Electrostatics Part 2

Given, charges on two rings are +Q and -Q, respectively as shown below. Potential at centre of ring A due to charge on ring A and charge onring B is given as $V_{A}=\frac{kQ}{a}-\frac{kQ}{\sqrt{s^{2}+a^{2}}}$ Similarly, potential at centre of ring B due to charge on ring B and charge on ring A is given as $V_{B}=-\frac{kQ}{a}+\frac{kQ}{\sqrt{s^{2}+a^{2}}}$ Potential difference between centre of both the rings is $\Delta V=V_{A}-V_{B}$ $=\frac{2kQ}{a}-\frac{2kQ}{\sqrt{s^{2}+a^{2}}}$ $=\frac{Q}{2\pi\varepsilon_{0}}\left(\frac{1}{a}-\frac{1}{\sqrt{s^{2}+a^{2}}}\right)$ $\left(\because k=\frac{1}{4\pi\varepsilon_{0}}\,\mathrm{Nm}^{2}\,\mathrm{C}^{-2}\right)$ Thus, potential difference between centre of both the rings is $\frac{Q}{2\pi\varepsilon_{0}}\left[\frac{1}{a}-\frac{1}{\sqrt{s^{2}+a^{2}}}\right]$