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As far as I know, Maxwell's equations can't be derived from anything more fundamental. Does this indicate that electrons have no internal structure? I mean to say that, in my view, the entire nature of electrons is contained within Maxwell's equations. Is this a correct viewpoint? Any suggestions are welcome.

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Maxwell's equations (ME) don't by themselves theoretically predict spin 1/2 matter, such as, e.g., electrons. The source term $j^{\mu}$ in ME could in principle consist of, say, scalar matter. It doesn't even have to arise from point sources. We need experiments to tell.

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Maxwell's equation don't say anything about the structure of charges, or about the smallest unit of charge. We put the structure of the charge (whether point particle or some continuous distribution) while solving the equations.

In classical electrodynamics electron is simply taken to be a point charge because it agrees with many excitements.

We assume electron is a point charge, solve the Maxwell's equations to see the nature of the fields, and do experiments to see how much those theoretical results agree with experimental data.

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Maxwell's equations do not contain information on electrons other than that charge is conserved. Even on this point they are not leading. If charge were not conserved then Maxwell's equations would simply not be valid.

Maxwell's equations contain three elements: the field theory of a massless, uncharged vector field, charge conservation and linear response theory of material media.

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