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Unformatted text preview: aldawsari (ma28683) HW13 Betancourt (16856) 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. 29.1-29.3 001 10.0 points An 18 . 1 turns circular coil with radius 7 . 72 cm and resistance 5 . 85 is placed in a magnetic field directed perpendicular to the plane of the coil. The magnitude of the magnetic field varies in time according to the expression B = a 1 t + a 2 t 2 , where a 1 = 0 . 0537 T / s, a 2 = 0 . 0526 T / s 2 are constants, time t is in seconds and field B is in Tesla. Find the magnitude of the induced emf in the coil at t = 8 . 15 s. Correct answer: 0 . 308759 V. Explanation: Let : n = 18 . 1 turns , r = 7 . 72 cm = 0 . 0772 m , R = 5 . 85 , a 1 = 0 . 0537 T / s , a 2 = 0 . 0526 T / s 2 , and t = 8 . 15 s . The area of the circular coil is A = r 2 = (0 . 0772 m) 2 = 0 . 0187234 m 2 , so from Faradays law, E = n d B dt = n dAB dt = nA dB dt = nA ( a 1 + 2 a 2 t ) = (18 . 1 turns) (0 . 0187234 m 2 ) [0 . 0537 T / s + 2 (0 . 0526 T / s 2 ) (8 . 15 s)] = . 308759 V , which has a magnitude of . 308759 V . 002 (part 1 of 2) 10.0 points In the arrangement shown in the figure, the resistor is 8 and a 3 T magnetic field is directed out of the paper. The separation between the rails is 4 m . Neglect the mass of the bar. An applied force moves the bar to the left at a constant speed of 8 m / s . Assume the bar and rails have negligible resistance and friction. m 1g 8 m / s 8 3 T 3 T I 4m Calculate the applied force required to move the bar to the left at a constant speed of 8 m / s. Correct answer: 144 N. Explanation: Motional emf is E = B v . Magnetic force on current is vector F = I vector vector B . Ohms Law is I = V R . The motional emf induced in the circuit is E = B v = (3 T) (4 m) (8 m / s) = 96 V . From Ohms law, the current flowing through the resistor is I = E R = 96 V 8 = 12 A . aldawsari (ma28683) HW13 Betancourt (16856) 2 Thus, the magnitude of the force exerted on the bar due to the magnetic field is F B = I B = (12 A)(4 m)(3 T) = 144 N . To maintain the motion of the bar, a force must be applied on the bar to balance the magnetic force F = F B = 144 N ....
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This note was uploaded on 01/27/2011 for the course PHYS 251 taught by Professor Gavrine during the Spring '10 term at Purdue University-West Lafayette.
- Spring '10