= Electromagnetic energy density
{title2=$u=\tfrac12(\mathbf E\cdot\mathbf D+\mathbf B\cdot\mathbf H)$}
In a linear isotropic nondispersive medium with time-independent <permittivity> $\epsilon$ and <magnetic permeability> $\mu$, the stored <electromagnetic energy> per volume is $u=\epsilon|\mathbf E|^2/2+|\mathbf B|^2/(2\mu)$. For a short derivation, the <Maxwell equations in matter> and the <divergence> identity for a <cross product> give $\nabla\cdot(\mathbf E\times\mathbf H)=-\mathbf H\cdot\partial_t\mathbf B-\mathbf E\cdot\partial_t\mathbf D-\mathbf J_f\cdot\mathbf E$. The <constitutive relations> turn the first two terms into $-\partial_tu$, proving the <Poynting theorem>. Choose $u=0$ when the <electric field> and <magnetic field> both vanish. Dispersive or time-dependent material response requires a different accounting of stored <energy>.
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