Question

A ring of radius r is moving at constant velocity v along axis of a circular loop. If current in loop is i and radius of loop is R where R>>r, then emf induced in ring when x>>R is

• A. $\frac{{\mu }_0\pi i{R}^2{r}^{2}v}{x^4}$
• B. $\frac{2{\mu }_0\pi i{R}^2{r}^2}{x^4}$
• C. $\frac{5}{3}\frac{{\mu }_0\pi i{R}^2{r}^2}{x^4}$
• D. $\frac{3}{2}\frac{{\mu }_0\pi i{R}^2{r}^{2}v}{x^4}$

Answer 1

The correct option is D $\frac{3}{2}\frac{{\mu }_0\pi i{R}^2{r}^{2}v}{x^4}$


$B=\frac{{\mu }_{0}i{R}^2}{2x^3}$ $\varphi =B.A=\frac{{\mu }_{0}i{R}^2}{2x^3}\pi r^2$

$\epsilon =\frac{d\varphi }{dt}=\frac{3}{2}\frac{{\mu }_0\pi i{R}^2{r}^{2}v}{x^4}$