Why are the electric and magnetic fields in an electromagnetic wave propagating through a conductor not in phase?

Abstract

Abstract Intermediate and advanced texts in electromagnetic theory frequently discuss infinite plane waves propagating through conducting media. They find that the magnetic field has a phase delay (relative to the electric field) that can be as large as π/4 rad depending upon the ratio of the conductivity to the product of the angular frequency and the permittivity [σ/(ω ϵ)]. The expressions given to calculate this phase delay are unnecessarily complicated and provide minimal physical insight. We provide a simple expression for the phase delay and then illustrate how to interpret it by first considering Ampere’s Law and Faraday’s Law separately and then coupling them together. In the classroom, this provides an excellent educational opportunity for our students since we make analogies between the phase shifts associated with Ampere’s Law and equivalent phase shifts in driven oscillators and alternating current RC circuits.