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. $\frac{\sqrt{2}q}{\pi\varepsilon_{0}a}$
• C. $\frac{q^{2}}{2\pi\varepsilon_{0}a}$
• D. $\frac{\sqrt{2}q^{2}}{\pi\varepsilon_{0}a}$

Answer 1

Answer: (D)

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

$V =\frac{4 q}{4 \pi \varepsilon_{0}(a \sqrt{2}) / 2} $
$=\frac{ \sqrt{2}q}{\pi \varepsilon_0 a}$
$ \therefore W_{0 \infty} =-W_{\infty 0} $
$=-(-q) V$
$=\frac{\sqrt{2} q^{2}}{\pi \varepsilon_{0} a}$