Question

A particle with charge $e$ and mass $m$, moving along the X-axis with a uniform speed $u$, enters a region where a uniform electric field $E$ is acting along the Y-axis. The particle starts to move in a parabola. Its focal length (neglecting any effect of gravity) is :

• A. $\frac{2m{u}^2}{eE}$
• B. $\frac{eE}{2m{u}^2}$
• C. $\frac{mu}{2eE}$
• D. $\frac{m{u}^2}{2eE}$

Answer 1

The correct option is D $\frac{m{u}^2}{2eE}$

$y=\frac{1}{2}\times \left[\frac{Ee}{m}\right]\times \frac{x^2}{u^2},y=\frac{eE}{2m{u}^2}{x}^2$ As $x^2=4ay,\therefore x^2=\frac{2m{u}^2}{eE}y,a=\frac{2m{u}^2}{4eE}=\frac{m{u}^2}{2eE}$