Continuous charge distribution

When charge is spread over a wire, a surface or a volume, it is described by a density rather than by listing charges.

Linear charge density λ = ΔQ/Δl (C m⁻¹), surface charge density σ = ΔQ/ΔS (C m⁻²) and volume charge density ρ = ΔQ/ΔV (C m⁻³).

Each element Δl, ΔS or ΔV is small on the everyday scale but still contains a very large number of charged particles, so the density is a smoothed average that ignores quantisation, like the density of a liquid.

The field of a continuous distribution is found the same way as for point charges: divide it into elements, find each element's field from Coulomb's law, and add them as vectors (an integral in the limit).

Coulomb's law with superposition gives the field of any distribution, discrete, continuous or mixed.