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Unformatted text preview: gilvin (jg47854) 20. Lenz and Faradays laws meyers (21235) 1 This print-out should have 26 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. This homework is due Tuesday, April 26, at midnight Tucson time. 001 (part 1 of 3) 10.0 points A rectangular loop of copper wire of resis- tance R has width a and length b . The loop is stationary in a constant, the magnetic field B at time t = 0 seconds is directed into the page as shown below. The uniform magnetic field varies with time t according to the rela- tionship B = B cos t , where and B are positive constants and B is positive when the field is directed into the page. B B B B b a n turns The direction of the induced current in the loop when t = 2 , after the magnetic field begins to oscillate is 1. clockwise. correct 2. undetermined, since the current is zero. 3. counter-clockwise. Explanation: When t = 2 , B = B cos 2 = 0; i.e. , the field has been decreasing, and is about to change direction. The induced current will be in a direction to oppose this change; i.e. , clockwise. 002 (part 2 of 3) 10.0 points What is the expression for the magnitude of the induced current in the loop as a function of time in terms of a , b , B , , R , t , and fundamental constants. 1. I = a bB R sin t 2. I = a bB R sin t 3. I = RB a b sin t 4. I = a b B R sin t 5. I = a b B R sin t correct 6. I = R B a b sin t Explanation: Calculating the flux, = a bB cos t. Calculating the emf , E = d dt (negative sign not required) = a b B sin t. Using Ohms Law I = E R = a b B R sin t. 003 (part 3 of 3) 10.0 points Select a sketch a graph of the induced cur- rent I vs t , taking clockwise current to be positive. 1. t I 2 3 2 2 5 2 3 gilvin (jg47854) 20. Lenz and Faradays laws meyers (21235) 2 2. t I 2 3 2 2 5 2 3 correct 3. t I 2 3 2 2 5 2 3 4. t I 2 3 2 2 5 2 3 5. t I 2 3 2 2 5 2 3 6. t I 2 3 2 2 5 2 3 Explanation: The graph is a sine wave with period 2 . t I 2 3 2 2 5 2 3 004 10.0 points A coil is wrapped with 382 turns of wire on the perimeter of a circular frame (of radius 62 cm). Each turn has the same area, equal to that of the frame. A uniform magnetic field is directed perpendicular to the plane of the coil. This field changes at a constant rate from 24 mT to 60 mT in 42 ms. What is the magnitude of the induced E in the coil at the instant the magnetic field has a magnitude of 49 mT? Correct answer: 395 . 412 V....
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