I’m trying to learn about the Lorentz contraction and it’s relation to magnetism. I have two questions about them.

1- I watched the “veritasium” video about the relativistic explanation of the magnetism(https://www.youtube.com/watch?v=1TKSfAkWWN0).

I can’t say anything about the reliability of the “veritasium channel” but I know it’s very popular. Here is one thing that puzzled me in the video:

At 1:28, the electrons of the wire is moving relative to the positively charged cat. So, from the cat’s perspective, the moving electrons should be subject to lorentz contraction and there should be a net force on the cat. But in the video, there isn’t.

At 1:50 the cat starts moving with the electrons. This time however, again from the cat’s perspective, the positive charges appear to be moving and because of the lorentz contraction, there is a net force (magnetic force) on the cat.

This seems to be same as the explanation from Purcell described here (Magnetism as a consequence of length contraction): http://physics.weber.edu/schroeder/mrr/mrrtalk.html

But how does this make sense? When the “test charge” is stationary in the lab frame, the moving charges on the opposite should have been contracted but they are appearantly not.

In other words, from the frame of the test charge, what is the difference between moving the wire electrons to the right and moving the wire nuclei to the left?

2- Do all the contraction/dilation effects of the special relativity work in tangential directions?

If a charge q1 is moving fast directly towards a stationary q2, there would be no magnetic force acting on q2. No contraction of q1 on the q1-q2 axis.

If the charges q1 and q2 are moving together on the same axis, again there would be no magnetic force acting on them. No contraction on the q1-q2 axis.

And from the form of the Biot-Savart equation we can see that the “length contraction effect” is dependent on the sinus of the angle between the directions of the moving charges.

These imply to me that the “length contraction” of an object A, could only be due to it’s tangential velocity component relative the point B (the circular motion of object A, around the center B). Is this right?