Problem 3.30

There are two thin wire rings, each of radius $R,$ whose axes coincide. The charges of the rings are $q$ and $-q .$ Find the potential difference between the centres of the rings separated by a distance $a$ .

\Delta \varphi=\frac{q}{2 \pi \varepsilon_{0} R}\left(1-\frac{1}{\sqrt{1+(a / R)^{2}}}\right)

Constant Electric Field in a Vacuum