A rectangular coil of 56 turns, dimensions 0.100 m by 0.200 m, and total resista

Question

A rectangular coil of 56 turns, dimensions 0.100 m by 0.200 m, and total resistance 10.0 H rotates with angular speed 32.0 rad/s about the y axis in a region where a 1.00-T magnetic field is directed along the x axis. The time t = 0 is chosen to be at an instant when the plane of the coil is perpendicular to the direction of B. Calculate the maximum induced emf in the coil. V Calculate the maximum rate of change of magnetic flux through the coil. Wb/s Calculate the induced emf at t = 0.050 0 s. V Calculate the torque exerted by the magnetic field on the coil at the instant when the emf is a maximum.

Explanation / Answer

a)

emf = N A B w

emf = (56) * (0.100*0.200) * (1.0) * (32.0)

emf = 35.84 V

b)

dphi/dt = emf = 35.84 Wb/s

c)

emf = (35.84) * sin(w t) = (35.84) * sin((32)*(0.05)) = 35.84 V

d)

i = V/R = (35.84)/(10) = 3.584 A

tau = N A i B = (56) * (0.100*0.200) * (3.584) * (1.0) = 4.01 N.m

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