Two Velocities in the Lorentz Law

[sawer]

Lorentz Force: $$\vec{F}=q\vec{v_1}\times\vec{B}$$

v1 is the velocity of particle.

And magnetic field is: $$\vec{B}=\frac{\mu_0}{4\pi}\vec{v_2}\times\frac{\hat{r}}{r^2}$$

If we combine them, we see that there are 2 velocities:

v1 and v2...

I just watched this video about relativity and magnetism:



So v1 is the velocity of the particle and v2 is the velocity of the particle in the wire. Right?

We need both of these velocities to get the relativistic effect, I mean length contradiction for the wire. Right?

 

[Simon Bridge]

In special relativity, you need to know the relative velocities of all the objects you are interested in.
The important thing is to concentrate on what the velocity is relative to.

Off those equations:
v1 would be of the test particle wrt the magnetic field.
v2 is the effective velocity of the particles in the current - in the video, this is being modeled by a line of charge - with respect to the wire.

How much info you need depends on what you want to know and what you already know. For instance:
To get the separation of the charges in the wire, knowing the separation at some other (known) relative velocity, you only need the new relative velocity.

The unification of electricity and magnetism is what the video is trying to show you - it's not a case of one causes the other: they are both aspects of the same kind of stuff.

 

[Simon Bridge]

hmmm... also see:
https://www.physicsforums.com/threads/neutrons-in-electromagnetic-fields.804150/#post-5049593