Question

$AB$ is a resistance less conducting rod which forms a diameter of a conducting ring of radius $\text{r}$ rotating in a uniform magnetic field $\text{B}$ as shown in the diagram. The resistors $\text{R}_{1}$ and $\text{R}_{2}$ do not rotate. Then the current through the resistor $\text{R}_{1}$ is

• A. $\frac{B \omega r^{2}}{2 R_{1}}$
• B. $\frac{B \omega r^{2}}{2 R_{2}}$
• C. $\frac{B \omega r^{2}}{2 R_{1} R_{2}}\left(R_{1} + R_{2}\right)$
• D. $\frac{B \omega r^{2}}{2 \left(R_{1} + R_{2}\right)}$

Answer 1

Answer: (A)

The equivalent diagram is

The induced emf across the centre and any point on the
circumference is
$\epsilon =\frac{1}{2}B\omega \ell ^{2}=\frac{B \omega r^{2}}{2}$
∴ Current through $R_{1}=\frac{B \omega r^{2}}{2 R_{1}}$