Current density

In electromagnetism, current density is the electric current per unit area of cross section. It is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space (i.e. it is a vector field). In SI units, the electric current density is measured in amperes per square metre.

Electric current density J is the electric current I (SI unit: A) per unit area A (SI unit: m²). Its magnitude is given by the limit:

For current density as a vector J, the surface integral over a surface S, followed by an integral over the time duration t₁ to t₂, gives the total amount of charge flowing through the surface in that time (t₂ − t₁):

The area required to calculate the flux is real or imaginary, flat or curved, either as a cross-sectional area or a surface. For example, for charge carriers passing through an electrical conductor, the area is the cross-section of the conductor, at the section considered.

The vector area is a combination of the magnitude of the area through which the mass passes through, A, and a unit vector normal to the area, ${\mathbf {\hat {n}}}$ ${\mathbf {\hat {n}}}$ . The relation is ${\mathbf {A}}=A{\mathbf {\hat {n}}}$ ${\mathbf {A}}=A{\mathbf {\hat {n}}}$ .

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