# Calculating H-Field with no free currents

1. Oct 17, 2015

### mrshneaky

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

A cubic block of uniform linear magnetic material is placed in an otherwise uniform magnetic field
Bo = Bo*. The block lies such that z^ is a normal of the top face.
a)Compute the new H field everywhere.
b)compute the new B field everywhere

2. Relevant equations & The attempt at a solution

My solution so far is based on the fact there are no free currents
ie curl(H) = 0

Using:
B = Bo +μo*M (1) (from hyper physics)
H
=B/μo -M (2) (from lecture notes)

substituting (1) into (2) I get:

H = Bo/μo

(I'm not sure if this is correct)

computing the B-field then using B=μ*H
I get:
**B**=μr*Bo note: μr is relative permittivty (μ/μo)

I'm not sure if this is correct regarding boundary conditions as M is discontinuous at the boundary of the cube.
ie the div(M) ≠ 0

and since div(H) = -div(M) (this can be shown by taking the divergence of (2) as div(B) = 0)

so div(H) should also not equal zero, however given the H field I calculated that's clearly not the case.

any tips for where I'm going wrong?