Question

I'm currently studying maxwell's equations in class, and my professor has explained the concept of displacement currents. The idea makes sense to me -- I mean, after all, isn't that entirely how a capacitor works? But one thing that doesn't click for me is: can you ever have electrical current (as in regular current; charge flowing; dQdt) AND displacement current in the same place, at the same time? Why/why not?

(If the question isn't phrased well enough, my apologies. I'd be happy to clarify. In the mean time, my question could be simplified to the following scenario: consider charged particles (like electrons) flowing through a conductive wire. Is there BOTH displacement current AND regular electrical current in that wire? Why/why not?My intuition is that you can't, but I can't help thinking about the fact that currents are driven by an EMF, which is in essence a potential difference, which implies the existence of an electric field wherever there is current, which then leads me to believe that we could find the displacement current of that same electric field.

Answer 1

Displacement current and regular electrical current cannot coexist simultaneously in the same region. Displacement current arises from a changing electric field, as in a capacitor, complementing conduction current. In a region with steady electric current (dQ/dt), lacking a changing electric field, displacement current is absent as per maxwell's equations.

Step-by-step explanation:

Maxwell's equations govern the behavior of electromagnetic fields, and one of them, Ampère's Law with Maxwell's addition, is particularly relevant to this question. The law relates the circulation of the magnetic field around a closed loop to the total electric current passing through the surface bounded by that loop. The addition by Maxwell includes a term involving the rate of change of electric flux, leading to the concept of displacement current.

In a steady-state current scenario, such as electrons flowing through a wire, the electric field remains constant, and there is no change in electric flux over time. As a result, the displacement current term becomes zero (dE/dt = 0). In contrast, in situations involving changing electric fields, like the charging or discharging of a capacitor, displacement current comes into play. This fundamental distinction means that in a wire with a continuous flow of charge (regular electrical current), there is no simultaneous presence of a changing electric field that would give rise to displacement current. Thus, they do not coexist in the same region at the same time.