**Maxwell's equations** (SI units) are

**∇**·**E** = ρ/ε_{0},
**∇**×**E** = -∂**B**/∂t,

**∇**·**B** = 0,
**∇**×**B** = μ_{0}**j** + (1/c^{2})∂**E**/∂t,

or, in macroscopic form,

**∇**·**D** = ρ_{f},
**∇**×**E** = -∂**B**/∂t,

**∇**·**B** = 0,
**∇**×**H** =
**j**_{f}** **+ ∂**D**/∂t.

In lih materials with** D** = ε**E** and
**B** =
** **μ**H** and
ε, μ = constant we have

**∇**·**E** = ρ_{f}/ε,
**∇**×**E** = -∂**B**/∂t,

**∇**·**B** = 0,
**∇**×**B** = μ**j**_{f} + εμ∂**E**/∂t.

Maxwell's equations are **linear equations** and the principle of
superposition holds**.
∇**·

∇

**Poynting's theorem**, **E**·**j** = -(∂u/∂t) -**∇·S** is a
statement of energy conservation.

u = (1/(2μ_{0}))B^{2} + (ε_{0}/2)E^{2} is
the **energy density** and

**S** = (1/μ_{0})(**E**×**B**) is the
**energy flux** in
the electromagnetic field.

We define the **momentum density** as
**g** = **S**/c^{2}.

If in electrodynamics we choose the Lorentz gauge defined through

**∇**·**A** = -(1/c^{2})∂Φ/∂t,

then Φ and each Cartesian component of **A** satisfy the inhomogeneous wave
equation.

**∇**^{2}Φ - (1/c^{2})∂^{2}Φ/∂t^{2} = -ρ/ε_{0},
**∇**^{2}**A** - (1/c^{2})∂^{2}**A**/∂t^{2}
= -μ_{0}**j**.

Φ(**r**,t) = (4πε_{0})^{-1}∫ρ(**r**', t')|_{ret}dr'/|**r**
- **r**'|, A_{i}(**r**,t) = (μ_{0}/(4π))∫j_{i}(**r**',
t')|_{ret}dr'/|**r** -
**r**'|,

with ρ(**r**', t')|_{ret} = ρ(**r**', t - |**r
**-** r**'|/c).

Choosing **∇**·**A** = 0 is called choosing the
**Coulomb gauge.**