Question

There are two thin wire rings, each of radius R, whose axes coincide. The charges on the rings are q and q.Evaluate the potential difference between the centers of the rings separates by a distance a.

• A. $\frac{q}{\pi {\epsilon }_0}\left[\frac{1}{R}+\frac{1}{\sqrt{R^2+a^2}}\right]$
• B. $\frac{q}{2\pi {\epsilon }_0}\left[\frac{1}{R}+\frac{1}{\sqrt{R^2+a^2}}\right]$
• C. $\frac{q}{2\pi {\epsilon }_0}\left[\frac{1}{R}-\frac{1}{\sqrt{R^2+a^2}}\right]$
• D. $\frac{2q}{\pi {\epsilon }_0}\left[\frac{1}{R}-\frac{1}{\sqrt{R^2+a^2}}\right]$

Answer 1

The correct option is D $\frac{2q}{\pi {\epsilon }_0}\left[\frac{1}{R}-\frac{1}{\sqrt{R^2+a^2}}\right]$

Potential at O

$V_1=\frac{hQ}{R}=\frac{hQ}{\sqrt{R^2+a^2}}$

Potential at $O_1$

$V_2=\frac{hQ}{\sqrt{R^2+a^2}}=\frac{hQ}{R}{V}_1-V_2=2hQ(\frac{1}{R}-\frac{1}{\sqrt{R^2+a^2}})$