Question

A point charge $q$ of mass $m$ is released (displaced slightly) along axis of ring from center of the ring of radius $R$ and having a uniform charge $Q$. Speed of point charge when its acceleration is maximum can be given by

• A. $\sqrt{\frac{0.586Qq}{4\sqrt{3}\pi {ϵ}_{0}mR}}$
• B. $\sqrt{\frac{Qq}{\pi {ϵ}_{0}mR}}$
• C. $\sqrt{\frac{Qq}{9\pi {ϵ}_{0}mR}}$
• D. $\sqrt{\frac{0.32Qq}{2\sqrt{3}\pi {ϵ}_{0}mR}}$

Answer 1

The correct option is D $\sqrt{\frac{0.32Qq}{2\sqrt{3}\pi {ϵ}_{0}mR}}$


Electric field is maximum at $\frac{R}{\sqrt{2}}$, and hence acceleration is also maximum at that point.

By conservation of energy: $\Rightarrow (V_1-V_2)q=\frac{1}{2}m{v}^2$

$\frac{kQq}{R}-\frac{kQq}{R}\sqrt{\frac{2}{3}}=\frac{1}{2}m{v}^2\Rightarrow \frac{2kQq}{mR}\left(\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}}\right)=v^2$