Question

Three charges $+3Q,+2Q$ and $-Q$ respectively are located at a distance $"a"$ from the origin as shown in the figure. $(k=\frac{1}{4\pi {ϵ}_0})$. A fourth charge $+3Q$ is slowly moved in from inifinite to the point O. The work done by an external agent in this process is

• A. $\frac{k{Q}^2}{a}\left[\frac{3}{\sqrt{2}+1}\right]$
• B. $\frac{k{Q}^2}{a}[\frac{3}{\sqrt{2}}-1]$
• C. $\frac{12k{Q}^2}{a}$
• D. $\frac{k{Q}^2}{a}\left(\frac{4}{3}\right)$

Answer 1

The correct option is C $\frac{12k{Q}^2}{a}$

The net electric potential at O is given by sum of electric potentials due to sum of individual potentials as,

$V=\frac{k}{a}[-Q+2Q+3Q]$

$V=\frac{k}{a}\left(4Q\right)$

The net electric potential at infinity is zero.

$\text{Work done in moving charge(3Q) from infinity to O is}=\Delta V\left(3Q\right)$

$=\left(\frac{k}{a}\right(4Q)-0)\left(3Q\right)=\frac{12k{Q}^2}{a}$