Question

Four equal charge 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. 0
• 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: (C)

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

Answer 2

We know that work done in moving a charge is W = Q∆V

Here $W = Q(V_{0} - V_{\infty})$ $V_{\infty} = 0$ ∴ W = Q × V₀

Also $V_{0} = 4 \times \frac{1}{4\pi\varepsilon_{0}}.\frac{Q}{a/\sqrt{2}} = \frac{4\sqrt{2}Q}{4\pi\varepsilon_{0}a} = \frac{\sqrt{2}Q}{\pi\varepsilon_{0}a}$So, $W = \frac{\sqrt{2}Q^{2}}{\pi\varepsilon_{0}a}$