What creates voltage? What causes electrons to move in a wire?

I was trying to break down how a transistor works to a friend, and I took a moment to think about electric current and voltages. I realised I do not understand where these phenomena come from. I understand (on a very very shallow level) how electrons interact through quantum electrodynamics, but I could not think of any way that this interaction should create voltage and electric current. I tried googling a bit, but I don't understand modern physics enough to narrow my search down.

1. What part of the Standard Model, Relativity, or any other modern physics theory describe voltage?

2. What creates voltage?

3. What causes electrons to move in a wire?

This comes from classical electrodynamics, there is no need to go to Standard model theory or quantum electrodynamics for this. The simple answer is that electric potentials, like electric fields, are just a way of characterizing the way charged particles interact with each other. So, charged objects create voltage analogous to the way that they create electric fields and interact with each other.

Voltage can be thought of as a measure of potential energy per unit charge. I.e. if you have a certain amount of charge $q$ (e.g. 2 Coulombs worth) in an electric field $E$, and you let that charge be pushed around, that charge will gain energy as it gets pushed. Specifically, if it gets pushed from point a to point b, and there is a potential difference of $\Delta V_{a->b}$ between those two points, then the charge $q$ would gain an energy equal to $\Delta E=q\Delta V_{a->b}$.

In this way, A voltage between two points is just a way of describing the electric field between those two points and the amount of energy charged objects will gain while moving between those points because of those fields. Electric fields are just being produced by some build-up of charge somewhere, e.g. on a capacitor. Voltage is indeed directly related to the electric field via $E = \nabla V$ where $\nabla$ is the gradient operator. In this way, voltage differences are also created by the build-up of charge.

More specifically, if you see for example a 12V battery, what that means is that when you connect the ends of the batter via, e.g. a copper wire, the battery will induce an electric field throughout the wire that pushes electrons in one direction along that wire. The electrons will gain an energy equal to $q_e \times 12 V$ if moving from one end of the battery to the other where $q_e$ is the charge of that electron. The 12 V is then a measure of how much energy the battery is capable of giving each electron.

Current is simply a measure of the amount of charge passing through some area (usually the area of some wire) during a given amount of time. Higher current means more charge is getting pushed through the cross-section of the wire.

Hope this helps.

• Do you really mean "causes electrons in that wire to be produced"? By "produced" do you mean created? I assume not but if so, could you explain the production mechanism? I think that part of the answer would benefit from rewording or clarification. Up to now I had understood that the electric field causes already existing free-electrons to drift and that no additional electrons are produced in the wire. – RedGrittyBrick Jun 1 '15 at 20:23
• Yes you're right. I didn't mean produced at all; I don't know how that word got there. I've changed the answer. – aquirdturtle Jun 2 '15 at 17:35