Question

$AB$ is a resistanceless conducting rod which forms a diameter of a conducting ring of radius $r$ rotating in a uniform magnetic field $B$ as shown in the figure. The resistance $R_1$ and $R_2$ do not rotate. Then current through the resistor $R_1$ is -

• A. $\frac{B\omega r^2}{2R_1}$
• B. $\frac{B\omega r^2}{2R_2}$
• C. $\frac{B\omega r^2}{2R_1{R}_2}(R_1+R_2)$
• D. $\frac{B\omega r^2}{2(R_1+R_2)}$

Answer 1

The correct option is A $\frac{B\omega r^2}{2R_1}$


The induced EMF across the centre$\left(O\right)$ and any point on the circumference is,

$\epsilon =\frac{1}{2}B\omega l^2=\frac{B\omega r^2}{2}$

The equivalent diagram is,

$\therefore$ Current through $R_1$,

$I_1=\frac{\epsilon }{R_1}=\frac{B\omega r^2}{2R_1}$