# EM: B field at boundary with different permeabilities

1. Aug 11, 2015

### 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.

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

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.

2. Aug 11, 2015

### TSny

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.