Electric current density

In electromagnetism, current density is the electric current per unit area of cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional area at a given point in space, its direction being that of the motion of the charges at this point. In SI units, the electric current density is measured in amperes per square metre.

Assume that A (SI unit: m²) is a small surface centred at a given point M and orthogonal to the motion of the charges at M. If I (SI unit: A) is the electric current flowing through A, then Electric current density J is given by the limit:

surface A remaining centred at M and orthogonal to the motion of the charges during the limit process.

The current density vector J is the vector whose magnitude is the electric current density, and whose direction is the same as the motion of the charges at M.

At a given time t, if v is the speed of the charges at M, and dA is an infinitesimal surface centred at M and orthogonal to v, then during an amount of time dt, only the charge contained in the volume formed by dA and l = vdt will flow through dA. This charge is equal to ...
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