Magnetic field at boundary between materials with different permeabilities

[Tinaaaaaa]

Homework Statement

Two magnetic materials are separated by a planar boundary. The first magnetic material has a relative permeability μr2=2; the second material has a relative permeability μr2=3. A magnetic field of magnitude B1= 4 T exists within the first material. The boundary is perpendicular to the field in the first material. What is the magnitude of the magnetic field in the second material? You may assume that the magnetic fields B and H are linearly related in both materials

Homework Equations

B=μ0*μr*H
boundary conditions= B is continuous perpendicularly and H is continuous in parallel

The Attempt at a Solution

So far I have
for material 1: B=μ0*μr*H1 => 4T=μ0*2*H=> H1=2/μ0
since it is perpendicular to the boundary, B1(per)=B2(per) so, B2(per)=4 T as well.
H2=4/3*μ0

im not too sure as to how to transition from the components to the magnitude. Does the fact that the boundary is perpendicular mean that all the components are also perpendicular so no parallel components? WHat about μ0?

thanks

 

[Charles Link]

You can compute $H$ in each region including outside of the material, but I think this one is trivial. I'm going to need to give it further study, but because of the geometry, and because $\nabla \cdot B=0$, I believe $B$ needs to be continuous everywhere. There's really nothing that needs to be computed if all you need to do is give an answer for $B$.