Magnetic field causing a force

[Sefrez]

Say you have a current set up in the plane of this page going to the right in a long straight wire (horizontal.) When I say current to the right I am not going by the standard but rather saying that the electrons are moving to the right. Not "positive" charged particles.

The electric field magnitude around the wire could then be defined as B = Ui/(2PIr) where r is the radial distance from the wire.

Now have an electron going to the right also, at the same rate as the current. Its velocity is parallel to the current.

By F = qV x B, the electron should experience a force of qVB where its direction should be towards the current carrying wire. V is defined as the velocity relative to the wire material, or the protons in the wire, if you will.

Now remove the wire and thus the protons leaving only the flow of electrons. Also remove all other electrons leaving one. There is now only two electrons moving to the right, one from the original wire and one being the other electron with velocity V.

Should the electron now experience a force? It seems as if it would be no because now neither have a velocity relative to each other. It is simply two particles side by side.

So this leads me to ask, does the magnetic field generated also depend on the other attributes? Like, protons or possibly even neutrons? Otherwise, I can't seem to differentiate these two scenarios and they seem to disagree. Maybe my reasoning is flawed?

 

[cragar]

If you have a current carrying wire, and the electron is going the same speed as the electrons in the wire, then in that frame it will appear that the protons are going the other way so it will see a B field. But also you need to factor in length contraction, You need to use Einsteins velocity addition rule for the relative speeds of the moving particles in the wire. Because of length contraction we will see a different line charge in the wire and a net E field. And the one where you remove everything except 2 electrons moving side by side. Yes there will be a force cause by the E field of each of the electrons. You bring up good points.
Relativistic electrodynamics is fun.
You don't need to worry about the neutrons they have no charge and no B field classically speaking.

 

[Sefrez]

Thanks for the reply, cragar. I see, so there is the protons that can relate to the electrons in defining a B field; taking them away changes the situation. As far as contraction, I have heard about that, but I have not studied any of it yet. I have really only taken one Physics class on classical mechanics and am now taking another class on what you could call part 2 (electrostatics and magnetism.) I guess I will continue to have these questions arise as I simply need more insight to answer them (not in the material I am learning.) I tell you though, I about kill myself with questions I have running through my head all day. Going over so much material in a short period (college for you...) doesn't help - leaves me with many questions!

Thanks again.

 

[cragar]

ya we can have protons or electrons moving with respect to each other and that will create a B field. Or they can just be moving by themselves. Moving charges create B fields. Thats good that you have a lot of questions running through your head.

 

[cragar]

ya we can have protons or electrons moving with respect to each other and that will create a B field. Or they can just be moving by themselves. Moving charges create B fields. Thats good that you have a lot of questions running through your head.