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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.
where the conductivity σ and resistivity ρ are rank-2 tensors, and electric field E and current density J are vectors. These tensors can be represented by 3×3 matrices, the vectors with 3×1 matrices, with matrix multiplication used on the right side of these equations. In matrix form, the resistivity relation is given by:
The total current density is the sum of the electron ... a diffusion current is superimposed on that due to conductivity. This diffusion current is governed by ...
The field dependence of the current density j through an ionic conductor, assuming a random walk model with independent ions under a periodic potential is given by: [8] where α is the inter-site separation.
Resistivity and conductivity are reciprocals: = /. Resistivity is a measure of the material's ability to oppose electric current. This formula is not exact, as it assumes the current density is totally uniform in the conductor, which is not always true in practical situations. However, this formula still provides a good approximation for long ...
Charge carrier density, also known as carrier concentration, denotes the number of charge carriers per volume. In SI units, it is measured in m −3. As with any density, in principle it can depend on position. However, usually carrier concentration is given as a single number, and represents the average carrier density over the whole material.
Complex conductivity for different frequencies assuming that τ = 10 −5 and that σ 0 = 1. The Drude model can also predict the current as a response to a time-dependent electric field with an angular frequency ω.
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 ...