Faraday\'s Law of Induction - Time Varying Magnetic Field Problem Consider the c
ID: 2299629 • Letter: F
Question
Faraday's Law of Induction - Time Varying Magnetic Field Problem Consider the cross - sectional view of the cylinder illustrated below. The volume of the cylinder is filled with a time varying magnetic field. A metal rod is placed across the cross - section of the cylinder thereby completing a circuit. Compute the power dissipated as a function of time between the ends of the rod if the resistance in the rod is 2ohm., R = 70 cm, l - 50 cm and B = Boe - tau where Bo = 0.55 T and tau = 0.1 seconds?Explanation / Answer
y = sqrt(R^2-l/2)^2) = sqrt(70^2-25^2) = 65.3 cm
r = R-y = 70-65.3 = 4.7
A = (pi/2)*r^2 = (3.14/2)*0.047^2 = 3.46813e?3 m^2
emf = dBA/dt = A*dB/dt = A*Bo*e^-t/tow * (-1/tow) = 3.46813e?3 * 0.55*e^-t/0.1*(-1/0.1) = 19.074715e?3*e^-10t
power = e^2/R = 19.074715e?3*e^-10t)^2/2 = 9.5373575e?3*e^-10t
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