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How to mathematically represent the fact that electric charge is a fundamental quantity? i.e. that it cannot be explained in terms of other things, for example, the normal force can be explained as electrostatic repulsion thus it is not fundamental. However, Coulomb's law is fundamental since it can't be explained in any other terms.

For example, the mathematical equivalent of conservation and quantization of charge are as follows $$\vec\nabla\cdot\vec J+\frac{\partial\rho}{\partial t}=0$$ $$Q=ne,\, n\in \mathbb{Z} $$ So is there an analogous version for fundamental nature of charge?

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    $\begingroup$ What do you mean by charge being a “fundamental quantity?” $\endgroup$
    – J. Murray
    Commented Aug 9, 2022 at 20:08
  • $\begingroup$ @J.Murray that it cannot be explained in terms of other things, for example, the normal force can be explained as electrostatic repulsion thus it is not fundamental. However, Coulomb's law is fundamental since it can't be explained in any other terms. All these remarks are only made with respect to classical EM. $\endgroup$
    – GedankenExperimentalist
    Commented Aug 9, 2022 at 20:13
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    $\begingroup$ So, if you consider Coulomb's law as fundamental then why don't you just use Coulomb's law as your way to "represent the fact that electric charge is a fundamental quantity"? $\endgroup$
    – hft
    Commented Aug 9, 2022 at 20:29
  • $\begingroup$ You could equally consider the field to be “fundamental” and then charge is derived as the divergence of the field. “Fundamental” is just a philosophical label, it has no mathematical or scientific meaning $\endgroup$
    – Dale
    Commented Aug 9, 2022 at 21:22

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