A circular coil consisting of one turn with a radius of 5.0 cm rotates about a diameter at a steady angular speed of 80 revolutions per minute. A uniform magnetic field B = 0.010 T is directed perpendicular to the axis of rotation. If the ends of the coil are connected to a 100 resistance, determine the heat produced in the circuit during one minute. Assume the resistance of the coil itself is negligible.

Step-by-step solution

Given: Number of turns, N = 1 Radius of the coil, r = 5.0 cm = 0.05 m Area of the coil, A = r^2 = (0.05)^2 = 2.5 10⁻³ m ^2 Angular speed, = 80 rpm = 80 2 60 = 8 3 rad/s Magnetic field, B = 0.010 T Resistance, R = 100 Time, t = 1 min = 60 s The maximum induced emf in the coil is: ₀ = N A B ₀ = 1 (2.5 10⁻³ ) 0.010 ( 8 3 ) ₀ = 20 10⁻⁵ ^2 3 = 2 10⁻⁴ ^2 3 V The average power dissipated as heat is given by: P = _ rms ^2 R = ₀^2 2R P = 1 2 100 ( 2 10⁻⁴ ^2 3 )^2 P = 1 200 4 10⁻⁸ ^4 9 = 10⁻⁸ ^4 450 W The total heat produced