Question

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

• A. Zero
• B. $\frac{\sqrt{2}{Q}^2}{4\pi {\epsilon }_{0}a}$
• C. $\frac{\sqrt{2}{Q}^2}{\pi {\epsilon }_{0}a}$
• D. $-\frac{Q^2}{2\pi {\epsilon }_{0}a}$

Answer 1

Answer: (C)

$\frac{\sqrt{2}{Q}^2}{\pi {\epsilon }_{0}a}$

Potential due to charges at the corner of a body of side $a$ is $V_c=\frac{1}{4\pi {\epsilon }_0}\frac{4Q}{a/\sqrt{2}}=\frac{\sqrt{2}Q}{\pi {\epsilon }_{0}a}$
Potential at infinity $V_{\alpha }=0$
so, work done in removing a charge $-Q$ from centre to infinity
$W=Q\Delta V=-Q(V_{\alpha }-V_c)=-Q\times \frac{\sqrt{2}Q}{\pi {\epsilon }_{0}a}=\frac{+\sqrt{2}{Q}^2}{\pi {\epsilon }_{0}a}$