[talanum1 (OP)]

We have ρ = e/Δv. Since for a point particle we make Δv infinitesimally small, doesn't this imply infinite charge density at the particle's position?

[Kryptid]

Yes. Ascribing any kind of density to a point will invoke infinities.

[evan_au]

What is the Charge Density of a Point Particle?

The electron is a point particle (as far as we know).
- But the electron has a wave function which effectively spreads the electron position over a finite volume.

For a water-soluble ion like OH^-, the negative charge is spread around 2 atoms, so a non-zero volume.

For a water-soluble ion like H⁺, it is effectively a proton, which has an extremely small volume compared to a Hydrogen atom.
- This electric field is so high that it attracts and re-orients nearby water molecules, so effectively the positive charge is spread over many water molecules (eg 20 - 50 water molecules)
- So again the electric field is not infinite.