a
\(E = kQ\left[ {\frac{1}{{{1^2}}} + \frac{1}{{{2^2}}} + \frac{1}{{{4^2}}} + \frac{1}{{{8^2}}} + ...\infty } \right]\)

\(E = kQ\left[ {1 + \frac{1}{4} + \frac{1}{{16}} + \frac{1}{{64}} + ...\infty } \right]\)\(1 + \frac{1}{4} + \frac{1}{{16}} + \frac{1}{{64}} + ...\infty \)

\({S_\infty } = \frac{a}{{1 - r}}\) \(a = 1\) , \(r = \frac{1}{4}\) \(1 + \frac{1}{4} + \frac{1}{{16}} + \frac{1}{{64}} + .....\,\infty = \frac{1}{{1 - 1/4}} = \frac{4}{3}\)

\(E = 9 \times {10^9} \times Q \times \frac{4}{3} = 12 \times {10^9}\,Q\,N/C\)

\(V = \frac{1}{{4\pi {\varepsilon _0}}}\left[ {\frac{{1 \times {{10}^{ - 6}}}}{1} + \frac{{1 \times {{10}^{ - 6}}}}{2} + \frac{{1 \times {{10}^{ - 6}}}}{4} + \frac{{1 \times {{10}^{ - 6}}}}{8} + .......\infty } \right]\)

\( = \,9 \times {10^9} \times {10^{ - 6}}\left[ {1 + \frac{1}{2} + \frac{1}{4} + \frac{1}{8} + ............\infty } \right] = 9 \times {10^3}\left[ {\frac{1}{{1 - \frac{1}{2}}}} \right]\)

\( = 1.8 \times {10^4}\,volt\)