Two identical thin rings each of radius R meters are coaxially placed at a distance R meters apart. If Q 1 coulomb and Q 2 coulomb are respectively the charges uniformly spread on the two rings, the work done in moving a charge q from the center of one ring to that of other is
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$W = q(V_{o_2} - V_{o_1})$
where $V_{0_1} = \frac{Q_1}{4 \pi \epsilon_0 R} + \frac{Q_2}{4 \pi \epsilon_0 R \sqrt{2}}$
and $V_{0 2} = \frac{Q_2}{4 \pi \epsilon_0 R} + \frac{Q_1}{4 \pi \epsilon_0 R \sqrt{2}}$
⇒ ⇒ $V_{o2} - V_{o1} = \frac{(Q_2 - Q_1)}{4 \pi \varepsilon_0 R} \left[ 1 - \frac{1}{\sqrt{2}} \right]$
So, $W = \frac{q \cdot (Q_2 - Q_1) (\sqrt{2} - 1)}{4 \pi \varepsilon_0 R} \cdot \frac{1}{\sqrt{2}}$
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