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 C

Step 1:Given

Uniform electric field in this region in the horizontal direction.

A small point mass carrying some positive charge.

Step 2: Formula

The force due to Electric field along $X$ axis is $qE$

Acceleration due to electric field is $a_E=\frac{qE}{m}$

Step 3:Trajectory of object in Electric Field

The force due to Electric field along $X$ axis is $qE$

Acceleration due to electric field is $a_E=\frac{qE}{m}$

Whereas the charge, $E$ is the Electric field and $m$ is the mass of charge

The force along $Y$ axis is $mg$

Acceleration along $Y$ axis is $g$

$X$ co-ordinate of particle after time $t$, $x=\frac{1}{2}\left(\frac{qE}{M}\right)t^2=k_1{t}^2$

$Y$ co-ordinate of particles after time $t$, $y=\frac{1}{2}g{t}^2=k_2{t}^2$

Now,

$\frac{y}{x}=\frac{Mg}{qE}$

$y=\left(\frac{Mg}{qE}\right)x$

$y=\left(\frac{k_1}{k_2}\right)x=kx$

Where $k_1,k_2$ and $k$ are some constant

So, we get a linear equation in $y$ and $x$

The net acceleration of object is $a_{net}$ will be constant.

So, the trajectory will be of straight line.

Hence, option C is correct