# Magnetic field energy conceptual question

1. Jun 27, 2013

### facenian

Hello, I have some trouble understanding an expression for the magnetic field energy .There are basically two different general expressions: a)$\int(\int_0^B\vec{H}.\delta{\vec{B}}) d^3r$ b)$\int(\int_0^A\vec{J}.\delta{\vec{A}}) d^3r$. For linear medium a) becomes$\frac{1}{2}\int\vec{H}.\vec{B} d^3r$,so far so good, the problem arises when many authors say that for linear medium we analogously have $U_m=\frac{1}{2}\int\vec{J}.\vec{A}d^3r$....(1)
I suspect that for the validity of the last equation to hold we also need homogeneity, linearity alone not being sufficient. For instance "Jackson" says that (1) holds assuming a linear relation between J and A which is correct, the problem is that such a linear relation between J and A does no follow from the linearity of the medium as he(Jackson) inidirectly implies later in his tex in the next paragraph 5.17
So I'm citing Jackson to back up my interpretation. I'd appreciate any comments.

Last edited: Jun 27, 2013
2. Jun 28, 2013

### facenian

Helo again, I just wanted to tell you that I solved the problem