# Invariance of charge

1. Nov 7, 2006

### quasar987

Today my professor gave us an argument in favor of why charge was frame invariant. It went like "if it were not, then moving neutral object would become charged, which is not something that we observe". It's not exactly that and it made sense at the time, but I'm missing a piece in the argument because if charge varies with speed and + and - charge varie equally in magnitude, then the object remains neutral.

So what is this argument exactly if you know of it? (it also involved gauss's law I think)

2. Nov 7, 2006

### Stingray

Think of a stationary wire with current flowing through it. The simplest model of that is a bunch of negative charges moving through a fixed lattice of positive charges. So if charge changed with speed, the wire's total charge would depend on the voltage applied to it.

3. Nov 7, 2006

### quasar987

So the wire would become charged as soon as we apply a voltage, which is something we do not observe.

4. Nov 7, 2006

### Stingray

Right. And since there are so many charges in a wire, even a tiny imbalance would be detectable.

5. Nov 8, 2006

### Ich

No, it wouldn't. Any effect would be cancelled immediately by a change of the number of electrons in the wire.

6. Nov 8, 2006

### bernhard.rothenstein

charge invariance and atom neutrality

I think that the most convincing argument is the electrical neutrality of an atom in which electrons move with different velocities arround the nucleus
Do you consider that charge invariance and the postulates of special relativity are sufficient for deriving the fundamental equations of relativistic eloctrodynamics without involving Maxwell? I am convinced.
The best things a physicist can offer to another one are information and criticism

7. Nov 8, 2006

### Stingray

Why would the number of electrons change significantly? Suppose the wire had negligible capacitance.

Anyway, I just looked this up in Feynman's lectures where I remembered the topic being discussed. He uses the argument that the conduction electrons and everything else in a conductor move at different speeds just due to temperature. So heating something up (or cooling it) would change its total charge if there were any speed-dependence.

I'm a little uncomfortable with bernhard's argument because I don't really like viewing electrons in atoms as moving at any particular speed. It's not clear that a (semi)classical description has any meaning at that level.

8. Nov 8, 2006

### quasar987

Then you're probably not comfortable with Feynman's argument either, since it implies viewing the electrons in the conductor as moving at a particular speed.

9. Nov 8, 2006

### Stingray

True, but I am more comfortable with it. Classical statistical mechanics makes a lot of accurate predictions even when it is being applied to a bunch of objects that aren't quite classical themselves. But there really isn't much at all about individual atoms that can be described classically.

10. Nov 11, 2006

### Meir Achuz

That charge is invariant is proven in several EM textbooks, using the 4D equivalent of Gauss's law. See for instance, Panofsky & Phillips,
"Classical E & M" or Franklin, "Classical Electromagnetism".

11. Nov 18, 2006

### Sheyr

So what is magnetism than? I thought that magnetic efects come from changes of charges magnitudes as observed in different frames...

I can not agree with the argument of your professor - the moving neutral object consists of both + and - charges, so if both move with the same velocities with respect to the rest frame there is no efect obverved.

12. Nov 18, 2006

### Thrice

Why would you expect them to vary equally?

13. Nov 19, 2006

### quasar987

I was only saying that the fact that a moving neutral body remains neutral does not prove that charge is invariant. It could be that + and - both change equally in magnitude so as to keep the object neutral.