نظرية ديناميكية للمجال الكهرومغناطيسي

${\displaystyle \mathbf {J} _{\rm {tot}}=}$ ${\displaystyle \,\mathbf {J} }$ ${\displaystyle +\,{\frac {\partial \mathbf {D} }{\partial t}}}$

${\displaystyle \mu \mathbf {H} =\nabla \times \mathbf {A} }$

${\displaystyle \nabla \times \mathbf {H} =\mathbf {J} _{\rm {tot}}}$

${\displaystyle \mathbf {f} =\mu (\mathbf {v} \times \mathbf {H}) - {\frac {\partial \mathbf {A} }{\partial t}}-\nabla \phi }$

${\displaystyle \mathbf {f} ={\frac {1}{\varepsilon }}\mathbf {D} }$

${\displaystyle \mathbf {f} ={\frac {1}{\sigma }}\mathbf {J} }$

${\displaystyle \nabla \cdot \mathbf {D} =\rho }$

${\displaystyle \nabla \cdot \mathbf {J} =-{\frac {\partial \rho }{\partial t}}\,}$.

${\displaystyle \nabla \times \nabla \times \mathbf {E} =-\mu _{o}{\frac {\partial }{\partial t}}\nabla \times \mathbf {H} =-\mu _ {o}\varepsilon _{o}{\frac {\جزئي ^{2}\mathbf {E} }{\جزئي t^{2}}}}$

${\displaystyle \nabla \times \nabla \times \mathbf {H} =\varepsilon _{o}{\frac {\partial }{\partial t}}\nabla \times \mathbf {E} =-\mu _{o}\varepsilon _{o}{\frac {\partial ^{2}\mathbf {H} }{\partial t^{2}}}}$

${\displaystyle \nabla \times \left(\nabla \times \mathbf {V} \right)=\nabla \left(\nabla \cdot \mathbf {V} \right)-\nabla ^{2}\mathbf {V} }$

${\displaystyle {\partial ^{2}\mathbf {E} \over \partial t^{2}}\ -\ c^{2}\cdot \nabla ^{2}\mathbf {E} \ \ =\ \ 0}$

${\displaystyle {\partial ^{2}\mathbf {H} \over \partial t^{2}}\ -\ c^{2}\cdot \nabla ^{2}\mathbf {H} \ \ =\ \ 0}$

${\displaystyle c={1 \over {\sqrt {\mu _{o}\varepsilon _{o}}}}=2.99792458\times 10^{8}}$متر في الثانية