This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Felder, Jacob Homework 11 Due: Nov 28 2006, 9:00 pm Inst: Vitaly 1 This printout should have 11 questions. Multiplechoice 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 ....
View
Full
Document
 Fall '08
 Opyrchal
 Work

Click to edit the document details