A magnetic field is perpendicular to the plane of a single-turncircular coil. Th

Question

A magnetic field is perpendicular to the plane of a single-turncircular coil. The magnitude of the field is changing, so that anemf of 0.82 V and a current of3.0 A are induced in the coil. The wire isthe re-formed into a single-turn square coil, which is used in thesame magnetic field (again perpendicular to the plane of the coiland with a magnitude changing at the same rate). What emf andcurrent are induced in the square coil? emf Enter a number. 1 V current Enter a number. 2 A Enter a number. Enter a number. emf Enter a number. 1 V current Enter a number. 2 A

Explanation / Answer

The induced emf is proportional to the area of the loop. So wecan write each area (circle and square) in terms of the length ofthe wire, which is the circumference of the circle and theperimeter of the square: .    circle:     L = 2r     r = L /2        and  area = r2 = L2/4 . square:   L = 4s       s =L/4         area =s2 = L2 / 16 . So the ratio of square area to circle areais    (L2 / 16) / (L2 / 4) =   0.7854 . So the emf induced in the square is   0.7854 timesthat of the circle or... .        emf = 0.7854*0.82 =    0.644 volts .    and   current = 0.7854 *3.0 =  2.356 A

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