Question

A charged particle of mass '$m$' and charge '$q$' is at rest. It is accelerated in a uniform electric field of intensity '$E$' for time '$t$'. The kinetic energy of the particles after time $t$ is

• A. $\frac{Eqm}{2t}$
• B. $\frac{E^2 q^2 t^2}{2m}$
• C. $\frac{2\text{E}^2\text{t}^2}{\text{mq}^2}$
• D. $\frac{\text{Eqt}}{\text{m}}$

Hint:

Work done by electric field $F \cdot d$ is another way to find $KE$, where $d = \frac{1}{2}at^2$.

Answer 1

The Correct Option is B

Step 1: Concept
Force on charge in electric field is $F = qE$, so acceleration $a = qE/m$.

Step 2: Meaning
Velocity after time $t$ (starting from rest) is $v = at = \frac{qEt}{m}$.

Step 3: Analysis
Kinetic Energy $KE = \frac{1}{2}mv^2 = \frac{1}{2}m\left(\frac{qEt}{m}\right)^2$.
$KE = \frac{1}{2}m \frac{q^2 E^2 t^2}{m^2} = \frac{q^2 E^2 t^2}{2m}$.

Step 4: Conclusion
The kinetic energy is $\frac{E^2 q^2 t^2}{2m}$. Final Answer: (B)