Question

A particle having mass $m$ and charge $q$ is at rest. On applying a uniform electric field $E$ on it,it starts moving. What is the kinetic energy when it travels a distance $x$ in the direction of force?

• A. $q^{2}Ex$
• B. $q{E}^{2}x$
• C. $qE{x}^2$
• D. $qEx$

Answer 1

The correct option is D $qEx$

When a particle of mass $m$ and carrying a charge $q$ is placed in a 'Uniform' electric field $E$, the field exerts a force $F$ on the particle,
$F=qE$

If the particle is left free, then it performs accelerated motion under teh force $F$. The acceleration of the particle is
$a=\frac{F}{m}=\frac{qE}{m}$

Let the particle start from rest.
Suppose, its velocity becomes $v$ after travelling a distance $x$ in the field
$v^2=u^2+2as$
$v^2=0+2\times \frac{qE}{m}\cdot x$
$v^2=\frac{2qE\cdot x}{m}$ ....(i)

The kinetic energy acquired by the particle is
$K=\frac{1}{2}m{v}^2=\frac{1}{2}m\times \frac{2qE}{m}\cdot x=qEx$