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Faraday\'s Law and Ohm\'s Law in one problem! A uniform magnetic field is orient

ID: 1268456 • Letter: F

Question

Faraday's Law and Ohm's Law in one problem! A uniform magnetic field is oriented into the page as shown above. The field is time-varying for all times t = 0 according to the following prescription: Bvect(t) = -B0 e-t/tau khat where B0 = 10.0 Tesla and tau = 2.00 seconds. A square hoops of conducting wire is embedded in the B-field as shown. The side of each square d = 0.50 meters. The loops includes a (physically small) resistor Rl = 20 Ohms. At time t = 2.0 seconds, calculate the current through the resistor. If the current is not zero, which way is it flowing? At time t = 2.0 seconds, calculate the magnitude and direction of any force that is applied to the bottom-most straight segment of the square loop due the magnetic field.

Explanation / Answer

A) emf = - d(phi)/dt = - A dB/dt

= - 0.25 x [Bo / (tau)] x e^-(t/2) = - 1.25 e^-(t/2)  V

emf at t = 2 = -1.25 x e^-1 = - 0.46 V

so i = emf / R = 0.46 / 20 = 0.023 A

since B is increasing so i is directed anticlockwise

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B) so F = iLB = 0.023 x 0.5 x 10e^-1 = 0.0423 N

from RH rule F is directed upwards