# Magnetism Proof

1. Nov 18, 2009

### Old Guy

1. The problem statement, all variables and given/known data
Prove $$\int\textbf{B}\cdot\textbf{H}d^{3}x=0$$. There is no current density.

2. Relevant equations

3. The attempt at a solutionThrough a vector identity and the divergence theorem, I get
$$\oint\Phi_{M}\textbf{B}\cdot{d}\textbf{a}$$ but don't know how to proceed. This seems close to Ampere's law with no enclosed current, but not quite.

2. Nov 18, 2009

### gabbagabbahey

What surface are you integrating over? What are the values of $\textbf{B}$ and $\Phi_M$ along that surface?

3. Nov 18, 2009

### Old Guy

He told us the problem was given to us intentionally very general, so none is specified. Could I argue that for an enclosed region in space with no enclosed magnetization, the integral is zero because all the flux in goes out again (kind of like the EM flux arguement)?

4. Nov 19, 2009

### gabbagabbahey

No, I don't think that works...

$$\oint\Phi_{M}\textbf{B}\cdot{d}\textbf{a}$$

does not represent the magnetic flux.

What is the exact wording on the original question? (If it's a problem from Jackson, just state the problem number)