# Magnetic Field Generation in a Vacuum Through Special Relativity

The way special relativity explains electromagnetism is that when electrons move, their lengths contract due to relativistic effects, even though they do not move at extremely high speeds. This contraction leads to a slight imbalance in charge density along the wire, making it seem as though the stationary protons are generating more force because the electrons' lack of force is more noticeable. This apparent additional force from the protons contributes to the overall magnetic field produced around the wire. However, in the context of a vacuum, such as in a cathode ray tube (CRT), there are no protons, only moving electrons. In this case, where does the perceived extra force come from? Without the presence of protons to create this apparent additional force, how is the magnetic field produced when the current flows through a vacuum?

• The special relativity argument can be done correctly. But as you have found, it quickly gets confusing and easy to get wrong. Here is a video on it. Veritasium's 'How Special Relativity Makes Magnets Work' - EXPLAINED (better). Maxwell's equations treat current as a source of magnetic field. This is how it is usually handled. Commented Jul 15 at 19:11
• Your premise is wrong. Electrons have no length. It is the length of the wire and spacing between electrons that change, causing a change in charge density. Commented Jul 15 at 19:56
• see physics.stackexchange.com/q/64703/195949 Commented Jul 15 at 22:32