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. $\frac {1}{4\,\pi\,\varepsilon_0}\frac {\sqrt2q_0Q}{R}$
• C. $\frac {1}{4\,\pi\,\varepsilon_0}\frac {(\sqrt2-1)q_0Q}{\sqrt2R}$
• D. $\frac {1}{4\,\pi\,\varepsilon_0}\frac {\sqrt2q_0Q}{(\sqrt2-1)R}$

Answer 1

Answer: (A)

Potential at the centre of each sphere will be $ V = \frac{1}{4 \, \pi \,\varepsilon_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