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 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 the time period of the resulting oscillatory motion in second. $\left(\frac{ q }{ m }=1 C / kg , E =1 \frac{ N }{ C }, d =2 m \right)$ ?

Answer 1

Electric force will accelerate the block
$a =\frac{ f }{ m }=\frac{ qE }{ m }$
velocity is acquired in traveling distance $d$ and time taken in this is $t$.
$d=\frac{1}{2} a^{2} $
$t=\sqrt{\frac{2 d}{a}}=\sqrt{\frac{2 md }{q E}}$
Since collision is elastic, the block will rebound with same speed, this motion is against acceleration so block will come to rest in same time and after traveling same distance will again accelerate and keep oscillatory motion.
$T =2 t =2 \sqrt{\frac{2 md }{ qE }}=\sqrt{\frac{8 md }{ qE }}$
$T =\sqrt{\frac{8 md }{ qE }} $