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A very small circular loop of radius a is concentric with a much larger circular loop of radius $b (> > a) .$ A constant current I is passed in the large loop which is kept fixed in space and the small loop is being rotated with constant angular velocity $ω$ about a diameter as shown. The resistance of the small loop is R and its self inductance is negligible. The current in the larger loop is clockwise. At t = 0 smaller loop lies in plane of large loop.

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External torque required to rotate smaller loop with constant angular speed is $\frac{ω}{R} {(\frac{π a^{2} μ_{0} I \sin ω t}{2 b})}^{2}$

Current in smaller loop is $\frac{μ_{0} π I a^{2} ω \sin ω t}{2 b R}$

External torque required to rotate smaller loop with constant angular speed is $\frac{ω}{R} {(\frac{π a^{2} μ_{0} I \sin ω t}{b})}^{2}$

Current in smaller loop is $\frac{μ_{0} π I a^{2} ω \sin ω t}{b R}$

answer is A, B.

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Detailed Solution

$(\frac{μ_{0} I}{2 π b}) π a^{2} \cos ω t = ϕ$

$i =$ current in small loop $= \frac{μ_{0} π I a^{2} ω \sin ω t}{2 b R}$
$τ$ due to magnetic field = $(π a^{2} i) B \sin θ$
$\frac{ω}{R} {(\frac{μ_{0} π a 2 I^{2}}{2 b})}^{2} (\sin ω t)$

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