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Magnetostatics Proof

  1. Apr 23, 2010 #1
    [PLAIN]http://img714.imageshack.us/img714/2757/96034584.png [Broken]
    1. The problem statement, all variables and given/known data

    In the image above, magnetic flux enters the first interface of a three-layer geometry at an angle θi. If all three media are non-conducting and have permeabilities μ1, μ2, and μ3.
    a.) show that the angle θo is independent of the value of μ2.
    b.) show that θo = θi, when μ1 = μ3.

    2. Relevant equations

    1.) B1N = B2N
    2.) (1/μ1)B1T - (μ2)B2T = Js

    3. The attempt at a solution

    Right off the bat, I know that since the media are non-conducting, that the surface currents at the boundaries are 0. Therefore, (1/μ1)B1T =(1/μ2)B2T. Using formula #2, I can plug in values for both regions 1 and 2, and I can do the same for regions 2 and 3, but then when comparing regions 1 and 3, that is where it gets tricky because following the same form as the standard regions, the θ in region 2 when comparing regions 2 and 3 would be equal to (90-θ). What I end up determining is θo = sin-1((μ11)(B1sinθi)/(B3tanθ). As you can see, this form for θo doesn't really help me much for part b.)

    If anyone can give me a word of advice or a path to start on that will lead me to the right answer, I would greatly appreciate it. Thank you much!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 25, 2010 #2
    I solved the problem. Thanks for those who attempted.
     
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