Question

$\begin{array}{c}\text{Four equal charges}Q\text{are placed at the four corners of a square of side a each. Work done i}\\ \text{removing a charge}-Q\text{from its centre to infinity is:}\end{array}$

• A. $zero$
• B. $\frac{\sqrt{2}{Q}^2}{4\pi {ϵ}_{0}a}$
• C. $\frac{\sqrt{2}{Q}^2}{\pi {ϵ}_{0}a}$
• D. $\frac{Q^2}{2\pi {ϵ}_{0}a}$

Answer 1

Answer: (C)

$\frac{\sqrt{2}{Q}^2}{\pi {ϵ}_{0}a}$

Work done $=(-Q)\Delta V$

$=(-Q)(V_f-V_i)$ $V_f=$ final potential

$V_i=$ initial potential

$=(-Q)(0-V_i)=Q{V}_i$

on 4 charges work done is given as:

$\Rightarrow W=Q[\frac{1}{4\pi {\in }_0}\times \frac{Q}{\frac{a}{\sqrt{2}}}]\times 4$

$=\frac{\sqrt{2}{Q}^2}{\pi {\in }_{0}a}$