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

5.2.4 Recap

Recap

Displacement current: $J_{d} = \partial D / \partial t$ $[A/ m^{2}]$ produces a magnetic field like a conduction current. It makes Ampère's law consistent for unsteady currents (the same circulation on every surface spanning $C$ ), carries the current across a capacitor gap with $i_{d} = d Ψ/ d t = C d v / d t$ , and is the term that allows waves.
Generalised Ampère law, Eq. (5.2.5): the source of $\nabla \times H$ is $J + \partial D / \partial t$ , which is divergence-free whether the currents are steady or not. Inside a capacitor with circular plates $H_{ϕ} = (ρ /2) (i / A)$ , joining the field of the wire at the rim.
Conduction or displacement: their ratio in a medium is $σ / (ω ε)$ , the loss tangent. Equal at $f_{c} = σ / (2 π ε)$ : a conductor below, a dielectric above.