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Unformatted text preview: dzifanu (sd26397) – hw 11 – opyrchal – (121102) 1 This printout should have 11 questions. Multiplechoice questions may continue on the next column or page – find all choices before answering. 001 10.0 points Find the magnetic flux through a 450turn solenoid of length 30 cm and radius 2 cm that carries a current of 2 A. The permeability of free space is 4 π × 10 7 T · m / A. Correct answer: 0 . 00213183 Wb. Explanation: Let : N = 450 , I = 2 A , r = 2 cm = 0 . 02 m , ℓ = 30 cm = 0 . 3 m , and μ = 4 π × 10 7 T · m / A , The magnetic field inside a long solenoid is B = μ N ℓ I , so the magnetic flux is Φ = N B A = N parenleftbigg μ N ℓ I parenrightbigg π r 2 = μ N 2 π r 2 I ℓ = (4 π × 10 7 T · m / A) (450) 2 . 3 m × π (0 . 02 m) 2 (2 A) = . 00213183 Wb . keywords: 002 10.0 points A coil is wrapped with 560 turns of wire on the perimeter of a circular frame (of radius 39 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 21 mT to 68 mT in 29 ms. What is the magnitude of the induced E in the coil at the instant the magnetic field has a magnitude of 56 mT? Correct answer: 433 . 678 V. Explanation: Basic Concepts: E = N d Φ B dt Φ B ≡ integraldisplay vector B · d vector A = B · A Solution: E = N d Φ B dt = N A Δ B Δ t = N π r 2 ( B 2 B 1 ) Δ t = (560) π (39 cm) 2 × (68 mT) (21 mT) 29 ms = 433 . 678 V E = 433 . 678 V . 003 10.0 points A coil with N 1 = 20 . 1 turns and radius r 1 = 10 . 8 cm surrounds a long solenoid of radius r 2 = 1 . 44 cm and N 2 ℓ 2 = n 2 = 520 m 1 (see the figure below). The current in the solenoid changes as I = I sin( ω t ), where I = 5 A and ω = 120 rad / s. R a b E ℓ 2 ℓ 1 Outside solenoid has N 1 turns Inside solenoid has N 2 turns A 1 A 2 dzifanu (sd26397) – hw 11 – opyrchal – (121102) 2 What is the magnitude of the induced emf , E AB , across the 20 . 1 turn coil at t = 1000 s? Correct answer: 0 . 00427891 V. Explanation: Faraday’s Law for solenoid E = N d Φ dt = N d ( BA ) dt . Magnetic field induced by solenoid B = μ n I . Faraday’s Law for solenoid E = N d Φ dt = N d ( BA ) dt ....
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 Spring '09
 PRODAN
 Physics, Magnetic Field, Correct Answer, Wire

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