion is opposite to the acceleration, it will come to rest after travelling same distance L in same time t. After stopoing it will beagain accelrated towards that wall adn so the block will execute oscillatroy motion with spain L and tme 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.