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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; $\frac{dQ}{dt}$) 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.

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  • $\begingroup$ a capacitor that is filled with a regular polarizable dielectric works that way but how does an unfilled capacitor work? How does the current in the wires stay divergence-free between the plates? Yes, charge accumulates on the plates but there is also an induced fluctuating magnetic field between the plates. There is no displacement current in the wire but between the plates. In the old days, some people were even teaching that, by analogy, displacement current is the polarization current of the vacuum. $\endgroup$
    – hyportnex
    Commented Nov 13, 2023 at 15:16
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    $\begingroup$ A capacitor with a "lossy" dielectric can be modeled as an ideal capacitor in parallel with an ideal resistor. $\endgroup$
    – Farcher
    Commented Nov 13, 2023 at 16:49

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In short, the answer to your question is yes, a displacement and conduction current can coexist. Consider the following set-up;

Two small spherical conductors with initial charge (+Q) and (-Q) far apart are connected by means of a conducting wire and now consider an Amperian loop around their midpoint. In this loop, evidently there is some conduction current and due to change in electric flux, a displacement current exists as well.

So, yes, if any charge carrier is flowing through your Amperian loop and the electric field in that region is also varying with time, then conduction and displacement current, both, will exist.

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  • $\begingroup$ As it’s currently written, your answer is unclear. Please edit to add additional details that will help others understand how this addresses the question asked. You can find more information on how to write good answers in the help center. $\endgroup$
    – Community Bot
    Commented Nov 30, 2023 at 7:49

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