Question about electromagnetism and frames of reference

[abdossamad2003]

in this text:

my question is in highlighted line:
"The two rods have the same length (in S) and contain the
same number of charges." why?

Considering that the negative rod has movement, it should have a shorter length than the positive rod according to a relativity!

 

[PeroK]

in this text:
View attachment 340896

my question is in highlighted line:
"The two rods have the same length (in S) and contain the
same number of charges." why?

Considering that the negative rod has movement, it should have a shorter length than the positive rod according to a relativity!

There was a long thread about this recently. If you set up a steady current in an infinite length of wire, then it's not clear whether the moving charges get closer together or not. It all depends on how you accelerate them.

If, however you consider a physically realistic large rectangular loop of wire, then the moving charges must have the same charge density, as no charges gave been added or taken away from the wire. This is in the rest frame of the wire.

This means that in the rest frame of the moving charges in a section of the wire, the charges must have got further apart. And the stationary charges will be closer together in this frame.

Note that there is no single rest frame of the moving charges throughout the whole loop.

 

[A.T.]

Considering that the negative rod has movement, it should have a shorter length than the positive rod according to a relativity!

Here is a diagram by @DrGreg that might help:
https://www.physicsforums.com/threads/explanation-of-em-fields-using-sr.714635/post-4528480

Previous similar threads:
https://www.physicsforums.com/threa...-a-current-carrying-wire.1058519/post-6981501
https://www.physicsforums.com/threads/electric-currents-and-length-contraction.930943/#post-5877453
https://www.physicsforums.com/threa...tion-of-electromagnetism.982883/#post-6284262
https://www.physicsforums.com/threa...magnetism-with-relativity.932270/post-5886984

 

[Sagittarius A-Star]

my question is in highlighted line:
"The two rods have the same length (in S) and contain the
same number of charges." why?

Considering that the negative rod has movement, it should have a shorter length than the positive rod according to a relativity!

The authors of this book assume, that the rest length of the rod, which is moving in frame $S$, is greater than the rest length of the other rod at rest in frame $S$.

"It is a well-known fact that a current-carrying wire is neutral ... in the lab frame", and therefore a positive surface charge density must compensate the negative volume charge density, according to
http://web.mit.edu/wangfire/misc/AJP000360.pdf