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:

This is the type of thing where the probability aspect of quantum mechanics seems it could "help".

- Solutions of Maxwell's equations | 48, 153, 2
- Maxwell's equations | 408, 1k, 27
- Particle physics | 137, 32k, 512
- Physics | 276, 46k, 825
- Natural science | 0, 61k, 2k
- Science | 0, 66k, 2k
- Ciro Santilli's Homepage | 262, 218k, 4k

- Electric current | 84
- Point particle | 22, 22, 1