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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?

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2 Answers 2

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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.

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  • $\begingroup$ 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. $\endgroup$ Jun 1, 2015 at 20:23
  • $\begingroup$ 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. $\endgroup$ Jun 2, 2015 at 17:35
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You have totally misunderstood the potential energy when an electrically charged object moves from one point to another point in an electric field.

Energy here is not any sort of kinetic energy which it can acquire, but it is the energy required to do the work of pushing or pulling the charged object from one point to another point in the electric field. It depends on the property of the charge of the object whether it is a repulsive force or attractive force on the object. It means that the repulsive or attractive force produced by the electronic field does the work of moving the object from the initial location $i$ to the final location f. In other words, provided energy = work, where the energy here is the electric potential energy in the electric field produced by the difference in the electric potential voltage between those two points in the electric field

$$W = -(U_f-U_i) = -q(V_f-V_i)$$

where $U_f-U_i$ is the change of the electric potential energy from the initial point $i$, the final point $f$, $q$ is the charge of the object, $V_f -V_i$ is the difference in the electric potential voltage between the initial point $i$ and the final point $f$ in the electric field.

There is not any kinetic nor potential energy gained by the moving charged object as the way how you have totally fundamentally misunderstood it here. Kinetic energy here is zero because before the charged object is moved by the electric force produced by the electric field, it is stationary ($V_i= 0$), and it stops at the final point ($V_f=0$) which means that $V_i=V_f$ or $K_i = K_f= m(0)^2/2=0$ or $K_f-K_i = 0$

The electric potential energy provided by the repulsive or attractive force produced by the difference in magnitude of the electric field at those two different points with 2 different distances away from the source of charge which has set up the electric field here is used up to do the work of moving it from the initial point to the final point

The charged object can gain electric potential energy only when an external or applied force purposely moves it from an initial point either outside the electric field or in the electric field to another location nearer or closer to the charge source which sets up the electric field. It is similar to an object being at a higher altitude have a larger gravitational potential energy than when it is at a lower altitude from the Earth's surface. The difference here is the closer you purposely move the charged object to the source of the same charge as its charge, the more electric potential energy it will get to move a longer distance when released and repelled by the same charge of the charge source at the location closer to the charge source, and traveling a longer distance always means much more work done to make it move, and the work done is equal to the magnitude of the electric potential energy required to do the work, and the energy is provided by the electric field.

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