EM: B field at boundary with different permeabilities

[Darren93]

Hey this isn't so much a homework problem but one I have just had an exam over. I have absolutely no idea how to calculate it and in all past papers/tutorial questions and the notes, makes no mention of the sort of problem. I'm not bothered over the exact answer, just how you go about it.

Homework Statement

Question: An interface between two materials, of relative permeability 5 and 8 respectively, lies in the xy plane. In the lower material (z lower or equal to 0, permeability 8) a B field is in the xy plane directed towards the origin at 10 degrees to the z-axis.
Calculate the magnitude and direction of the B field in the upper medium.

2. The attempt at a solution
The previous question leads you to the fact that at a boundary perpendicular B field is constant. So i guessed you had to make use of that. I said the perpendicular component is =lBlcos(10). Thus I said the z competent in the top material is also this. I then had no idea how to go about the rest. For the B field to vary change in permeability must vary this. So I said magnitude of B in top half is 8/5 larger than below. I then came up with an expression for magnitude of B field in the x-y plane in the top that along with the known z corresponds to 8/5 the magnitude of B. Then I calculated angle between this and the z component.

Does any of that sound correct, I had no idea the effect of change in permeability at boundary and guessed it increased by a factor of 1.6. I would be amazed if that was correct. The entire question is just terrible if you ask me.

 

[TSny]

Question: ...a B field is in the xy plane directed towards the origin at 10 degrees to the z-axis.

Did you mean to write xz plane or maybe yz plane here?

You treated the normal component of B correctly, but the way you treated the magnitude of B is not correct.
There is another boundary condition that deals with the tangential component of B that you can use.