Question

Two identical rings each of radius $R$ are co-axially placed. The distance between their centres is $R$. Same charge $Q$ is placed on each ring. How much work will be done in moving a test charge from the centre of one ring to that of the other ?

• A. Zero
• B. $\frac{1}{4\pi {\epsilon }_0}\frac{\sqrt{2}{q}_{0}Q}{R}$
• C. $\frac{1}{4\pi {\epsilon }_0}\frac{(\sqrt{2}-1)q_{0}Q}{\sqrt{2}R}$
• D. $\frac{1}{4\pi {\epsilon }_0}\frac{\sqrt{2}{q}_{0}Q}{(\sqrt{2}-1)R}$

Answer 1

Answer: (A)

Potential at the centre of each sphere will be $V=\frac{1}{4\pi {\epsilon }_0}\left[\frac{Q}{R}+\frac{Q}{\sqrt{2}R}\right]$
Since potential difference between the two centres is zero, therefore work done is also zero