Proving: \int\textbf{B}\cdot\textbf{H}d^{3}x=0

[Old Guy]

Homework Statement

Prove \int\textbf{B}\cdot\textbf{H}d^{3}x=0. There is no current density.

Homework Equations

The Attempt at a Solution

Through 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.

 

[gabbagabbahey]

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

 

[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)?

 

[gabbagabbahey]

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)?

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)