A rectangular coil of N turns and of length a and width b is rotated at frequency
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A rectangular coil of N turns and of length a and width b is rotated at frequency ƒ in a uniform magnetic field B, as indicated in Figure. The coil is connected to co-rotating cylinders, against which metal brushes slide to make contact.
(a) Show that the emf induced in the coil is given (as a function of time t) by
ξ = 2πƒNαbB sin(2πƒt) = ξ0 sin(2πƒt).
This is the principle of the commercial alternating-current generator.
(b) What value of Nab gives an emf with ξ0 = 150 V when the loop is rotated at 60.0 rev/s in a uniform magnetic field of 0.500 T?
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