We can consider small area element ∆s on the surface of the conduct. This area element is very small on the macroscopic scale, but big enough to include a very large number of electrons. If ∆q is the amount of charge on this element, we define surface charge density [ ] at the area element by
= ∆q / ∆s
We can repeat the process at different points on surface of the conductor and thus arrive at a continuous function , called the surface charge density. at the microscopic level, charge distribution is discontinuos.
When charge is distributed along a line, straight or curved, we define linear charge density
= ∆q / ∆l
where ∆l is a small line element of wire on the macroscopic scale that includes a large number of microscopic charged constituents and ∆q is the charge contained in that line element.
The volume charge density is defined in a similar manner as
ρ = ∆q / ∆v
Where ∆q is the charge included in the macroscopically small volume element ∆v that include a large number of microscopic charged constituents. The units of ρ are c/m3.