# 22 - Kapoor(mk9499 – oldhomework 22 – Turner –(60230...

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Unformatted text preview: Kapoor (mk9499) – oldhomework 22 – Turner – (60230) 1 This print-out should have 12 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 6) 10.0 points A rolling axle is pushed along horizontal rails, ℓ = 0 . 777 m apart, at a constant speed v = . 714 m / s. A resistor R = 14 . 9 Ω is connected to the rails at points a and b as shown in diagram and is the only significant resistance in the loop. There is a uniform magnetic field B = 4 . 28 T vertically downward. a b R v B rolling axle What is the induced current in the resis- tor? Correct answer: 0 . 159359 A. Explanation: Let : B = 4 . 28 T , ℓ = 0 . 777 m , v = 0 . 714 m / s , and R = 14 . 9 Ω . Ohm’s law: I = E R The magnitude of the induced emf is E = B ℓ v , which gives an induced current of I = V R = B ℓ v R = (4 . 28 T)(0 . 777 m)(0 . 714 m / s) 14 . 9 Ω = . 159359 A . 002 (part 2 of 6) 10.0 points What is the magnitude of the horizontal force F required to keep the axle rolling at constant speed? Correct answer: 0 . 529958 N. Explanation: As the axle moves toward the resistor, the area of the current loop decreases. Hence the induced vector B ind is downward giving I clockwise from above. The magnetic force (by the ex- ternal field) acting on the axle is F mag = I ℓ B to the right. Hence the applied force required to cancel the magnetic force has the same magnitude (but the opposite direction). F app = I ℓ B = ( B ℓ ) 2 v R = . 529958 N . The axle must be pushed towards the resistor. 003 (part 3 of 6) 10.0 points Which end of the resistor ( a or b ) is at the highest potential while the axle is still to the right of the resistor? 1. b correct 2. a Explanation: Before rolling past the resistor, current flows through R from b to a , hence b is at a higher potential. After going past the re- sistor, Lenz’s law dictates that the induced vector B ind is now upward. This requires the current to reverse direction and becoming counter- clockwise. However, the emf across the axle does not change sign so the current goes through R in the same direction (from b to a , away from the resistor)....
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22 - Kapoor(mk9499 – oldhomework 22 – Turner –(60230...

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