ポインティング・ベクトル
ポインティング・ベクトルの発散は
∇ ⋅ S = ∇ ⋅ ( E × H ) = H ⋅ ( ∇ × E ) − E ⋅ ( ∇ × H ) = − H ⋅ ∂ B ∂ t − E ⋅ ∂ D ∂ t − E ⋅ j {\displaystyle {\begin{aligned}\nabla \cdot {\boldsymbol {S}}&=\nabla \cdot ({\boldsymbol {E}}\times {\boldsymbol {H}})\\&={\boldsymbol {H}}\cdot (\nabla \times {\boldsymbol {E}})-{\boldsymbol {E}}\cdot (\nabla \times {\boldsymbol {H}})\\&=-{\boldsymbol {H}}\cdot {\frac {\partial {\boldsymbol {B}}}{\partial t}}-{\boldsymbol {E}}\cdot {\frac {\partial {\boldsymbol {D}}}{\partial t}}-{\boldsymbol {E}}\cdot {\boldsymbol {j}}\\\end{aligned}}}
となる。 ここで電磁場のエネルギー密度は
u = 1 2 ( E ⋅ D + H ⋅ B ) {\displaystyle u={\frac {1}{2}}({\boldsymbol {E}}\cdot {\boldsymbol {D}}+{\boldsymbol {H}}\cdot {\boldsymbol {B}})}