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. The resistors $R_{1} and R_{2}$ do not rotate. Then current through the resistor R1 is :

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\frac{B ω r^{2}}{2 R_{2}}

\frac{B ω r^{2}}{2 R_{1}}

\frac{B ω r^{2}}{2 R_{1} R_{2}} (R_{1} + R_{2})

\frac{B ω r^{2}}{2 (R_{1} + R_{2})}

answer is A.

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Detailed Solution

The induced emf across the centre and any point on the circumference is

$| e | = \frac{1}{2} B ω l^{2} = \frac{B ω r^{2}}{2}$

Current through $R_{1} = \frac{B ω r^{2}}{2 R_{1}}$

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