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Gauss' law for electricity and magnetism, Ampere's law and Biot-Savart's law — all of these laws are crucial for understanding electromagnetism and Maxwell's equations.

But I want to know how each of them derived their laws. If anyone could give me a link to any article or suggest me any kind of books then that would be big help too. I want to learn their methods for deriving these laws in a rigorous way.

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    $\begingroup$ It's generally better to ask one question at a time given our format here, so I would recommend that you edit this question to remove your question about the permeability & permittivity constants and ask it in a separate post. $\endgroup$
    – Michael Seifert
    Jun 2, 2021 at 18:41
  • $\begingroup$ Coulomb’s constant doesn’t have to be written as $1/4\pi\epsilon_0$. In Gaussian units it’s just $1$. You don’t need any permittivity and permeability constants for vacuum. It’s just a convention that SI has them. $\endgroup$
    – G. Smith
    Jun 2, 2021 at 18:49
  • $\begingroup$ Have you done any of your own research? Tried looking up short bio's of gauss, ampere, and biot and savart? Where should we start? These men were researchers in active fields, they developed theories building on a lot of work, and the laws themselves as we know them have their own long histories. $\endgroup$
    – Sam Gallagher
    Jun 13, 2021 at 18:16
  • $\begingroup$ If I recall correctly, Biot&Savart got it form experiments, Gauss got it from mathematics (Gauss theorem) but published after Maxwell's, and Ampère did not derive Ampère law but Ampère force law for two wires with DC currents. $\endgroup$
    – Mauricio
    Feb 3 at 16:13

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