Question

A charged particle of mass $m$ and charge $q$ is released from rest in uniform electric field $E$. Neglecting the effect of gravity, the kinetic energy of the charged particle after t second is

• A. $\frac{E \,q^{2} \,M}{2\, t^{2}}$
• B. $\frac{2 \,E^{2}\, t^{2}}{m\, q}$
• C. $\frac{E^{2} \,q^{2} \,{t }^{2}}{2\, m}$
• D. $ \frac{ E\,q\,m}{ t } $

Answer 1

Answer: (C)

Force on particle $= F = qE$
Hence, acceleration of particel $= a =\frac{ F }{ m }=\frac{ qE }{ m }$
Initial speed $= u =0$
Hence, final velocity $= v = u + at =\frac{ qEt }{ m }$
Kinetic energy $= K =\frac{1}{2} mv ^2=\frac{1}{2} m \left(\frac{ qEt }{ m }\right)^2$
$ \Longrightarrow K=\frac{E^2 q^2 t^2}{2 m} $