Current density is a measure of the density of electrical current. In a conductor, it is defined as the ratio of electric current to cross-sectional area of the conductor, measured in amperes per square meter.

Electrical current is a coarse, average quantity that tells what is happening in an entire wire. If we want to describe how the charges move through a conductor in more detail, we use the concept of the current density:

$J=nqv\_d=\backslash rho\; v\_d\; \backslash !\backslash$

where

$J\; \backslash !\backslash$ is the current density in amperes per square metre

$n\; \backslash !\backslash$ is the particle density in count per cubic metre (m^-3)

$q\; \backslash !\backslash$ is the individual particles' charge in coulombs

$\backslash rho\; =\; nq\; \backslash !\backslash$ is the charge density in coulombs per cubic metre

$v\_d\; \backslash !\backslash$ is the particles' average drift velocity in meters per second

Current density can also be calculated with a simpler and usually more practical equation:

$J\; =\; \{I\; \backslash over\; A\}\; \backslash !\backslash$

where

$I\; \backslash !\backslash$ is the electric current in amperes

$A\; \backslash !\backslash$ is the area through which the current is flowing in square metres

Current density is an important consideration in the design of electrical and electronic systems. Most electrical conductors have a finite, positive resistance, making them dissipate power in the form of heat. The current density must be kept sufficiently low to prevent the conductor from melting or burning up, or the insulating material failing. In superconductors excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property.

^* - A short explanation of the current density

Electromagnetism

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