Question

in a uniform electric field if a charge is fired in a direction different from the line of electric field then the trajectory of charge will be

1. circle

2.straight line

3. parabola

4.ellipse

Answer 1

When a charge is kept in an electric field it experience a force.

here, electric field acts in X-axis so Force will be in same direction and it will cause $x$ displacement in X-axis.

$F=qE⟹m{a}_x=qE$

$a_x=\frac{qE}{m}$

Displacement will be,

$x=u_{x}t+\frac{1}{2}{a}_x{t}^2⟹x=0+\frac{1}{2}{a}_x{t}^2$

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

In Y-axis no force os acting so, displacement in Y-axis will be;

$y=ut⟹t=\frac{y}{u}$

Putting value of time in eq(1)

$x=\frac{1}{2}\frac{qE}{m}{\left(\frac{y}{u}\right)}^2$

$x\propto y^2$

This is same as equation of parabola, so

in a uniform electric field if a charge is fired in a direction different from the line of electric field then the trajectory of charge will be: parabola