Q 12-02-169JEE MainJEE Main 2019 (10 Jan, Shift 2)Medium
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:
Answer: (C) $\dfrac{Q^2}{4\pi\epsilon_0}\left(1+\dfrac1{\sqrt5}\right)$
Distances from the origin: $2, 2$ for $(0,\pm2)$ and $\sqrt{16+4} = 2\sqrt5$ for $(4,\pm2)$.
$$W = QV_O = \frac{Q^2}{4\pi\epsilon_0}\left(\frac12+\frac12+\frac{1}{2\sqrt5}+\frac{1}{2\sqrt5}\right) = \frac{Q^2}{4\pi\epsilon_0}\left(1+\frac{1}{\sqrt5}\right)$$
Solution by Sreeraj P, M.Sc Physics