Question

A thin circular ring of area $A$ is held perpendicular to a uniform magnetic field of induction $B$. A small cut is made in the ring and a galvanometer is connected across the ends such that the total resistance of the circuit is $R$. When the ring suddenly squeezed to zero area, the charge flowing through the galvanometer is :

• A. $\frac{BR}{A}$
• B. $\left(AB\right)/R$
• C. $ABR$
• D. $\left(E^{2}A\right)/R^2$
• E. $none$

Answer 1

Answer: (B)

$\left(AB\right)/R$

Magnetic Flux

$\varphi =BA$

$\Delta \varphi =\Delta \left(BA\right)=B\Delta A=BA$

Induced EMF

$E=\frac{\Delta \varphi }{\Delta t}=\frac{BA}{\Delta t}$

$i=\frac{E}{R}=\frac{BA}{R\Delta t}$

$\frac{Q}{\Delta t}=\frac{BA}{R\Delta t}$

$Q=\frac{BA}{R}$