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I recently discovered this answer which explains how batteries maintain a constant potential difference. So what I understood was that batteries spew out electrons on the cathode, and by doing this they create an electrical field. When this field becomes strong enough, it stops the redox reactions occurring in the battery. This causes the potential difference to become constant as there is no more charge accumulation.

The last part didn't really make sense to me, I thought voltage had nothing to do with the charge density. I thought some amount of energy is taken from the electron during the reactions occurring in the battery, creating a potential difference (aka voltage). It wouldn't be too far-fetched to make some connection to charge density as well, but I don't have the knowledge to make such conclusions. So is my original understanding of how a potential difference is generated correct or does charge density also play a role?

Kryptic Coconut
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1 Answers1

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Charge density plays an indirect role and can be calculated once the size, geometry, and materials that encompass the charge are specified. Once you specify the geometry (e.g. parallel fixed metallic plates), the size (e.g. area A, separated by distance d), and the materials (e.g. air) then charge density can be related to voltage. In the example of a parallel metallic plates $$V= \frac{Q}{C} = \frac{Q}{\epsilon A/d} = \frac{Q}{A} \frac{d}{\epsilon}$$once the material (given by it's permittivity $\epsilon$) and geometry are known, V is proportional to charge density (Q/A) on the plates.

Once the voltage due to charge accumulation reaches a certain level, the electrochemical reaction is incapable of supplying enough energy to an electron to increase this voltage, and the reaction mostly stops. The reaction must stop, because if it didn't, charge accummulation would continue and the voltage would increase without bound.

A battery cell maximum voltage is dependent on the specific electrochemical reaction driving it, because that specific reaction determines the amount of energy supplied to each electron. But the reaction is started and stopped by voltage which is a product (literally) of geometry and charge density.

AndyW
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