Q. Four equal point charges Q each are placed in the xy plane at (0, 2), (4, 2), (4, -2) and (0, -2). The work required to put a fifth charge Q at the origin of the coordinate system will be :

Solution:

Potential at origin = $\frac{KQ}{2} + \frac{KQ}{2} +\frac{KQ}{\sqrt{20}} + \frac{KQ}{\sqrt{20}}$
(Potential at $\infty$ = 0) $ =KQ \left(1+ \frac{1}{\sqrt{5}}\right) $
$\therefore $ Work required to put a fifth charge Q at origin is equal to $ \frac{Q^{2}}{4\pi\varepsilon_{0}} \left(1+ \frac{1}{\sqrt{5}}\right) $

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