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329fall09hw7 - ECE 329 Homework 7 Due 5 PM 1 Faradays Law...

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ECE 329 Homework 7 Due: October 13, 2009, 5 PM 1. Faraday’s Law states that the emf E calculated for any closed loop C in 3-D space equals the decay rate - d Ψ dt of magnetic flux Ψ B · dS . For a loop C with a fixed shape, the emf is E = C E · dl in terms of electric field E in the reference frame of the loop. In that case, Faraday’s law is written as C E · dl = - d dt S B · dS where the line and surface integrals are taken in directions compatible with the right hand rule. a) What is the emf E over any fixed loop C in a region where B = 0 at all times? b) What is the emf E over any fixed loop C in a region where B is non-zero but time-independent? c) If B is time-independent, can the line integral 12 E · dl calculated in the region between (arbi- trary) fixed points P 1 and P 2 depend on the path taken from P 1 to P 2 ? Explain your reasoning. d) Can the emf E calculated for a moving or deforming loop C be non-zero if B is non-zero but time-independent (i.e., static)? Explain.
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