question_answer

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)  \[\frac{{{Q}^{2}}}{2\pi {{\varepsilon }_{0}}a}\]

Correct Answer: A

Solution :

 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 \[W=Q({{V}_{\infty }}-{{V}_{0}})\] \[W=Q{{V}_{0}}\] \[=\frac{4\sqrt{2}{{Q}^{2}}}{4\pi {{\varepsilon }_{0}}a}\] \[W=\frac{\sqrt{2}{{Q}^{2}}}{\pi {{\varepsilon }_{0}}a}\]