Question

Four identical free point positive charges q(=1$\mu$C) each are located at the four corners of a square of side 1m. A negative charge is placed at the centre of the square to obtain equilibrium of all the charges. What is the total potential energy (in milli Joules) of the system assuming the reference point at infinity?

Answer 1

In gen, electric potential (V) due to a point charge, Q at a distance r is given by ;

$V=\frac{1}{4\pi {\epsilon }_0}.\frac{q}{r}$

Hence, total electric potential due to four equal point charge each of charge q at the centre of the square of side A is obtained by setting $r=\frac{A}{\sqrt{2}}$

$V=4\times \frac{1}{4\pi {\epsilon }_0}.\frac{q}{\frac{A}{\sqrt{2}}}$

$V=\frac{1}{4\pi {\epsilon }_0}.\frac{4\sqrt{2}q}{A}$

Putting $q=1\mu C,A=1m$;

$V=\frac{1}{4\pi {\epsilon }_0}.\frac{4\sqrt{2}}{1}$

$V=\frac{\sqrt{2}}{\pi {\epsilon }_0}\mu J$