# Newbie Problems on Electrodynamics

1. Aug 26, 2004

### Wong

May anyone please show me how to derive the "magnetic field energy density" in a medium, which equals $$\frac{1}{2}H \cdot B$$?

I would be very pleased if anyone could show me how to derive (step-bystep) the conservation of energy equation *in a medium* (not in vacuum) i.e. $$\nabla\cdot S + \frac{\partial v}{\partial t} = -E \cdot J$$, where $$v = \frac{1}{2}(E \cdot D + B \cdot H)$$ and S is the poynting vector. (N.B. The medium may not be linear i.e. D may not be proportional to E, H not to B)

Last edited: Aug 26, 2004
2. Aug 26, 2004

### Wong

Sorry for asking....I understand now, that the equation I posted only works for linear quasistatic media. Thus D should be proportaional to E and H to B and the derivation is essentially the same as in the vacuum case.