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Let's say I had the following laboratory set-up:

enter image description here

Two conductive plates with an electrical potential $\phi$ between them, and a fluctuating potential $\phi$ (created by some arrangement of fluctuating charges) outside the plates. How could I stop the potential outside $\phi'$ the plates from affecting the potential $\phi$ inside the plates?

My educated guesses:

  1. A simple battery. A battery holds a constant voltage, but the relationship between voltage and $\phi$ is complicated: Are the $V$ in electronics and the $\phi$ in physics the same?

  2. A battery in parallel with a diode with a forward voltage equal to the desired $\phi$ between the plates. It's a diode's job to hold a desired voltage between two parts of a circuit. Again it depends on the relation between voltage and $\phi$.

  3. Some device to keep the charge (q) on the plates the same. No idea what'd do that though.

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  • $\begingroup$ Regarding the 'complicated' relation between V and $\phi$, if there are no changing magnetic fields, you can consider them to be the same. It's not that V is the quantity applied to the plates and $\phi$ is the quantity in the space between them, like you seem to imply here. $\endgroup$
    – Peltio
    Commented Oct 25, 2022 at 6:17
  • $\begingroup$ To clarify: you are free to use different symbols if you like but if there are no changing magnetic fields or the role of the changing magnetic field is negligible, then a voltage V between the plates will result in a potential difference $\Delta\phi=V$ between them and a linear increase of potential from one plate to the other (as implied by the gradient color in your figure) $\endgroup$
    – Peltio
    Commented Oct 25, 2022 at 6:31
  • $\begingroup$ If the potential is being held constant, then a polarization current will flow. Of course the potential outside of the plates will penetrate the edges of this capacitor slightly. If you can't have that, then you place the entire capacitor inside a Faraday cage and you are done with the problem. $\endgroup$
    – FlatterMann
    Commented Oct 25, 2022 at 7:15

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