# What empirical evidence is there for displacement current?

I wonder what more or less direct measurements of the displacement current exist. I know that the existence of em waves demonstrates its existence, though somewhat indirectly. I also know that there have been sensitive magnetic field measurements between charging parallel plate capacitors, but it has been argued that these can be explained in terms of the conduction currents flowing within the plates (Bartlett, Am. J. Phys. 58 (12), 1168 (1990) ). Any others?

Update: I ran across an interesting article showing an alternative to the displacement current to make Maxwell's equations consistent with charge conservation, but it fails to predict em waves (Wolsky, Euro. J. Phys. 36 (2015) 035019). It's interesting because it underscores that the displacement current is a theoretical construct. Is there evidence for it that does not invoke Faraday's law?

• I'm not sure I understand the question. The displacement current is just $\partial \mathbf{D} / \partial t$, so it's not something whose existence you can prove or disprove. Do you mean evidence for its appearance into Ampère's law? – Javier Sep 12 '15 at 14:53
• @Javier Yes. Maxwell theorized the displacement current was the correct addition to Ampère's law to restore charge conservation, but it was a conjecture, subject to experimental test. I was curious about how that theory had been tested. Since posting, I think I have found most of the experiments in the literature (along with a major debate about whether people should attribute reality to the displacement current at all), but there's not much there if you don't include em waves. – pwf Sep 14 '15 at 16:13
• The paper A Direct Experimental Inspection of Displacement Currents says in the Abstract:"In recent years, along with the evolution of measurement technologies, the researchers are attempting to validate directly the displacement current in the experiment. The paper proposes and fulfills one phase measurement experiment to scrutinize the orientation of displacement currents. The test results do not coincide with theoretical values of the classical electromagnetic theory" – Energizer777 Nov 16 '15 at 7:19
• EM waves in a vacuum- literally all sunlight and starlight you've ever seen- is the best evidence for displacement current. – Whit3rd Nov 23 '17 at 8:25
• @Whit3rd Thanks for contributing, but I think you have missed the point. Please re-read the OP and comments. – pwf Dec 5 '17 at 21:17

R. Van Cauwenberghe is regarded as author of the first direct measurement of the displacement current, in 1929, as you can check in this link that will redirect you to the Journal de Physique.

For a more recent experiment, check this paper from the Physical Review Letters: it also provides a short interesting historical introduction about the attempts to measure the displacement currents. I suggest you not to skip the footnotes!

The simplest evidence is the ac current going through a perfectly insulating capacitor with capacitance $C$ $$i= j\omega C v$$ where $i$ and $v$ are the complex current and voltage amplitudes, $j$ is the imaginary unit, and $\omega$ is the angular frequency of the ac voltage and current.

The conduction current in the wires continues as a displacement current $$i_D=Aj\omega \epsilon E$$ in the dielectric of the capacitor. $A$ is the area of the capacitor, $E$ is the electric field ac amplitude, $\epsilon$ is the absolute dielectric permittivity. This displacement current flowing in the dielectric is equal to the current through the capacitor given above.

## protected by Qmechanic♦Nov 23 '17 at 6:26

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