Question

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

Answer 1

Given that ,

Mass of partcle, $m$ and charge on particle $Q$

Initial velocity of particle in both axis $u_x=0$ and $u_y=0$

Let us consider uniform electric field $E$ in $X-direction$

So accelertation of particle in $X-direction$, $a_x=\frac{QE}{m}$..

Hence , $x=\frac{1}{2}{a}_x{t}^2=\frac{1}{2}(\frac{QE}{m})t^2$...........................(1)

Acceleration in $Y-direction$ ,, $a_y=-g$

hence , $y=\frac{1}{2}{a}_y{t}^2=\frac{1}{2}(-g)t^2$...................................(2)

Dividing both equation we get :

$\frac{x}{y}=-\frac{QE}{mg}$

$⟹\text{Required Trajectory},y=-(\frac{mg}{QE})x$