Question

Two identical thin rings, each of radius r metres, are coaxially placed at a distance (r) metres apart. If q1 coul and q2 coul are respectively. The charges uniformaly spread on the two rings. The work done in moving a charge (q) from the centre of one ring to that of other is

Answer 1

Two identical thin rings, each of radius r metres, are coaxially placed at a distance (r) metres apart. If q1 coul and q2 coul are respectively. The charges uniformaly spread on the two rings. The work done in moving a charge (q) from the centre of one ring to that of other is.

solution : potential at the centre of ring 1, $V_1=\frac{Kq_1}{r}+\frac{Kq_2}{\sqrt{r^2+r^2}}$

$V_1=\frac{kq_1}{r}+\frac{kq_2}{\sqrt{2}r}$

potential at the centre of ring 2, $V_2=\frac{kq_2}{r}+\frac{kq_1}{\sqrt{2}r}$

now, workdone by moving a charge Q from the centre of one ring to that of other , W = q∆V

= q$\left[\frac{kq_2}{r}+\frac{kq_1}{\sqrt{2}r}-\frac{kq_1}{r}-\frac{kq_2}{\sqrt{2}r}\right]$

= $\frac{kq}{r}\left[(q_2-q_1)+\frac{(q_1-q_2)}{\sqrt{2}}\right]$

hence answer is $\frac{kq}{r}\left[(q_2-q_1)+\frac{(q_1-q_2)}{\sqrt{2}}\right]$