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Question

Physics Question on electrostatic potential and capacitance

Four equal charges qq each are placed at four corners of a square of side a each. Work done in carrying a charge −q-q from its centre to infinity is

A

zero

B

2qπε0a\frac{\sqrt{2}q}{\pi\varepsilon_{0}a}

C

q22πε0a\frac{q^{2}}{2\pi\varepsilon_{0}a}

D

2q2πε0a\frac{\sqrt{2}q^{2}}{\pi\varepsilon_{0}a}

Answer

2q2πε0a\frac{\sqrt{2}q^{2}}{\pi\varepsilon_{0}a}

Explanation

Solution

Potential at the centre OO of the square due to four equal charges qq at the corners


V=4q4πε0(a2)/2V =\frac{4 q}{4 \pi \varepsilon_{0}(a \sqrt{2}) / 2}
=2qπε0a=\frac{ \sqrt{2}q}{\pi \varepsilon_0 a}
∴W0∞=−W∞0\therefore W_{0 \infty} =-W_{\infty 0}
=−(−q)V=-(-q) V
=2q2πε0a=\frac{\sqrt{2} q^{2}}{\pi \varepsilon_{0} a}