Question

A point charge $-q$ is carried from a point A to another point B on the axis of a charged ring of radius 'r' carrying a charge $+q$/ If the point A is at a distance $\frac{4}{3}$r from the centre of the ring and the point B is $\frac{3}{4}$r from the centre but on the opposite side, what is the net work that need to be done for this?

• A. $-\frac{7}{5}\frac{q^2}{4\pi {\epsilon }_{0}r}$
• B. $-\frac{1}{5}\frac{q^2}{4\pi {\epsilon }_{0}r}$
• C. $\frac{7}{5}\frac{q^2}{4\pi {\epsilon }_{0}r}$
• D. $\frac{1}{5}\frac{q^2}{4\pi {\epsilon }_{0}r}$

Answer 1

Answer: (B)

$-\frac{1}{5}\frac{q^2}{4\pi {\epsilon }_{0}r}$

$W=U_B=V_A$
$W=-\frac{Kqq}{\sqrt{r^2+\frac{9}{16}{r}^2}}+\frac{K{q}^2}{\sqrt{r^2+\frac{16}{9}{r}^2}}$
$=-\frac{4k{q}^2}{5r}+\frac{3k{q}^2}{5r}=-\frac{k{q}^2}{5r}$
$=-\frac{1}{5}\frac{q^2}{4\pi {\epsilon }_{0}r}$