# What exactly is electric potential (what's wrong with my picture of it)?

In my book, the potential at a point is defined as the work done on a charge to take it from infinity to the point against the field whereas the gravitational potential of a ball is the work done on it to take it to a height against the gravitational field

But the problem with this is that according to this, the potential of an electron will only depend on its distance from positive terminal(clarification at the end). So if an electron passes through resistance its potential drop should not increase because it's like saying that if a ball while falling encounters a wall and breaks through it then the drop in its potential energy will be higher compared to the same distance (thickness of wall) traveled through air, which is wrong

But this is also wrong. So what exactly is electric potential?

(clarification) I said that potential of an electron will only depend on its distance from positive terminal as, potential is the amount of potential energy stored in an electron because of force from holes(at positive terminal) comparing it to earth and ball will help so let's do it, here the holes are like earth that attract the ball(electron), and the potential energy is stored when we lift the ball to a height against gravitational attraction(recharging battery by taking electrons to negative terminal) now we can use the potential energy by letting the ball go and convert the potential energy into kinetic energy and we can use the kinetic energy to do some work (eg.letting the ball hit a box and make it move) we can also use potential energy stored in electrons to do work by letting the electrons flow ans using kinetic energy of moving electrons to do work but they are too small and move too slowly (few cm/second) to be useful that way, so we cleverly use relativity to make them do work how relativity makes magnets work (there is a problem in the video I will correct it below) but the point is that electrons and holes only know how much far they are from each other (like ball's potential energy is only dependent on its distance from earth not on what is resistance of medium through which it is traveling) so how can potential energy of electrons depend on anything else like resistance of wire or something

Correction in video- probable question in mind after watching video will be that why when the positive charge (cat) is stationary, the moving negative charges don't contract and attract the positive charge(cat).

Answer to that question-When the cat is stationary, in its frame the only things moving are the electrons (and not the space between them). So the electrons get squished but the distance between its centers is the same, and the charge density remains the same.

However when the cat is moving everything moves except the electrons, in the cat frame. So the protons and the space between them contracts, effectively changing the charge density and creating an electric force in the cat frame, or a magnetic force in the stationary frame.

• The problem with using other physical analogies to describe electricity is that while the analogy can help visualize something, you still need an idea of what it is approximating to understand things. My favorite analogy is to think of the electrons as a compressible fluid similar to a gas. Potential is point pressure and voltage is pressure difference. The free electrons are bouncing around and off eachother like gas molecules "trying" to avoid each other and pressure can be changed by either changing the energy(velocity) of electrons or increasing/decreasing the density of electrons.
– K H
Mar 10, 2021 at 10:13
• As far as the positive charge in your video, a positive charge is usually not a proton, but a full atom that is missing one or more electrons. The bulk of the electrons stay put in their own atom(Although an electron from a stable shell can switch places with an electron in a conducting shell, but ignoring this, the bulk of electrons at any given time are staying at home.) These atoms stay put because they're connected to neighboring atoms with ionic, covalent or in the case of most conductors metallic bonds.
– K H
Mar 10, 2021 at 10:23
• Ooops molecular solids are also mentioned, held together by London dispersion forces, dipole-dipole forces or hydrogen bonds.
– K H
Mar 10, 2021 at 10:24
• Just reading your first paragraph alone, it looks like you (or your book) have some confusion between potential and potential energy, which are two different things. Mar 10, 2021 at 13:46

Not gonna read your entire question, but seems the explanation of your book is overly complicated for no reason. When people cannot explain things simply, it usually means they don't understand them themselves.

If you relate to a cylinder filled with water that has a hole at the bottom:

• The potential (Volts) is the "pressure" at that hole
• The current (Amps) is how much water goes through that hole
• The power is the multiplication of these two
• The energy is the power over time.

I think this relates to your gravitational field but is handier to understand.

• +1 for "When people cannot explain things simply, it usually means they don't understand them themselves." which is indeed a fact. Mar 10, 2021 at 10:14
• But what will potential difference mean in this analogy Mar 10, 2021 at 12:10
• @SubhranshuSharma Potential difference in this analogy means difference in height. Mar 10, 2021 at 12:15
• I asked this question first on physics stack exchange and many people asked me to clarify why potential should only depend on distance from terminal which made this explanation complicated and Everything should be made as simple as possible, but not simpler. And latest theory of magnetic force uses relativity and you can't make it any simpler. And yes I don't know what potential is that's the point of asking (not intending to be rude) Mar 10, 2021 at 12:15
• You can see potential as a latent force. Magnetism is perhaps based on relativity, but relativity is an incomplete theory at this point, especially towards gravity. If you go really deep things fall apart thus simple analogies sometimes makes sense. For electricity it depends if aim at an understanding for doing electronics or if you want to know the deep physics, truth is they are not really known. For example it was recently discovered electron is not a point particule but a probability cloud around the nuclei, thus what you learn might already be outdated. Mar 10, 2021 at 18:24

A system of charges, fixed in space, create a field of electrical forces, called E, where E is a 3D vector: E(x,y,z)

Gauss showed that E is conservative, that is, rot(E) = 0.

A conservative field of forces is so nice that you can define a work function.

The work function tells you how much work a probe charge has to do to move from point A to point B.

The work function is defined as follows:

ΔV = Integral from A to B of (E • dl) where • is the scalar product

ΔV = V(B) - V(A)

If A is infinity than ΔV is referred to infinity and, only in this case, you may talk about "the potential of B".

We don't have moving charges here. The system of charges is fixed in space.

I can't read your handwriting, but I think the misconception you have is about the field coming from the positive terminal and being influenced by the distance from the positive terminal.

The secret is to remember that each charge carrier causes its own field. The overall electric field strength at a point is the sum of the influence of all the nearby point charges.

In wires this is electrons. In a conductor, they spread out as much as possible to make the field uniform across the surface of the conductor.

In a circuit, the battery is continually adding new charge carriers at one end and removing them from the other.

Resistors don't impair the field itself, but they do affect the movement of the charge carriers in the process of "spreading out".