Question

A region consists of uniform electric field $E$ and uniform gravitational field $g$ as shown in figure. A particle of charge $Q$ and mass $m$ begins to move in this region. Deduce an equation for its trajectory.

• A. $y=mg{x}^2$
• B. $y^2=\frac{mg}{Q}x$
• C. $y=-\frac{mg}{QE}x$
• D. $y=\frac{2mg}{QE}x$

Answer 1

The correct option is C $y=-\frac{mg}{QE}x$

Here, $E$ is in positive $x-$ direction, then force $F_x$ experienced by charge along $+x-$axis will be

$F_x=QE$

$\therefore a_x=\frac{QE}{m}$

Using second equation of motion in $x-$ direction

$x=u_{x}t+\frac{1}{2}{a}_x{t}^2$

$\because u_x=0;a_x=\frac{QE}{m}$

$\therefore x=\frac{QE}{2m}{t}^2...........\left(1\right)$

Similarly, for gravitational field
$a_y=-g$

$\therefore y=-\frac{1}{2}g{t}^2.........\left(2\right)$

Solving $\left(1\right)$ and $\left(2\right)$, we get equation of trajectory

$y=-\left(\frac{mg}{QE}\right)x$

This is an equation of straight line.