Question

The given two fixed rings of radius R lie in XY plane as shown in the figure. Linear charge density of the rings A and B varies as per the relation $\lambda ={\lambda }_0\sin \theta$ and $\lambda ={\lambda }_0\cos \theta$ respectively where $\theta$ is measured from +x axis. Distance between the centre of the two rings is $r>>R$.

• A. Force of interaction between the two ring is $\frac{3}{4}\times \frac{{\lambda }_0^2\pi }{{ϵ}_0}(\frac{R}{r}{)}^4$
• B. Force of interaction between the two ring is $\frac{3}{2}\times \frac{{\lambda }_0^2\pi }{{ϵ}_0}(\frac{R}{r}{)}^4$
• C. Potential energy of interaction between the two ring is $\frac{\pi {\lambda }_0^2{R}^4}{4{ϵ}_0{r}^3}$
• D. Potential energy of interaction between the two ring is zero.

Answer 1

The correct option is C Potential energy of interaction between the two ring is $\frac{\pi {\lambda }_0^2{R}^4}{4{ϵ}_0{r}^3}$

Potential energy$=\frac{1}{4\pi {ϵ}_0}\frac{\pi {\lambda }_0^2{R}^4}{r^3}$

when $\lambda ={\lambda }_0\cos \theta \theta =90°$

and $r=$ radius of ring B

$R=$ radius of ring A