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

Answer 1

Answer: (D)

From parabola

$y=\frac{1}{2} \times\left[\frac{E e}{m}\right] \times \frac{X^{2}}{u^{2}} $
$=\frac{E \cdot e}{2 m u^{2}} \cdot X^{2}$
As $X=4 a y $ (for parabola)
$\therefore X^{2} =\frac{2 m u^{2}}{E \cdot e} \cdot y$
$a =\frac{2 m u^{2}}{4 E \cdot e}=\frac{m u^{2}}{2 E \cdot e}$