Newbie Problems on Electrodynamics

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The discussion focuses on deriving the magnetic field energy density in a medium, expressed as 1/2 H · B. Participants seek a step-by-step explanation of the conservation of energy equation in a medium, specifically the equation involving the Poynting vector and energy density. It is noted that the derivation is similar to that in a vacuum but must account for non-linear media where D is not necessarily proportional to E, and H is not proportional to B. Clarification is provided that the original equation only applies to linear quasistatic media. The conversation emphasizes the complexities of electrodynamics in different media.
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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)
 
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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.
 

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