What is voltage, is it the amount of electrons or the concentration of electrons/ions?

Voltage is the difference in the "concentration" of electric potential energy (energy per charge) between two points. It is what makes charged particles flow (current). A big pool and a small pool with the same concentration of electrons will have the same concentration of electric potential energy. Thus, no voltage or potential difference between the pools. Usually we say there is a voltage across a nerve cell membrane if there is a difference in the concentration of charged particles (ions) inside and outside the membrane. Osmotic pressure, not voltage, is the reason cells burst. When the concentration of ions in the cell increases, more water is drawn into the cell and this is why they burst. Sorry, I don't understand the last question.

Anonymous. Your question on voltage and your analogy of two "pools" of electrons seems weak. You are using the word pool to mean source or reservoir. I don't know how you "concentrate" electrons. The differential electrical charges between two points would be the measure of relative voltage. Connecting them would allow a flow of current to equalize the charges. The flow would likely be a spark.

Voltage is not an amount of electrons. It is a potential level, i.e. a property of a point in space that expresses how much objects want to be in a position. Positions with lower potentials are more desirable. [Losing the anthropomorphic analogy, objects that are in a position of potential x will be propelled towards a position with potential y by a force that is proportional to the difference x-y (the derivative, actually)]. Potential -and therefore voltages- is best explained by an example: height. An object that is in a higher location x will travel in the steepest direction to a lower position y. For gravitation of normal objects on Earth, height is the same as potential. (more precisely, they are proportional as E=mgh). This idea is ubiquitous in physics and not limited to height. An example, which is used a lot in geology and biology, and which you implicitly mentioned in your question is http://en.wikipedia.org/wiki/Water_potential. Height is still a factor, but it is not alone: gravitational, capillary and osmotic effects come together and determine the most desirable locations for water, i.e. those with lowest potential. Higher positions are generally less desirable (again, E=mgh), but high concentration and small capillaries (among others) can increase the attractiveness of a position. This is why water flows from the moist ground through tree's xylem and up to (comparatively) dry locations, against the gravitational force. TL;DR: In electrostatics, height is out of the picture as a quantity. Here, positions with less equal / more opposite charge are more attractive. Think of a position with a higher electric potential as if it is :higher:, and think of charged particles as balls rolling downhill. Do not think of charges as if they are concentrations. The reason for this is that a charged particle creates an electric field, which influences the potential of the space around it. More charges generate a larger electric field. The spacing of the electrons does not matter much at the scale of neurons. Concentrations, however, are all about the spacing of particles -- that's really all they are. So the two quantities are not related and should not be confused. (stop TLDR) About your more specific inquiry to diabetic neuropathy; I am not a doctor, but diabetic neuropathy seems to be more of an umbrella term for diabetes-linked neuron pathologies, rather than a single disease. I could not find a type that causes neurolysis. I also would not think that a high electrolyte concentration would cause a cell to burst, especially a neuron cells because taking up and releasing electrolytes is really what they are all about. In any case, a sudden release of many electrolytes might cause pain-transferring neurons to be activated (taking up K and Ca is how they communicate) and cause a slight prickle [speculation, no source]. An actual electrical shock would be way out of proportion. **Voltage is actually the difference between potentials of two locations, thus it expresses how much objects in position x want to go from position y.

First of all, you don't use voltage to say something about a single point or particle. Asking what is the voltage of a "pool of electrons" is like asking what is the distance of a frog. Distance from "where" to the frog? Just as a measurement of distance requires two points, so does voltage. Voltage is a measurement of the difference in electrical potential between two points. For example, between the positive and negative terminals of a battery. Obviously an accumulation of charged particles at one or both points contributes to a voltage between the two points. The more electrons accumulated at one point, the higher the voltage between the two points. The more positive ions at the other point, again, the higher the voltage. If you have a finite resistance, then a current can flow. Current is a movement of charged particles. The equation for the flow of current through a resistor is V=I*R, where V is voltage, I is current, and R is resistance, with units of volts, amps, ohms, respectively. The direction of the current flow, by convention, is opposite the direction of the flow of electrons. This is due to the unfortunate choice of sign convention when deciding to consider electrons negatively charged and protons positively charged.   Regarding the 2nd part of your question... Our cells contain Sodium Potassium Pumps (sometime referred to merely as Sodium Pumps) which facilitate moving Sodium and Potassium Ions through the cell membrane to regulate the concentration of these ions in our cells. The main enzyme involved is http://en.wikipedia.org/wiki/Na%2B/K%2B-ATPase. I can't speak about various pathologies involving the enzyme without doing further reading myself, so I'll stop here. All I can say is that if your Sodium Potassium Pumps completely stop working, you'll die. The loss of effectiveness in Sodium Pumps is a main cause of Kidney failure.

This is just a small addition to the other answers. There are two kinds of properties; Intensive and Extensive, and it's a good idea to bear this in mind whenever you come across a new property. Intensive: the value (or size or bigness) does not depend on how much you have. Temperature is intensive: the temp of a cup of coffee does not halve if you pour half of the coffee away.  Pressure is another. If I put a partition up dividing a room into two halves, the pressure in each half of the room is still one atmosphere. Electrical potential (which is measured in volts and is sometimes called 'voltage') is intensive. If you build a car battery twice as big, or a hundred times as big, it still has a potential of 12V.  Extensive; the value does depend on the size. Mass is extensive.... twice as much weighs twice as much. Volume is too. The amount of energy released in a chemical reaction is extensive. How much work a battery will do is extensive.

The correct terminology is Potential not Voltage. Simple Version: No the Potential won't be the same-the charges will feel a greater net repulsion, as there are greater number of them packed here. Mathematical Approximation: This is an application of Gauss' Law.Let us model our swimming pool as a sphere- for easy mathematics. As you can see the potential depends on the quantity \dfrac{Q}{R}. But a constant concentration of electrons implies C=\dfrac{Q}{R^3} is what is constant. ThusV=\dfrac{Q}{4\pi\epsilon R}. V=\dfrac{CV}{4\pi\epsilon R}. \approx\dfrac{CR^2}{4\pi\epsilon}Thus you can see a clear relation with R^2 !Thanks for A2A.

Current is the amount of charge in Coulombs passing a point on one second. It is measured in Coulombs/second a.k.a amperes Voltage is electric potential difference. Voltage is the amount of work that can be done per Coulomb and it has the units Joules per Coulomb. Joules is a unit of energy. So the units of voltage are Joules / Coulomb. In a 10V battery, every single Coulomb of charge coming out of the battery is able to do 10 Joules of work.

About your question concerning voltage.   Voltage is a scalar potential describing the electrical field. When the distribution of the scalar potential---voltage---is completely decided, the entire electrical field fulfilling the space is certain. The force imposed on a particle carrying electic charges positioned in the field is therefore decided.   In a plainer language, you can imagine the voltage as the level of water. When the water stays in a higher position, it has the innate tendency to flow towards a lower position. So do charges. When they are in a higher electric potential level', they tend to flow to a lower 'potential level'. At the same time you notice one fact: whether the charge stream exists or not just depends on whether there is a level difference; it is not related with whether there is a lot of water or little.   You probably have twinged two irrelevant concepts together---voltage and charge carrying particle concentration.   About the your additional inquiry, The first fact is, cells do not 'burst' when they absorb too many sodium ions. They will burst when when absorb too much water. Secondly, the amount of ions in almost any cell is considerably small, therefore you do not have to worry that it can create such an electric signal which can make your brain produce the feeling of pain or getting shocked. The problem which results from excessive amount of certain elements is the normal physiological function is significantly disturbed, which is very severe than pure slight electric shock.

You have to accept the idea that voltage is not a thing or an object or a chunk of power you can pick up and carry around. It is just a term derived from mathematical formulas of electrical or electronic results of other electrical or electronic factors.   Voltage is a measure of the difference in electric potential between two points in space, a material, or an electric circuit, expressed in volts. The International System standard value for one volt is derived from a couple of formulas;   Law of power in a circuit, P = I x E (Power in watts equals the current times the voltage). Thus in most homes in the US, the watts you use (and pay for over a time period) is a result of the current (in amps) flowing through your electric meter at a certain voltage. You see that in your electric bill each month as kilowatt hours (KWh). All of that means that if you use a toaster rated at 1200 watts with a voltage of 120 volts for one hour with 10 amps flowing through it, you have used 1.2 KWh.   Ohm's Law, V = I x R, (volts equals the current times the resistance), states that the http://en.wikipedia.org/wiki/Electric_current through a conductor between two points is directly http://en.wikipedia.org/wiki/Proportionality_(mathematics) to the http://en.wikipedia.org/wiki/Potential_difference across the two points.   There is another expression describing voltage using the terms coulomb and joule. I won't go into it.   By the way, the speed at which electrons move through an electronic circuit, through the wiring of a city's power service or though your body's nervous system is the speed of light (299,792,458 meters per second or 186,282 miles per second). That's faster than a '57 Chevy.