Question

Four equal charges $Q$ are placed at the four corners of a square of side '$a$' each. Work done in removing a charge $-Q$ from its centre to infinity is:

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

Answer 1

Answer: (C)

$\sqrt{2}{Q}^2/\pi {ϵ}_{0}a$

We know P.E. between $Q_{1}and{Q}_2=\frac{k{Q}_1{Q}_c}{r}$

Now P.E. reduced when $-Q$ is removed

is $4\times \left(\frac{k\left(Q\right)(-Q)}{\frac{a}{\sqrt{2}}}\right)=\frac{-\sqrt{2}{Q}^2}{ϵl_{0}a}$

Now work done $=$ change in P.E $=0-\left(\frac{-\sqrt{2}{Q}^2}{\pi l_{0}a}\right)$

$=\frac{\sqrt{2}{Q}^2}{\pi {ϵ}_{0}a}$