Electromagnetic Fields and Waves: Notes, Solved Problems and Interactive Lab

5.4.2 Recap

Recap

Continuity equation, Eq. (5.4.2): $\nabla \cdot J + \partial ρ_{v} / \partial t = 0$ , charge is conserved. In a steady state it is Kirchhoff's current law. Demanding it forces the displacement current into Ampère's law.
Charge relaxation: charge placed inside a conductor decays as $e^{- t / τ}$ with $τ = ε / σ$ and reappears on its surface.
The whole course in four equations: Eq. (5.1.1) with $D = ε E$ , $B = μ H$ , $J = σ E$ and the Lorentz force $F = q (E + v \times B)$ . Their wave solutions travel at $1/ μ_{0} ε_{0} = 3 \times 1 0^{8} m/s$ , the speed of light.