Magnetic potential energy

1. Hassan2

411
Dear all,

I'm reading a paper on finite element magnetic field analysis. Basically there are two approaches to this. One is to use Maxwell equation and the other is to define an energy functional, discretize the problem and minimize the functional with respect to the unknowns.

The paper takes the second approach. The functional is given as:

$E=\int_{V}(\int_{0}^{B}H.dB)dv-\int_{V}J.Adv$

J is the source current density and A is the magnetic vector potential ( $B=\nabla \times A$)

The first term is the stored energy. My question is about the second term. It seems to be the magnetic energy given to the system. I need your help to interpret and understand the second term because in electromagnetic text books, the second term (divided by 2, and without the negative sign) is proved to be equal to the first term in the linear case. I'm totally confused with this energy functional.