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A rectangular coil of length a and width b consisting of N turns is rotated at...

A rectangular coil of length a and width b consisting of N turns is rotated at a frequency f in a uniform magnetic field as shown in the Figure. The coil is connected to two co-rotating cylinders against which metallic brushes make a sliding electrical contact. This is the basic design of an alternating current generator. (a) Find the emf,

E, induced in the coil as a function of time in

terms of B, N, a, b, and f. (b) Design a loop that will produce a root-mean-square emf of 120 V when rotated at 60.0 revolutions/s in a field of 0.5 T. This time dependent emf is equivalent to that of a wall socket in your home.

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