Current density and Ohm's law
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 is current in the conductor, is the current density, and is the differential cross-sectional area vector.
The current density (current per unit area) in materials with finite
resistance is directly proportional to the
electric field in the medium. The proportionality constant is called the
conductivity of the material, whose value depends on the material concerned and, in general, is dependent on the temperature of the material:
The reciprocal of the
conductivity of the material is called the
resistivity of the material and the above equation, when written in terms of resistivity becomes:
semiconductor devices may occur by a combination of drift and diffusion, which is proportional to
diffusion constant and
charge density . The current density is then:
with being the
elementary charge and the electron density. The carriers move in the direction of decreasing concentration, so for electrons a positive current results for a positive density gradient. If the carriers are holes, replace electron density by the negative of the
hole density .
anisotropic materials, σ, ρ and D are
In linear materials such as metals, and under low frequencies, the current density across the conductor surface is uniform. In such conditions,
Ohm's law states that the current is directly proportional to the potential difference between two ends (across) of that metal (ideal)
resistor (or other
where is the current, measured in amperes; is the
potential difference, measured in
volts; and is the
resistance, measured in
alternating currents, especially at higher frequencies,
skin effect causes the current to spread unevenly across the conductor cross-section, with higher density near the surface, thus increasing the apparent resistance.