Question

A block of mass m containing a net positive charge q is placed ona smooth horizontal table which terminates in a vertical wall as shown in figure (29-E2).The distance of the block from the wall is d. A horizontal electric field E towards right is switched on. Assuming elastic collisions (if any) find he time period of the resulting oscillatory motion. Is it a simple sharmonic motion?

Answer 1

The block does noot undergo SHM.
$d=ut+\frac{1}{2}a{t}^2$
Here, u = 0, $a=\frac{qE}{m}$

$t_1=\sqrt{\frac{2d}{a}}=\sqrt{\frac{2dm}{qE}}v=u+at=\frac{qE}{m}\sqrt{\frac{2dm}{qE}}$
Again $u=v-a{t}_2=0$
or $t_2=\frac{v}{a}=\frac{\frac{qE}{m}\sqrt{\frac{2dm}{qE}}}{a}=\sqrt{\frac{2dm}{qE}}$
Total time
$T=t_1+t_2=2\sqrt{\frac{2dm}{qE}}=\sqrt{\frac{8dm}{qE}}$