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In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. [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.
For negative charges, the sign of the current density is opposite to the velocity of the charges. [2]: 749 In SI units, current density (symbol: j) is expressed in the SI base units of amperes per square metre. [4]: 22 In linear materials such as metals, and under low frequencies, the current density across the conductor surface is uniform.
Then the electric field and current density are constant and parallel, and by the general definition of resistivity, we obtain ρ = E J , {\displaystyle \rho ={\frac {E}{J}},} Since the electric field is constant, it is given by the total voltage V across the conductor divided by the length ℓ of the conductor:
Regardless of the driving force, the current density is found to be greatest at the conductor's surface, with a reduced magnitude deeper in the conductor. That decline in current density is known as the skin effect and the skin depth is a measure of the depth at which the current density falls to 1/e of its value near the surface. Over 98% of ...
Since the E field is uniform in the direction of wire length, for a conductor having uniformly consistent resistivity ρ, the current density J will also be uniform in any cross-sectional area and oriented in the direction of wire length, so we may write: [40] =.
Critical temperature T c, the temperature below which the wire becomes a superconductor; Critical current density J c, the maximum current a superconducting wire can carry per unit cross-sectional area (see images below for examples with 20 kA/cm 2). Superconducting wires/tapes/cables usually consist of two key features:
At very high frequencies, the current no longer flows in the wire, but effectively flows on the surface of the wire, within a thickness of a few skin depths. The skin depth is the thickness at which the current density is reduced by 63%.
The formula for evaluating the drift velocity of charge carriers in a material of constant cross-sectional area is given by: [1] =, where u is the drift velocity of electrons, j is the current density flowing through the material, n is the charge-carrier number density, and q is the charge on the charge-carrier.