d
(d) Potential at the centre of rings are
\({V_{{O_1}}} = \frac{{k.q}}{R} + \frac{{k( - q)}}{{\sqrt {{R^2} + {d^2}} }}\), \({V_{{O_2}}} = \frac{{k( - q)}}{R} + \frac{{kq}}{{\sqrt {{R^2} + {d^2}} }}\)
\(==>\) \({V_{{O_1}}} - {V_{{O_2}}} = 2kq\,\left[ {\frac{1}{R} - \frac{1}{{\sqrt {{R^2} + {d^2}} }}} \right]\)\( = \frac{q}{{2\pi {\varepsilon _0}}}\left[ {\frac{1}{R} - \frac{1}{{\sqrt {{R^2} + {d^2}} }}} \right]\)