# HW25_pdf - mcconnell(kam2342 – homework25 – Turner...

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Unformatted text preview: mcconnell (kam2342) – homework25 – Turner – (60230) 1 This print-out should have 10 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 2) 10.0 points An electric motor has 115 turns of wire wrapped on a rectangular coil, of dimensions 2 . 3 cm by 4 . 33 cm. Assume that the mo- tor uses 11 . 6 A of current and that a uniform . 618 T magnetic field exists within the mo- tor. What is the maximum torque delivered by the motor? Correct answer: 0 . 821032 N m. Explanation: Let : w = 2 . 3 cm , ℓ = 4 . 33 cm , I = 11 . 6 A , and B = 0 . 618 T . Force : vector F = I vector ℓ × vector B Torque : vector τ = vectorr × vector F Power : P = τ ω . Magnetic force exerted on the 4 . 33 cm side is, F = N I ℓ B = (115 turns) (11 . 6 A) (0 . 0433 m) (0 . 618 T) = 35 . 697 N . So, the maximum torque on the loop due to the magnetic field is τ max = F × w = (35 . 697 N) × (0 . 023 m) = . 821032 N m . 002 (part 2 of 2) 10.0 points If the motor rotates at 4170 rev / min, what is the peak power produced by the motor? Correct answer: 358 . 529 W. Explanation: P = τ ω = (0 . 821032 N m) (436 . 681 s − 1 ) = 358 . 529 W . 003 10.0 points A long solenoid has a coil made of fine wire inside it and coaxial with it. I Outside solenoid has n turns per meter Inside coil has N turns r R Given a varying current I in the outer solenoid, what is the emf induced in the inner loop? 1. E =- π Rμ N dI dt 2. E =- π R 2 μ nN dI dt correct 3. E =- π Rμ n dI dt 4. E =- π r μ nN dI dt 5. E =- π r μ N dI dt 6. E =- π r 2 μ nN dI dt 7. E =- π r μ n dI dt 8. E =- π Rμ nN dI dt 9. E =- π R 2 μ n dI dt 10. E =- π r 2 μ n dI dt Explanation: The magnetic field of a solenoid is B = μ nI . The magnetic flux is Φ B = B · A = ( μ nI ) ( π R 2 ) , mcconnell (kam2342) – homework25 – Turner – (60230) 2 so the emf is E =- d Φ B dt =- π R 2 μ nN dI dt . We are interested in the emf in the inner coil, so we use the smaller area of the inner coil rather than the larger solenoid area. keywords: 004 (part 1 of 2) 10.0 points Two infinitely long solenoids (seen in cross section in the figure below) thread a circuit. Given: a = 0 . 6 m , r 1 = 0 . 2 m , r 2 = 0 . 1 m , Δ B Δ t = 90 T / s , R l = 8 . 7 Ω , R m = 5 . 6 Ω , and R r = 2 . 5 Ω , as in the figure below. The magnitude of B inside each solenoid is the same and is 300 T at time t = 0. B in B out I l I m I r r 2 R m R l R r r 1 a a a What is the magnitude of the current, I m , in middle resistor, R m ? Correct answer: 0 . 625938 A. Explanation: Basic Concept: Faraday’s Law: E =- d Φ B dt Ohm’s Law: I = V R Junction Rule: n summationdisplay i =1 I i = 0 Solution: Note: The side-length, a , of the circuit loop is not necessary for this problem....
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HW25_pdf - mcconnell(kam2342 – homework25 – Turner...

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