Question

A ring of radius $R$ carries a charge $+q.$ A test charge $-q_0$ is released on its axis at a distance$\sqrt{3}R$ from its centre. How much kinetic energy will be acquired by the test charge when it reaches the centre of the ring?

• A. $\frac{1}{4\pi {\epsilon }_0}\frac{q{q}_0}{R}$
• B. $\frac{1}{4\pi {\epsilon }_0}\left(\frac{q{q}_0}{2R}\right)$
• C. $\frac{1}{4\pi {\epsilon }_0}\left(\frac{q{q}_0}{\sqrt{3}R}\right)$
• D. $\frac{1}{4\pi {\epsilon }_0}\left(\frac{q{q}_0}{3R}\right)$

Answer 1

The correct option is A $\frac{1}{4\pi {\epsilon }_0}\frac{q{q}_0}{R}$

Potential due to ring at distance $\sqrt{3}R$

$\begin{array}{c}{V}_1=\frac{1}{4\pi {\in }_0}\times \frac{q}{\sqrt{R^2+3R^2}}=\frac{1}{4\pi {\in }_0}\frac{q}{2R}\\ Atcentrepotential{V}_2=\frac{1}{4\pi {\in }_0}\frac{q}{R}\\ K.E.=q_0\left(V_2-V_1\right)=\frac{1}{4\pi {\in }_0}\frac{q.q_0}{2R}\end{array}$