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In figure, R is a fixed conducting ring of negligible resistance and radius a. PQ is a uniform rod of resistance r. It is hinged at the center of the ring and rotated about this point in clockwise direction with a uniform angular velocity $ω$ . There is a uniform magnetic field of strength B pointing inward and r is a stationary resistance. Then

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current through r is zero

current through r is $(2 {Bωa}^{2}) / 5 r$

direction of current in external resistance r is from center to circumference

direction of current in external resistance r is from circumference to center

answer is B.

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Detailed Solution

Equivalent circuit:

Current is from S to O, i.e., from circumference to centre

Applying KVL in the upper loop ,

$\frac{1}{2} B ω a^{2} - \frac{I}{2} . \frac{r}{2} - I . r = 0 \Rightarrow I = \frac{2 B ω a^{2}}{5 r}$

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