Maxwell's equations

#Electromagnetism

Maxwell's equations inside matter

Polarization creates bound charge

ρ_{b} = - \vec{\nabla} \cdot \vec{P}

Magnetic properties of solids -> Magnetic Polarization M creates bound Current Density

{\vec{J}}_{b} = \vec{\nabla} \times \vec{M}

In the non static case change of polarization causes a Polarization Current

\vec{J_{p}} = \frac{\partial \vec{P}}{\partial t}

Gauss Law becomes:

\nabla \cdot E = \frac{1}{ϵ_{0}} (ρ_{f} + ρ_{b}) = \frac{1}{ϵ_{0}} (ρ_{f} - \nabla \cdot P)

\nabla \cdot D = ρ_{f}

where D Electric Displacement Field