Question

Four equal charges Q are placed at four corners of a square of each side a. Work done in removing a charge $ -Q $ from its centre to infinity is

• A. $ zero $
• B. $ \frac{\sqrt{2}\,{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}a} $
• C. $ \frac{\sqrt{2}\,{{Q}^{2}}}{\pi {{\varepsilon }_{0}}a} $
• D. $ \frac{{{Q}^{2}}}{2\pi {{\varepsilon }_{0}}a} $

Answer 1

Answer: (A)

Potential at centre 0 of the square
$ {{V}_{0}}=4\left( \frac{Q}{4\pi {{\varepsilon }_{0}}(a/\sqrt{2})} \right) $ Work done in shifting charge from centre to infinity
$ W=Q({{V}_{\infty }}-{{V}_{0}}) $
$ W=Q{{V}_{0}} $
$ =\frac{4\sqrt{2}{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}a} $
$ W=\frac{\sqrt{2}{{Q}^{2}}}{\pi {{\varepsilon }_{0}}a} $