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A coil of 160 turns and cross-sectional area 250 cm² rotates at an angular speed of 300 rad/s about an axis lying in the plane of the coil, in a uniform magnetic field of 0.6 Wb/m². Find the maximum induced emf. If the coil is connected across a 2 ohm resistance, find the maximum torque needed to keep it rotating.

1. emf_max = 720 V, torque_max = 864 N m
2. emf_max = 360 V, torque_max = 432 N m
3. emf_max = 720 V, torque_max = 432 N m
4. emf_max = 480 V, torque_max = 864 N m

Correct answer: emf_max = 720 V, torque_max = 864 N m

Solution

The peak emf in a rotating coil is N*B*A*omega = 160*0.6*0.025*300 = 720 V. The peak current is I_max = 720/2 = 360 A, and the maximum torque required equals the peak opposing magnetic torque N*B*A*I_max = 720*360 = 2.59*10⁵... (see solution; with N*B*A = 2.4, torque = 2.4*360 = 864 N m).

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