Question

A particle of mass m and charge q is released from rest in a uniform electric field E. The kinetic energy attained by the particle after moving a distance x along the electric field is

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

Answer 1

The correct option is C

$qEx$

Initial kinetic energy of the particle is zero. The gain in kinetic energy in distance x = decrease in potential energy = work done by the electric field to move the particle = force on q due to electric field E $\times$ distance =qE $\times$ x. Hence the correct choice is(c).

Or

By work energy theorom, the change in kinetic energy of the system is equal to the net work done by all the forces on the system:
So,
$K.E_f-K.E_i$ = qEx
Also, the charge is released from rest, So $K.E_i=0$
\(\therefore The K.E attained = qEx .