Question

The radius of the circular conducting loop shown in Fig. is $R$. Magnetic field is decreasing at a constant rate $\alpha$. Resistance per unit length of the loop is $\rho$.
Then, the current in wire $AB$ is ($AB$ is one of the diameters)

• A. $\frac{R\alpha }{2\rho }$ from $A$ to $B$
• B. $\frac{R\alpha }{2\rho }$ from $B$ to $A$
• C. $\frac{R\alpha }{\rho }$ from $A$ to $B$
• D. $0$

Answer 1

The correct option is A $\frac{R\alpha }{2\rho }$ from $A$ to $B$

We know

$e=\frac{d\varphi }{dt}=A\frac{dB}{dt}$

$Resistance=2\pi R\rho$

$e=\pi R^2\alpha$

$I=\frac{e}{Resistance}$

$=\frac{\pi R^2\alpha }{2\pi R\rho }$

$=\frac{R\alpha }{2\rho }$ From A to B