Question

A charged particle of mass m and charge q is released from rest in an electric field of constant magnitude E. The kinetic energy of the particle after time t is

Answer 1

Explanation:

Step 1; Formula used

A force is generated because of the elective field.

$$\begin{gathered} F=qE \\ a=\frac{qE}{m} \end{gathered}$$

Step 2:

As the particle starts from rest and acceleration is constantly applying the equation of motion.

$$\begin{gathered} V=u+at \\ V=0+\frac{qEt}{m} \\ V=\frac{qET}{m} \end{gathered}$$

Then,

$$\begin{gathered} K.E.=\frac{1}{2}m{v}^2=\frac{1}{2}m{\left(\frac{qEt}{m}\right)}^2 \\ =\frac{1}{2}m\frac{q^2{E}^2{t}^2}{m^2} \\ =\frac{q^2{E}^2{t}^2}{2m} \end{gathered}$$

Hence, The answer is $\frac{q^2{E}^2{t}^2}{2m}$.