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, 149, 2
- Maxwell's equations | 413, 1k, 26
- Particle physics | 137, 28k, 449
- Physics | 276, 39k, 680
- Natural science | 0, 48k, 1k
- Science | 0, 52k, 1k
- Ciro Santilli's Homepage | 262, 181k, 3k

- Electric current | 84