B and H in a magnetic material

[darkpsi]

Homework Statement

griffiths 6.13:
Suppose the field inside a large piece of magnetic material is B_o, so that H_o = (1/u_o)B_o - M. Now a small spherical cavity is hollowed out of the material. Find the field at the center of the cavity, in terms of B_o and M. Also find H at the center of the cavity, in terms of H_o and M.

Homework Equations

closed integral (H * dl) = I_fenc

The Attempt at a Solution

Well since I thought that the free current inside the cavity would be zero, that made H also zero. Because H was zero, M = 1/u_o B.
So M = u_oH_o / B_o.
Therefore B = u_o²H_o / B_o
And H = 0 = u_oH_o / B_o - M.
I guess I'm just confused because I'm not real sure how to approach the problem; this was all I could think of.

btw, a link to the various symbols would obviously be welcomed.

 

[Jhero]

Thank you for sharing your attempt at solving this problem. It seems that you are on the right track, but there are a few things you could consider in your approach.

Firstly, it is important to remember that the field inside a magnetic material is not just determined by the external field (Ho) and the magnetization (M), but also by the material's permeability (uo). So, the equation you used (H = uoHo / Bo - M) is not complete.

Secondly, it is important to consider the boundary conditions at the interface of the cavity and the magnetic material. Since the magnetic material has a non-zero magnetization, there will be a surface current at the interface, which needs to be taken into account when finding the field at the center of the cavity.

To solve this problem, you can use the boundary conditions for magnetostatics, which state that the tangential components of the magnetic field must be continuous at the interface. Using this condition, along with the equation for the magnetic field inside a material (H = uoB), you should be able to find the field at the center of the cavity in terms of Bo, M, and uo.

As for the symbols, you can refer to the textbook or online resources for a list of commonly used symbols in electromagnetism. It may also be helpful to draw diagrams to aid in your understanding of the problem.

I hope this helps and good luck with your solution.