Question

Four equal charges $q$ each are placed at four corners of a square of side a each. Work done in carrying a charge $-q$ from its centre to infinity is

• A. zero
• B. $\frac{\sqrt{2}q}{\pi {\epsilon }_{0}a}$
• C. $\frac{q^2}{2\pi {\epsilon }_{0}a}$
• D. $\frac{\sqrt{2}{q}^2}{\pi {\epsilon }_{0}a}$

Answer 1

Answer: (D)

Potential at the centre $O$ of the square due to four equal charges $q$ at the corners

$V=\frac{4q}{4\pi {\epsilon }_0(a\sqrt{2})/2}$
$=\frac{\sqrt{2}q}{\pi {\epsilon }_{0}a}$
$\therefore W_{0\infty }=-W_{\infty 0}$
$=-(-q)V$
$=\frac{\sqrt{2}{q}^2}{\pi {\epsilon }_{0}a}$