# The energy of the magnetic field

1. Jan 27, 2008

### Psi-String

The energy of the magnetic field, by definition, is the energy needed to establish the field. So if we establish the magnetic field by steady current, we need to establish the current. My question is, in the derivation of

$$U = \frac{1}{2 \mu_0} \int B^2 d\tau$$

it seems that the work we done is to against the induced electric field due to the varying current while establishing the current. But how about the kinetic energy of the charge particle?? Don't we need to include this energy or it is small enough that we can neglect it??

Last edited: Jan 27, 2008