c
\(A\) is the midpoint

of \(PS\)

\({\therefore \quad PA = AS = L}\)

\({AR = AQ = \sqrt {{{(SR)}^2} + {{(AS)}^2}} }\)

\({ = \sqrt {{{(2L)}^2} + {{(L)}^2}}  = L\sqrt 5 }\)

Electric potential at point \(A\) due to the given charge configuration is

\(V_{A} =\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{q}{P A}+\frac{q}{A S}+\frac{(-q)}{A Q}+\frac{(-q)}{A R}\right]\)

\(=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{q}{L}+\frac{q}{L}-\frac{q}{L \sqrt{5}}-\frac{q}{L \sqrt{5}}\right]\)

\(=\frac{1}{4 \pi \varepsilon_{0}}\left[\frac{2 q}{L}-\frac{2 q}{L \sqrt{5}}\right]=\frac{1}{4 \pi \varepsilon_{0}} \frac{2 q}{L}\left[1-\frac{1}{\sqrt{5}}\right]\)