There is an explanation in the Wikipedia. Unfortunately the article is quite verbose and doesn't clearly explain why both positive and negative charges vary density even if only one is moving.
It is also not possible to figure out with respect to which frame of reference they shrink/expand. Can this be made more clear or is there a source that already does so?
Actually, I resorted to wikipedia after Feynmann because he said something like
model of a wire with a current of positive charges, separated by an
average distance, L. The wire has to be electrically neutral in the
lab frame, so there must be a bunch of negative charges, at rest,
separated by the same average distance. Therefore there's no
electrostatic force on a test charge Q outside the wire.
I have got this quotation from the last answer. I do not understand why nobody, who discusses the relativistic density growth, cannot see the problem. How, after saying that
- motion increases density and
- positive charges are moving
can they say that we have negative charges, standing still in the same frame, having the same density? I see that when positive charges are stopped, their density drops and we'll get the negative charge prevailing. No current = object is charged negatively! Do you see that? This means that all objects in the Universe must be negatively charged in order to be neutral when positive charge starts moving in them. But, we know that objects are normally neutral. So, when current appears in the loop, you must first explain where the extra charge is coming from and why the loop remains neutral. But, teachers do not do that. They have a conspiracy to avoid discussing this simplest case and jump immediately to the case of test charge moving at speed of current charges. So, is it right that all objects in your Universe are electrically charged when no current circulates in them?
Best Answer
follow the link at WP:
The simplest, and the full derivation of Magnetism as a Relativistic side effect of ElectroStatics by Hans de Vries. His paper linked in that page is very clear.
Motion of charge is needed to perceive a magnetic field.
In the Maxwell equations the 'Ampère's circuital law' says :
no current and no electric field variation(a) in time -> curl of magnetic field = 0
and Gauss's law for magnetism : divergence of of magnetic field = 0
(a) An electric field variation is created by charges in motion.
How can we presume that the magnetic field, that only exists in presence of motion and is observer dependent, has the same fundamental existence as the electostactic field that exists in all circunstances ?
'Motion' by itself can not be an entity creator. Luckily special relativity brings order.
edit add:
I will recall an example from a common life experience: rainfall. You are not in motion and rain is falling in a non windy day. It falls uniformly downwards and you get equally wetted from all sides.
The moment you start running you will get more wetted in your front than in your backside, i.e. more droplets per unit time will hit your front than your back. Your motion created the illusion/perception that the rainfall is not uniform.
Now, using relativity, we can reverse the situation: it is a windy day and you are stopped ...
In the same way a test charge in motion irt a uniformly charged wire will perceive it as having more charge from ahead than from behind.
This fundamental question about what is real versus what is perceived make me wonder why so many theorists are trying to find magnetic monopoles. Inglorious and Insane task. There is more to Physics than equations. KISS (keep it simple, stupid).
The fundamental question is: can motion create anything? NO.