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1. The problem statement, all variables and given/known data

The picture attached to this question shows a magnetic slab with μ_{r}= 50. A thin conducting film (with μ_{r}= 1) lies on top of the slab and carries a surface current of 1.0[A/mm] directed out of the page. If magnitude of B_{1}= 0.01 [T] and θ_{1}= 10^{o}, find magnitude of B_{2}and θ_{2}.

I apologize in advance for my bad recreation of the image in the text!

2. Relevant equations

1.) B_{1n}= B_{2n}

2.) (1/μ_{1})B_{1t}- (1/μ_{2})B_{2t}= J_{s}

3. The attempt at a solution

So, for starters, I am assuming μ_{1}= μ_{o}= (4*pi)e^{-7}. Please let me know if I cannot make this assumption, but I believe I can. Because angles are involved that are not perfectly 90^{o}, I have to include sines and cosines in the equations above. Using formula #1 --> (0.01)*cos(10^{o}) = B_{2}cos(θ_{2}) = 0.009848. Using formula #2 to find θ_{2}, I can plug in values to have:

(1/μ_{o})0.01*sin(10^{o}) - (795774.72)B_{2}sin(θ_{2}) = 1000[A/m]

Solving for θ_{2}, I find that the angle is 90^{o}. However, this is not the answer in the back of the book. The answer for θ_{2}in the back of the text is 86.2^{o}and a magnitude of B_{2}to be 0.15[T]. I was also not receiving this value for B_{2}. I have a feeling that my problem is that I cannot assume that μ_{1}= μ_{o}. Please help me! Thanks for all help in advance!

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# Homework Help: Normal/Tangential magnetic flux density problem

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