# When current flows through 2 parallel wires (same amount of current)

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1. Jun 24, 2015

### jeevesh

when current flows through 2 parallel wires (same amount of current); the protons in the first wire would see the electrons drifting in a direction and also in the other wire (in the same direction). They would appear to be contracted in the direction which they flow due to length contraction. electrons in both wire would appear to be contacted to the proton so how could feel a attraction and the same question follows for electrons

2. Jun 24, 2015

### goodphy

I don't understand what attraction means. Is it the force between electron and proton? In wires, only free electrons in conduction band can flows and their velocity is far less than relativistic regime as far as I know. But the only information propagation is close to the speed of light.

3. Jun 24, 2015

### bcrowell

Staff Emeritus
You don't say so explicitly, but it sounds like you're trying to understand the classic argument from relativity, based on two parallel wires, that if electric forces exist, so must magnetic forces. There are some ingredients from that argument that you're missing. (1) You have to consider two different frames of reference. (2) The forces on a proton are those due to both the electrons and the protons in the other wire. (Any forces from the proton's own wire vanish by symmetry.) I have a presentation of the argument in this book: http://www.lightandmatter.com/lm/ (section 23.2).

4. Jun 24, 2015

### jeevesh

I am only 15 years old and do not know the type of symmetry you are talking about would you please explain a little about this symmetry in easy terms

5. Jun 24, 2015

### bcrowell

Staff Emeritus
For simplicity, let's say only one wire exists, it only contains protons, and the protons are not moving. In other words, we just have a bunch of protons like beads on a straight string, uniformly spaced. Let's say that the wire is on the z axis. Then there is no direction that the force on a proton could point. It can't have an x component, because there is no reason for, e.g., the positive x direction to be considered different from the negative x direction. The same applies to y and z. Therefore the force on the proton is zero.

6. Jun 25, 2015

### jeevesh

So what is the symmetry here?

7. Jun 25, 2015

### Ibix

If there's just one wire, then there's cylindrical symmetry.

That tells you immediately that any force on a proton or electron due to the wire it's in could not point in a radial direction. If it pointed in one direction, which one? You could rotate the wire around its axis and nothing would change, but the force would have to rotate to be consistent with where it was before. That makes no sense - so any force must be in the line of the wire.

But in the line of the wire, the thing that matters most is the charged particles nearby - and there are as many of them infront of any given proton or electron as there are behind. That means that you can make the same argument as above. Flip the wire end-for-end and nothing changes, but any force would have to flip too to be consistent.

This second step is obviously an approximation, since the wire is not of infinite length and a proton or electron will typically be nearer one end than the other. But it's not a bad approximation as long as you think of the wire as "long".

Recognising what symmetries there are in a situation is a very useful trick for short-circuiting complex calculations. In this case, it means that when you are thinking about a proton or electron in one of the wires, you cn ignore the other protons and electrons in that same wire, and only worry about fields from the other wire.