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Question

Four charges +q,q and q are to be arranged respectively at the four corners of a square ABCD of side 'a'
(i) Find the work required to put together this arrangement.
(ii) A charge qo is brought to the centre of the square, the four charges being held fixed. How much extra work is needed to do this

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Solution

Work done in bringing charge +q at point A
WA=0
Work done in bringing charge -q to the point B

WB=WAB=q×14πεoqa =q×14πεoq2a
Work done in bring the charge +q to the point C
WC=WAC+WBC

=q×14πεo.qa2+q×=(14πεoqa)

=14πϵo.q2a214πεo.q2a

Work done in bringing a change -q to the point D
WD=WAD+WBD+WCD

=q×14πϵoqa+(q)(14πε0qa2) +(q)×14πεo.qa

Total work done W=WA +WB+WC+WD

=2×14πεoq2a24×14πεoq2a(24)

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