Maxwell Equation

The Maxwell equations are described

$${\rm div} {\bf D} = \rho$$ (1)

$${\rm div} {\bf B} = 0$$ (2)

$${\rm rot} {\bf E} = - \frac{\partial {\bf B}}{\partial t}$$ (3)

$${\rm rot} {\bf H} = {\bf J} + \frac{\partial {\bf D}}{\partial t}$$ (4)

The electric field ${\bf E}$ (Vm$^{-1}$) and magnetic field ${\bf H}$ (Am$^{-1}$) are related to the electric displacement (or dielectric flux density or electric flux density) ${\bf D}$ (Cm$^{-2}$) and magnetic-flux density (or magnetic induction) ${\bf B}$ (T:tesla = NA$^{-1}$m$^{-1}$)

$${\bf D} = \epsilon \epsilon_0 {\bf E}$$ (5)

$${\bf B} = \mu \mu_0 {\bf H}$$ (6)

Here $\epsilon$ and $\epsilon_0$ are the dielectric constant (no dimension) and electric permittivity of free space [8.854187817 $\times 10^{-12}$ Fm$^{-1}$ (= CV$^{-1}$m$^{-1}$)], respectively and $\mu$ and $\mu_0$ are magnetic permeability (no dimension) and magnetic permeability of free space ( $4\pi \times 10^{-7}$ NA$^{-2}$), rspectively. We can assume the Ohm's law for the current ${\bf J}$ and the electric field

$${\bf J} = \sigma {\bf E}$$ (7)