Electric current electrons into the conduction band. The current-carrying electrons in the conduction band are known as "free electrons", though they are often simply called "electrons" if that is clear in context. Current density is a measure of the density of an electric current. It is defined as a vector whose magnitude is the electric current per cross-sectional area. In SI units, the current density is measured in amperes per square metre. where "formula_6" is current in the conductor, formula_7 is the current density, and formula_8 is the differential cross-sectional area vector. The current density (current per unit area) "formula_7" in materials
Current density is the charge density (SI unit: coulombs per cubic metre), in which "n"(r, "t") is the number of particles per unit volume ("number density") (SI unit: m), "q" is the charge of the individual particles with density "n" (SI unit: coulombs). A common approximation to the current density assumes the current simply is proportional to the electric field, as expressed by: where E is the electric field and "σ" is the electrical conductivity. Conductivity "σ" is the reciprocal (inverse) of electrical resistivity and has the SI units of siemens per metre (S⋅m), and E has the SI units of newtons