Question

# A rectangular coil of N turns and of length a and width b is rotated at frequency in a uniform magnetic field , 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 This is the principle of the commercial alternating-current generator. (b) What value of Nab gives an emf with when the loop is rotated at 60.0 rev/s in a uniform magnetic field of 0.500 T?

Medium
Solution
Verified by Toppr

## (a) It should be emphasized that the result, given in terms of , could as easily be given in terms of or even where is a phase constant . The angular position of the rotating coil is measured from some reference line (or plane), and which line one chooses will affect whether the magnetic flux should be written as or Here our choice is such that since the coil is rotating steadily, increases linearly with time. Thus, (equivalent to ) if is understood to be in radians (and would be the angular velocity). since the area of the rectangular coil is , Faraday's law leads towhich is the desired result, shown in the problem statement. The second way this is written is meant to emphasize that the voltage output is sinusoidal (in its time dependence) and has an amplitude of (b) We solvewhen rev/s and T. The three unknowns are a, and which occur in a product; thus, we obtain

Solve any question of Magnetism and Matter with:-