Magnetostatics: Proof for θi, μ1, μ2, and μ3

[satchmo05]

[PLAIN]http://img714.imageshack.us/img714/2757/96034584.png

Homework Statement

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

Homework Equations

1.) B_1N = B_2N
2.) (1/μ₁)B_1T - (μ₂)B_2T = J_s

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)B_1T =(1/μ₂)B_2T. 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 θ_o = sin^-1((μ₁/μ₁)(B₁sinθ_i)/(B₃tanθ). As you can see, this form for θ_o 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!

 

[satchmo05]

I solved the problem. Thanks for those who attempted.