(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The xy-plane serves as the interface between two different media. Medium 1 (z < 0) is filled with a material whose µ_{r}=6, and medium 2 (z > 0) is filled with a material whose µ_{r}=4. If the interface carries a current (1/µ0)ˆy (y- hat) mA/m, and B2 = 5ˆx (x-hat) + 8ˆz (z-hat) mWb/m2 , find H_{1}and B_{1}.

2. Relevant equations

H = 1/μ_{0}B - M.

H_{above}- H_{below}= K_{f}x ^n (n-hat)

3. The attempt at a solution

I know I am not doing this right because it seems to simple and my linear algebra isn't the best (I forgot some of the concepts) but this is what made sense to me:

H_{2}= 1/(μ_{0}4) [5 ^x + 8 ^z]

Sub that into the second equation.

so

1/(μ_{0}4) [5 ^x + 8 ^z] - H_{1}= 1 ^y

=>

1/(μ_{0}4) [5 ^x + 8 ^z] - 1/(μ_{0}6)B_{2}= 1 ^y

I change it into vector coordinates

1/μ_{0}(5/4, 0, 8/4) - 1/μ_{0}(x/6, -6/6, z/6) = 1 ^y

Then solve for x and z.

I get H_{1}= 1/(μ_{0}) (7.5/6 ^x - 1 ^y + 12/6 ^z)

and B_{1}= 7.5 ^x - ^y + 12^z

Am I going about this right or am I all the way in Mars right now?

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# Homework Help: XY plane as the interface between two media

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