Understanding the concept of voltage in electrode reactions

Background: I'm currently reading "Electrochemical methods: fundamentals and applications," by Allen J. Bard. In chapter 1, he has the following setup:


[![enter image description here](https://i.stack.imgur.com/bKtoC.png)](https://i.stack.imgur.com/bKtoC.png)


He then states that we incorporate the power supply such that the potential of the Pt electrode is more negative than that of the Ag/AgBr electrode. This leads to reduction of H+ at the Pt electrode. Here's my question:


Let's assume that potential is kQ/r, where 'k' is the coulomb constant, 'Q' is the "constant charge" that affects 'q' (a variable charge), and 'r' is the distance between 'q' and 'Q.' I'm having issues applying that concept/formulation of potential to the setup described here.


* What would 'r' refer to exactly in this context?
* In the situation where H+ is reduced, the implication is that there's a net movement of electrons towards the platinum electrode. This means that's there's a net force on electrons whose direction is towards the platinum electrode. I don't know how to relate this finding to the statement that the potential at the Pt electrode is more negative than the potential at the other electrode.


Any help is appreciated.




To restate the question as I understand it, there are two parts: 1) if you look at the platinum electrode as a capacitor, what is the distance between the "plates", and 2) what is the direction of electron flow in the reduction of H+ to H2?


I'll start with the second question: because there is reduction occuring at the platinum electrode, the electrons are flowing from the platinum surface to the hydrogen ions. In order for that to be accomplished, the electrode has a build-up of electrons, or negative charges. Because opposite charges attract, positive ions from solution will start to accumulate near the platinum electrode. This charge separation acts as a capacitor. Terms you may encounter that refer to this effect are "the electrical double layer", or "double layer region", or "double layer capacitance". On a molecular level, this effect is used to describe the regions as the inner and outer Helmholtz planes. Therefore, r is the distance between the "plates" or planes in the double layer. This is governed by the radii of the ions.


The image below, from Wikipedia <https://en.wikipedia.org/wiki/Double-layer_capacitance> illustrates this concept.


[![enter image description here](https://i.stack.imgur.com/KoQAz.png)](https://i.stack.imgur.com/KoQAz.png)


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