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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 ρ is the charge density, which can (and often does) depend on time and position, ε 0 is the electric constant, μ 0 is the magnetic constant, and J is the current per unit area, also a function of time and position.
Indeed, the efficiency of the Rashba–Edelstein effect and of the inverse Rashba–Edelstein effect can be estimated by means of the Rashba–Edelstein length, i.e., the ratio between the charge current density, flowing on the surface of the investigated material, (i.e., a surface charge current density) and the three-dimensional spin current ...
Here E and D are the electric field and displacement field, respectively, B and H are the magnetic fields, P is the polarization density, M is the magnetization, ρ is charge density, J is current density, c is the speed of light in vacuum, ϕ is the electric potential, A is the magnetic vector potential, F is the Lorentz force acting on a body ...
The Poynting vector appears in Poynting's theorem (see that article for the derivation), an energy-conservation law: =, where J f is the current density of free charges and u is the electromagnetic energy density for linear, nondispersive materials, given by = (+), where
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 ...
The current density j is observed to be proportional to the applied electric field and follows Ohm's law where the prefactor is the specific electrical conductivity. Since the electric field and the current density are vectors Ohm's law is expressed here in bold face.
where: is the rate of change of the energy density in the volume. ∇•S is the energy flow out of the volume, given by the divergence of the Poynting vector S. J•E is the rate at which the fields do work on charges in the volume (J is the current density corresponding to the motion of charge, E is the electric field, and • is the dot product).