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

Answer 1

Answer: (B)

$\frac{\sqrt{2}q^{2}}{\pi\varepsilon_{0}a}$

Answer 2

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

$V = \frac{4q}{4\pi\varepsilon_{0}(a\sqrt{2})/2} = \frac{\sqrt{2q}}{\pi\varepsilon_{0}a}$

$W_{0 \rightarrow \infty} = - {{W_{\infty}}_{\rightarrow}}_{0} = - ( - q)V = \frac{\sqrt{2}q^{2}}{\pi\varepsilon_{0}a}$