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Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points, which (in a static electric field) is defined as the work needed per unit of charge to move a test charge between the two points. (from Wikipedia)

What exactly is a point in this definition? The voltage of a neuronal cell can be measured for example and a living cell is not exactly what I intuitively understand to be a point. Let's say I have such a cell with an electrical potential $V_m$ of $-80mV$ (is this the same as saying the cell has a voltage of $-80mV$?).

Am I right then that the voltage is a relative measure between the cell and the extracellular fluid? And is the voltage of this fluid then just the symmetric inverse, i.e. $V_{extra}=80mV$? How then can the voltage be measured between two bodies (neuron and extracellular fluid), because the concentration of charged ions might not be uniform across the fluid (or across the cell)? Could the voltage also be measured between two organelles within the cell or between the entire human body and the air surrounding it?

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Voltage is always a potential difference, so you need two "points" to define one.

Technically speaking, a neuron doesn't have a voltage and the extracellular space doesn't have a voltage; there's only a voltage between the inside and outside of the cell. However, because technically speaking a neuron doesn't have a voltage, it can be reasonable shorthand to say "voltage of a cell" when you mean "potential difference between inside and outside of a cell". I wouldn't let that imprecision in terminology get you tripped up. In neuroscience we use the convention that the potential difference is with respect to the inside of the cell.

Yes, you can measure different voltages among intracellular compartments, as well. Yes, you can also have voltage gradients within cells and outside cells, though because these are aqueous solutions with dissolved ions, voltage tends to equalize in these compartments quite quickly (until confronted with the capacitance of a membrane). That is, if the concentration of charged ions is not uniform across the inside of a cell, there's going to be a net movement of charged ions inside the cell until things are effectively isopotential.

Measuring voltage with the air is going to be difficult, because air is an excellent insulator. But yes, you could define a potential difference between some place in the human body and something outside. If you've ever gotten a static "shock" you've abruptly discovered that there was a sizable voltage between the surface of your skin and whatever you just touched.

Undergraduate neuroscience textbooks typically have an extensive section on measurement and interpretation of biological voltages; two I would recommend are Purves' "Neuroscience" and Kandel's "Principles of Neural Science". The Wikipedia page "membrane potential" also seems like a good introduction.

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    $\begingroup$ Brilliant answer, thanks. $\endgroup$
    – timtam
    Feb 4, 2022 at 22:27

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