Consider configuration of a system of four charges each of value +q . work done by external agent in

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2. Electric Potential and Capacitance

hard

Consider the configuration of a system of four charges each of value $+q$ . The work done by external agent in changing the configuration of the system from figure $(1)$ to figure $(2)$ is

A

$\frac{{k{q^2}}}{a}\left( {3 - \sqrt 2 } \right)$

B

$\frac{{ - k{q^2}}}{a}\left( {3 + \sqrt 2 } \right)$

C

$\frac{{k{q^2}}}{a}\left( {3 + \sqrt 2 } \right)$

D

$\frac{{ - k{q^2}}}{a}\left( {3 - \sqrt 2 } \right)$

Solution

$\mathrm{W}_{\mathrm{ext}}=\mathrm{U}_{\mathrm{f}}-\mathrm{U}_{\mathrm{i}}$

$\mathrm{U}_{\mathrm{i}}=\frac{4 \mathrm{kq}^{2}}{\mathrm{a}}+\frac{2 \mathrm{kq}^{2}}{\sqrt{2 \mathrm{a}}}$

$\mathrm{U}_{\mathrm{f}}=\frac{4 \mathrm{kq}^{2}}{\sqrt{2 \mathrm{a}}}+\frac{2 \mathrm{kq}^{2}}{2 \mathrm{a}}$

Standard 12

Physics

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