[1] 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 positive charges at this point.
In SI base units, the electric current density is measured in amperes per square metre.
[2] Assume that A (SI unit: m2) is a small surface centered at a given point M and orthogonal to the motion of the charges at M. If IA (SI unit: A) is the electric current flowing through A, then electric current density j at M is given by the limit:[3]
with surface A remaining centered 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 positive charges at M. At a given time t, if v is the velocity 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
For example, as integrated circuits are reduced in size, despite the lower current demanded by smaller devices, there is a trend toward higher current densities to achieve higher device numbers in ever smaller chip areas.
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, the insulating material failing, or the desired electrical properties changing.
At high current densities the material forming the interconnections actually moves, a phenomenon called electromigration.
In superconductors excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property.
The analysis and observation of current density also is used to probe the physics underlying the nature of solids, including not only metals, but also semiconductors and insulators.
Electric current is a coarse, average quantity that tells what is happening in an entire wire.
Conductivity σ is the reciprocal (inverse) of electrical resistivity and has the SI units of siemens per metre (S⋅m−1), and E has the SI units of newtons per coulomb (N⋅C−1) or, equivalently, volts per metre (V⋅m−1).
The above conductivity and its associated current density reflect the fundamental mechanisms underlying charge transport in the medium, both in time and over distance.
Aside from the material properties themselves, the application of magnetic fields can alter conductive behaviour.
[9] In dielectric materials, there is a current density corresponding to the net movement of electric dipole moments per unit volume, i.e. the polarization P:
which is an important term in Ampere's circuital law, one of Maxwell's equations, since absence of this term would not predict electromagnetic waves to propagate, or the time evolution of electric fields in general.
This relation is valid for any volume, independent of size or location, which implies that:
Regulations for building wiring list the maximum allowed current of each size of cable in differing conditions.
In transformers designed for high frequencies, loss is reduced if Litz wire is used for the windings.
This is made of multiple isolated wires in parallel with a diameter twice the skin depth.
For the top and bottom layers of printed circuit boards, the maximum current density can be as high as 35 A⋅mm−2 with a copper thickness of 35 μm.
In the semiconductors field, the maximum current densities for different elements are given by the manufacturer.
Exceeding those limits raises the following problems: The following table gives an idea of the maximum current density for various materials.
Even if manufacturers add some margin to their numbers, it is recommended to, at least, double the calculated section to improve the reliability, especially for high-quality electronics.
One can also notice the importance of keeping electronic devices cool to avoid exposing them to electromigration and slow diffusion.
This enables researchers to compare ionic currents in cells of different sizes.
[18] In gas discharge lamps, such as flashlamps, current density plays an important role in the output spectrum produced.
Low current densities produce spectral line emission and tend to favour longer wavelengths.
High current densities produce continuum emission and tend to favour shorter wavelengths.