Question

A block of mass m containing a net positive charge q is placed on a smooth horizontal table which terminates in a vertical wall as shown in figure. The disance of the block from the wall is d. A horizontal electric field E towards right is switched on. Assuming elastic collisions(if any) find the time period of the resulting oscillary motion. Is it a simple harmonic motion?

Answer 1

The block does not undergo. SHM since here the acceleration is not proportional to displacement and not always opposite to displacement. When the block is going towards the wall the acceleration is along displacement and when going away from it the displacement is opposite to acceleration.

The force experience by particle is :

$F=qE$

Therefore, the acceleration will be:

$a=\frac{qE}{m}$

Time taken to go towards the wall is the time taken to goes away from it till velocity is

$d=ut+\frac{1}{2}a{t}^2$

$\Rightarrow d=\frac{1}{2}\times \frac{qE}{m}\times t^2$

$\Rightarrow t^2=\frac{2dm}{qE}\Rightarrow t=\sqrt{\frac{2md}{qE}}$

$\therefore$ Total time taken for to reach the wall and com back(Time period)

$=2t=2\sqrt{\frac{2md}{qE}}=\sqrt{\frac{8md}{qE}}$.