A block having charge `q` mass m is resting on a smooth horizontal surface at a distance `d` from the wall as shown. Discuss the motion of the block when a uniform electic field E is applied horizontally towards the wall assuming that collision of the block with the wall is completely elastic

Explanation

The situation is shown in Fig. Electric force `vec(F)= q vec(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 its motion is opposite to the acceleration, it will come to rest after travelling same distance L in same time t. After stopping it will be again accelerated towards the wall and so the block will execute oscillatory motion with .span. L and time period
`T=2t = 2 sqrt((2mL)/(qE))`
However, as the restoring force F(=qE) when the block is moving away from the wall is constant and not proportional to displacement x, the motion is not simple harmonic.