Question

A point charge is surrounded symmetrically by six identical charges at distance r as shown in the figure. How much work is done by the forces of electrostatic repulsion when the point charge q at the centre is removed at infinity:

• A. Zero
• B. $\frac{6q^2}{4\pi {ϵ}_{0}r}$
• C. $\frac{q^2}{4\pi {ϵ}_{0}r}$
• D. $\frac{12q^2}{4\pi {ϵ}_{0}r}$

Answer 1

The correct option is B $\frac{6q^2}{4\pi {ϵ}_{0}r}$

Here the work done would be the change in potential experienced by the test charge.
The potential at infinity would be zero as r = infinity.
The potential due to single charge is given as
$U=\frac{kq{q}^{{}^{\prime }}}{r}$
here q = q'
Now, the potential due to the six charges would be
$U=\frac{6k{q}^2}{r}$
So, the work done would be
W = U - 0
or
$W=\frac{6k{q}^2}{r}$