Potential vs. Voltage: Explained

[Dale]

btw, can you give me a practical situation? Perhaps you are referring to cases where a practical situation can be approximated to an infinite one - which can then be solved?

I gave one above, but here is another one of immense importance in the field of neuroprosthetics and neurophysiology:

Let's say that you want to analyze the flow of ions across a small patch of a neuron's cell membrane. If the patch is small enough (e.g. patch clamp experiments) then the local fields are well approximated by considering the membrane to be a pair of infinite sheets of charge. A sheet of charge has the same problem at infinity as a line of charge, so you couldn't use that approach if you insist on a 0 potential at infinity for a sheet of charge. If you relax that requirement then the problem becomes relatively easy to solve and the results are quite accurate and powerful.

 

[sophiecentaur]

I get it now - thanks.
You avoid having to consider 'end effects'; smart.

 

[dE_logics]

A section of my notes -

Electric potential -
As we have all read since childhood, its the work done (in joules) to bring 2 charges together/apart (from/to infinity) of the same/different polarity, this is just an example, actually its the work done to move a charge through an EF (and cause E.F is a conservative field, the same energy is stored in form of P.E).
The reason for taking infinity is cause if a point is taken, it will no longer be called potential, but something else (the next heading actually).
Its Potential = W/Q by this the unit of potential will be j/c which is called 'voltage'.
So if we encounter such an arrangement such that the work done per columb is one joule, then the potential is too 1 V.
This definition is working as expected, its a known fact that In a constant current source if the resistance in the circuit is made to increase, the potential increases too, that is to pass through the resistance, more work needs to be done.

Potential difference -
Usually the electric potential computed is WRT earth, in fact electric potential is an understatement cause its not defined WRT what it has the potential (its usually WRT earth) and is relative to infinitely (that is work done to bring that charge from infinity to that point).
The term potential difference is a complete statement, cause in this the PD is relative, I mean, if the PD between Earth and some point is 1.5, then the work done to transfer a charge form that point to Earth is 1.5 J.
If its not WRT earth, and the potential difference WRT another point jumps to 20 V, then the work done to transfer a charge form that point to Earth is 20 J, so P.D is relative.
Though P.D is a major criteria determining the work done by a charge (or many charges), it can happen that if with the same P.D, the resistance of the circuit is decreased, more energy is produced at the same potential difference.
The reason for this is that definition of potential difference is work done per charge, so if the no. of charges per unit time (rate of charge flow) increases, though the work done per charge will remain constant, so the total energy delivery will change.
Initially just assume that the momentum (and so velocity) of electrons in a circuit is directly proportional to the P.D, it will be explained later...what actually happens.

Its to be taken into account that in a circuitry having a constant voltage of EMF E, the the energy dissipated in the outer circuit (that is out of the battery), is equal to the EMF of the battery, as we talk about a constant voltage source delivering energy, this definition described is the aim of the constant voltage source that is no matter what happen constant voltage source will deliver the rated energy per charge...of course some can't do that by 100% that is have a bit of inaccuracy.