Question

A fourth charge with charge $+3q$ is slowly moved in from infinity to point $P$. How much work must be done in this process?

• A. $\frac{3q^2}{\sqrt{2}\pi {ϵ}_{0}a}$
• B. $\frac{3q^2}{2\pi {ϵ}_{0}a}$
• C. $\frac{3q^2}{\sqrt{3}\pi {ϵ}_{0}a}$
• D. $\frac{3q^2}{4\pi {ϵ}_{0}a}$

Answer 1

The correct option is A $\frac{3q^2}{\sqrt{2}\pi {ϵ}_{0}a}$

$\begin{array}{c}Wehave\\ u=\frac{k\left(q\right)\left(3q\right)}{x}+\frac{k\left(2q\right)\left(3q\right)}{x}+\frac{k\left(-q\right)\left(3q\right)}{x}\\ =\frac{6k{q}^2}{x}:x=\frac{9}{\sqrt{2}}\\ =\frac{6k{q}^2\sqrt{2}}{a}\\ =\frac{6q^2\sqrt{2}}{4\pi {\epsilon }_{0}a}=\frac{3q^2}{\sqrt{2}\pi {\epsilon }_{0}a}\\ Hence,theoptionAiscorrectanswer.\end{array}$