Four equal point charges Q each are placed in the x y 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:

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TestHub · Accepted Answer

Work done in bringing the fifth charge at origin is equal to change in the potential energy of the system of charges.
$W_{e x t} = Δ U$ $= U_{f} - U_{i}$ if $U_{i} = 0$ (assumed)

$W_{e x t} = U_{f} - 0$ $= [\frac{K Q^{2}}{2} + \frac{K Q^{2}}{2} + \frac{K Q^{2}}{2 \sqrt{5}} + \frac{K Q^{2}}{2 \sqrt{5}}]$
Hence, the work done in bringing the fifth charge at the origin is
$W_{e x t} = \frac{Q^{2}}{4 π ε_{0}} [1 + \frac{1}{\sqrt{5}}]$ .

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