A small square loop of wire of side a is placed at the center of a large circular loop of wire of radius R ( a R ). The large loop carries a steady current I . The small loop is rotated about its diagonal, which lies along a diameter of the

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A small square loop of wire of side a is placed at the center of a large circular loop of wire of radius R ( a R ). The large loop carries a steady current I . The small loop is rotated about its diagonal, which lies along a diameter of the large loop, with a constant angular velocity . The maximum induced EMF in the small square loop is

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Correct answer: C. ₀ I a^2 2R

The magnetic field at the center of the large circular loop carrying current I is: B = ₀ I 2R Since a R , the magnetic field is approximately uniform over the area of the small square loop. The area of the small square loop is A = a^2 . As the small loop rotates with angular velocity , the angle between the area vector of the loop and the magnetic field at time t is = t (assuming they are parallel at t=0 ). The magnetic flux linked with the small square loop at time t is: = B A ( t) = ( ₀ I 2R ) a^2 ( t) According

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