# Homework Help: Finding B, M, and H for an infinite conducting slab

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1. Dec 3, 2015

### phys-student

1. The problem statement, all variables and given/known data
We have an infinite slab of conducting material, parallel to the xy plane, between z = −a and z = +a, with magnetic susceptibility χm. It carries a free current with volume current density J = J0z/a in the x direction (positive for z > 0, negative for z < 0). The integrated current density across the whole slab is therefore zero. What are H (auxiliary field), B (magnetic field), and M (magnetization) (magnitude and direction)? What is the bound current?

2. Relevant equations
Ampere's law: ∫B⋅dl=μ0*Ienc
Magnetic dipole moment: m=I*a
Bound currents: Jb=∇×M (volume bound current) and Kb=M×n (surface bound current)
Definition of H: H=(1/μ0)*B-M
Ampere's law in terms of H: ∫H⋅dl=Ifenc

3. The attempt at a solution
I'm not really even sure where to start with this one. I thought finding the magnetization was what I needed to do as a starting point but I'm not entirely sure how to do that. I also was wondering if my starting point should be to find H by defining an Amperian loop inside the slab, but I'm also unsure of how to do that because the current is equal in magnitude and opposite in direction in the top and bottom sections of the slab so won't it just cancel out giving me an result of H = 0? If anyone could point me in the right direction it would be appreciated.

2. Dec 3, 2015

### phys-student

Someone please help me. I have no idea what I'm doing and need to get this assignment done ASAP. I know now that I need to find H first using Ampere's law but am having a hard time understanding how to define my Amperian loop