Four identical charges +50 μC each are placed, one at each corner of a square of side 2 m. How much external energy(in J) is required to bring another charge of +50 μC from infinity to the centre of the square ?

Now, potential at the centre due to any one of the charges is

               $=\frac{1}{4\pi {\epsilon }_0}·\frac{(50 \times {10}^{-6 })}{\left(\sqrt{2}\right)}$

$\therefore$Potential at the centre of square 

         $$\begin{gathered} V_0= 4 \times \left[\frac{9 \times {10}^9 \times 50\times {10}^{-6}}{\sqrt{2}}\right] \\ =90\sqrt{2}\times {10}^4 V \end{gathered}$$

Work done in bringing a charge (q = 50 μC) from $\infty$ to centre of the square is

$$\begin{gathered} \therefore W=q{V}_0 \\ = 50\times {10}^{-6}\times 90\sqrt{2}\times {10}^4 \\ = 63.64 \mathrm{J} \end{gathered}$$