Quantisation of Charge

Statement

Every observable charge in nature is an integer multiple of the elementary charge $e$:

Basis

Charge quantisation is not derived from more fundamental laws within classical electrostatics — it is an experimental fact, originally established by Millikan's oil drop experiment (1909–1913).

The proton carries charge $+e$, the electron $-e$. All macroscopic charges arise from the transfer or accumulation of electrons (or, in ionised matter, protons).

Quarks

Quarks carry fractional charges ($\pm e/3$, $\pm 2e/3$), but they are permanently confined inside hadrons by the strong force. No fractionally charged object has ever been isolated. At the level of observable particles, quantisation in units of $e$ holds without exception.

Practical implication

For macroscopic charges (say $1\,\mu\text{C} \approx 6 \times 10^{12}$ electrons), $n$ is enormous and the discreteness is imperceptible. The continuum approximation used in Gauss's law and Coulomb's law is entirely valid.