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as the title suggest, Can I show the existence of magnetic field using only special relativity and invariant of electric charges?

ziv
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    What is a yes or no answer without any detail worth? Unless you are sitting a multiple choice exam right now... – Nephente Mar 10 '21 at 09:27
  • No one wil ask me this question in multiple choice exam. It matter because physics should be set of true statement. I dont want answer that consist of too many words and goes around the topic. I only want a hint for which way to go in order to find the explanation myself – ziv Mar 10 '21 at 09:58
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    But you should not restrict the answer. If someone wants to explicitly explain it. Instead, request for both. – Swayam Jha Mar 10 '21 at 11:21
  • You are right. I edited the question – ziv Mar 10 '21 at 11:29
  • https://physics.stackexchange.com/q/615500/ , https://physics.stackexchange.com/q/586741/ – HolgerFiedler Mar 11 '21 at 05:33

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The magnetic field has some origin from special relativity and you can show How the concept of magnetic field appears, starting from special relativity. This is very well done on Electricity and Magnetism By Purcell. You can look at it if interested.

But the book sometimes leads to the false statement that special relativity is sufficient for the magnetic field which is not true.

The fundamental sources of the magnetic field are electric currents and magnetic dipole moments (changing electric field also can also create magnetic field). Intrinsic magnetic dipole moments exist at the fundamental level and they directly create magnetic fields. Most subatomic particles have magnetic dipole moments and therefore act like little bar magnets. For instance, an electron has an electric charge and an intrinsic magnetic dipole moment. Therefore, an electron directly creates an electric field from its electric charge, and a magnetic field from its magnetic dipole moment, even when at rest. When moving, an electron also creates a magnetic field from its motion (because a moving electric charge constitutes an electric current).

More on this can be found here

Young Kindaichi
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  • Thanks, I took electricity and magnetism two years ago and the course follow Purcell's book (I also took it from the library). Since then I had that question. So you also spotted the reason of why I'm asking it – ziv Mar 10 '21 at 15:31