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## 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