A circular coil of one turn with a radius of 5.0 cm is rotated about a diameter at a constant angular speed of 80 revolutions per minute. A uniform magnetic field B = 0.010 T exists in a direction perpendicular to the axis of rotation. Determine the average of the squares of the emf induced over a long period.

Step-by-step solution

The magnetic flux linked with the coil at any time t is given by = N A B ( t) . The induced emf is = - d dt = N A B ( t) . The square of the induced emf is ^2 = (N A B )^2 ^2( t) . The average value of ^2( t) over a long period (or one complete cycle) is 1 2 . Therefore, the average of the squares of the emf is ^2 = 1 2 (N A B )^2 . Given values: N = 1 r = 5.0 cm = 0.05 m A = r^2 = (0.05)^2 = 2.5 10⁻³ m ^2 B = 0.010 T = 80 2 60 = 8 3 rad/s Substituting these values: N A B = 1 (2.5 10⁻³) 0.010 ( 8 3 ) = 20 ^2 3 10⁻⁵