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In the context of <Maxwell's equations>, it is <vector field> that is one of the inputs of the equation.

<Maxwell's equations with pointlike particles>{full} asks if the theory would work for pointlike particles in order to predict the evolution of this field as part of the equations themselves rather than as an external element.

Measured in <amperes> in the <International System of Units>.


Electric current

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= Pointlike particle
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This idealization does not seems to be possible at all in the context of <Maxwell's equations with pointlike particles>.


Point particle

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In the standard formulation of <Maxwell's equations>, the <electric current> is a convient but magic input.

Would it be possible to use <Maxwell's equations> to solve a system of <pointlike particles> such as electrons instead?

The following suggest no, or only for certain subcases less general than <Maxwell's equations>:
* https://physics.stackexchange.com/questions/498892/solution-to-maxwell-lorentz-equations
* https://physics.stackexchange.com/questions/380741/complete-classical-description-of-two-interacting-charges
This is the type of thing where the probability aspect of <quantum mechanics> seems it could "help".


Ciro Santilli @cirosantilli 37

 Incoming links: Maxwell's equations with pointlike particles