Question

Q. 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 \(\mathrm{t}\) 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

Solution:
When charge \(q\) is released in uniform eiectric field Ethen its acceleration
$$
a=\frac{q E}{m} \text { (constant) }
$$
So, its motion will be uniformly accelerated motion and its velocity after \(t\) second is given by
$$
v=a t=\frac{q E}{m} t
$$
The KE of charged particle
$$
\begin{aligned}
&K E=\frac{1}{2} m v^{2}=\frac{1}{2} m v^{2} \\
&=\frac{1}{2} m\left(\frac{q E}{m} t\right)^{2} \\
&=\frac{q^{2} E^{2} t^{2}}{2 m}
\end{aligned}
$$

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