# Origin of field deduced from potential

Related: Tubelights+power lines pictures?

I would've edited this into the above question, but I realized that there' enough to it to qualify as a new one. Plus this seems to be a confusion of many people (including me).

I've already been able to explain part of this, so I'll put that explanation first just to make the question clearer.

The original question is as follows: In a circuit, you can have potential, but what is the origin of the field associated with it? Conducting wires have no net field, just some tiny opposing fields popping in and out of existence which facilitate current.

Explaining this for a simple capacitor is easy: With a charged (parallel plate) capacitor, one can see that we have a field between the plates but not in the rest of the circuit (for simplicity we can assume that the capacitor is just being shorted. So, traversing a different path in the line integral for potential gives a zero p.d, clearly a contradiction. After thinking about it, I realized that there is a significant fringe field near the terminals of the capacitor, which contributes heavily to the potential. SO the rest of the wire is equipotential without a field, and we have a p.d. only at the terminals due to the fringe fields. IMO there will be similar fringe fields that explain where the battery's potential comes from.

Now, I can't seem to get a similar explanation for current through a resistor. I fail to see any field being formed.

And my main issue is this: Let's say we set up a power line parallel to the ground. It may carry AC or DC current. Either way, it has a p.d with the ground at every point in time, which may vary. P.d. $\implies$ field, but I don't see any. In the AC situation, it could be from EMI, though I doubt that EMI is strong enough to produce the required field strength. In DC, @akhmateli mentioned charge being distributed on the wire surface, but I doubt that as well.

So where does the field come from? Is my explanation for a capacitor correct?

Oh, and in your explanation, I'd prefer no "this comes from the potential" or "these charges move due to the p.d.". I want one that talks about fields and charges only. I've had too many explanations of this which talk about "the field comes from the potential", which is IMO cheating.

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Pushing those electrons through the resistor requires a force. The simple picture is that the electrons are running into atoms and losing energy, but disturbing the atoms as they go and creating almost frictional heating.

A quantum mechanical description might be more accurate but this model is good enough. It's like pushing water through a pipe. Flow = pressure / (resistance per inch * inches of pipe).

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Yes, it required a force, but where did the force come from? Eventually, E fields come from charge distributions or varying B fields. I see neither here (in the DC case). – Manishearth Feb 29 '12 at 3:07
Well, we have to break it down. We have to go into how a battery works, I suppose. We need to find out why a battery only produces a certain amount of potential energy per electron.There could be a thing that produced a certain amount of field. – sonardude Feb 29 '12 at 4:01
In the lab, I have a bench top power supply that supplies either constant voltage or I can set it to supply constant current to my circuit. It's down to the way I set it up. – sonardude Feb 29 '12 at 4:02
In the case that I set it up to provide constant current, it will separate charges (and keep increasing voltage) until it measures the current I specified. – sonardude Feb 29 '12 at 4:05
When I say increasing voltage, I mean increasing field strength as well. Field * distance = potential. Wires, being perfect conductors (of fields) don't count in the distance calculation. Resistors do though. – sonardude Feb 29 '12 at 4:08

Credit @akhmateli: The battery spreads a surface charge over the wire. This causes a net field outside leading to potential differences. Near a resistor, due to resistance to flow, these charges accumulate outside the resistor and create a field.

See http://www.astrophysik.uni-kiel.de/~hhaertel/PUB/voltage_IRL.pdf for more details.

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