121homework 10

121homework 10 - Felder, Jacob Homework 11 Due: Nov 28...

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Unformatted text preview: Felder, Jacob Homework 11 Due: Nov 28 2006, 9:00 pm Inst: Vitaly 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page find all choices before answering. The due time is Central time. 001 (part 1 of 1) 10 points Given: = 1 . 25664 10- 6 N / A 2 . A 1 m long large coil with a radius of 17 . 8 cm and 390 turns surrounds a 7 . 3 m long solenoid with a radius of 7 . 8 cm and 6600 turns, see figure below. The current in the solenoid changes as I = I sin(2 f t ) , where I = 30 A and f = 60 Hz. 7 . 3 m 1 m Inside solenoid has 6600 turns Outside coil has 390 turns 17 . 8 cm 7 . 8 cm 36 E = E sin t Find the maximum induced emf E in the large coil. Correct answer: 95 . 7827 V. Explanation: Let : R = 36 , r 1 = 17 . 8 cm = 0 . 178 m , r 2 = 7 . 8 cm = 0 . 078 m , A 1 = r 2 1 = 0 . 0995382 m 2 , A 2 = r 2 2 = 0 . 0191134 m 2 , N 1 = 390 , N 2 = 6600 , 1 = 1 m , 2 = 7 . 3 m , n 1 = N 1 1 = 390 turns / meter , n 2 = N 2 2 = 904 . 11 turns / meter , I = 30 A , and = 2 f = 376 . 991 rad / s . 2 1 Inside solenoid has N 2 turns Outside coil has N 1 turns A 1 A 2 R E = E sin t Basic Concepts: Faradays law E =- N d dt . Solution: The angular velocity is = 2 f = 2 (60 Hz) = 376 . 991 rad / s . The solenoid carries a current I = I sin t. The maximum magnetic field in the solenoid is B max 2 = N 2 I 2 = (6600)(30 A) (7 . 3 m) = 0 . 0340841 T , where B 2 = B max 2 sin t. The flux 12 through coil 1 due to coil 2 (the solenoid) is 12 = B 2 A 2 , so the mutual inductance is M 12 = N 1 12 I = N 1 B 2 A 2 I = N 1 N 2 A 2 2 = (390)(6600)(0 . 0191134 m 2 ) (7 . 3 m) = 0 . 00846905 H , Felder, Jacob Homework 11 Due: Nov 28 2006, 9:00 pm Inst: Vitaly 2 where A 2 = (0 . 078 m) 2 = 0 . 0191134 m 2 . The induced emf is E 1 =-M 12 dI dt =-M 12 I d dt sin t = M 12 I cos t = (0 . 00846905 H)(30 A) (376 . 991 rad / s) cos t = (95 . 7827 V) cos t, where the maximum emf is E max 1 = 95 . 7827 V . keywords: 002 (part 1 of 1) 10 points A plane loop of wire of area A is placed in a region where the magnetic field is perpendicu- lar to the plane. The magnitude of B varies in time according to the expression B = B e- at ....
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121homework 10 - Felder, Jacob Homework 11 Due: Nov 28...

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