Question

A small point mass carrying some positive charge on it, is released from the edge of a table. There is a uniform electric field in this region in the horizontal direction. Which of the following options then correctly describe the trajectory of the mass? (Curves are drawn schematically and are not to scale).

• A.
• B.
• C.
• D.

Answer 1

The correct option is A


Acceleration of the particle along $X$ axis $a_X=\frac{qE}{m}$
Acceleration of the particle along $Y$ axis $a_Y=g$
so, after time interval $t$
Distance travelled along $X$ axis,
$x=\frac{1}{2}\frac{qE{t}^2}{m}$.......$\left(1\right)$
Distance travelled along $Y$ axis
$y=\frac{1}{2}g{t}^2$.........$\left(2\right)$

from equation $\left(1\right)$ and $\left(2\right)$

$\frac{x}{y}=\frac{\left(qE/m\right)}{g}$

$\Rightarrow y=\frac{mg}{qE}x$

which is the equation of the straight line .


Hence , option $\left(C\right)$ is correct.