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329fall08hw3 - ECE 329 Homework 3 Due 5PM 1 Faradays Law...

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ECE 329 Homework 3 Due: Sept 16, 2008, 5PM 1. Faraday’s Law states that induced emf or circulation E ≡ ± C E · d l calculated around any closed loop C in space equals the decay rate of magnetic Fux, Ψ B ² S B · d S , through any surface S bounded by the loop — that is, ³ C E · d l = - d dt ´ S B · d S for line and surface integrals taken in directions consistent with the right hand rule. Based on this law: a) What is the induced emf E over any ±xed loop C calculated in a region where B =0 at all times? b) Can the emf E calculated for a moving or deforming loop C be non-zero if B ± =0 but constant in time (i.e., static)? Explain. c) If B is time-independent, can the line integral ² 12 E · d l calculated in the region between ±xed points P 1 and P 2 depend on the path taken from P 1 to P 2 ? Explain your reasoning. 2. ²or B = B 0 ( t cos( ωt x + sin( ωt z ) Wb/m 2 , ±nd the induced emf E around the following closed paths: a) A rectangular path going from (0 , 0 , 0) to (1
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