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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.
Hence the probability current (density) is in SI units: = / = [(^ ^) | |] + () where S is the spin vector of the particle with corresponding spin magnetic moment μ S and spin quantum number s . It is doubtful if this formula is valid for particles with an interior structure.
The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal nĚ‚, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
In physics, the Poynting vector (or Umov–Poynting vector) represents the directional energy flux (the energy transfer per unit area, per unit time) or power flow of an electromagnetic field. The SI unit of the Poynting vector is the watt per square metre (W/m 2 ); kg/s 3 in base SI units.
The dependence of the current density on the applied electric field is essentially quantum mechanical in nature; (see Classical and quantum conductivity.) A qualitative description leading to Ohm's law can be based upon classical mechanics using the Drude model developed by Paul Drude in 1900. [18] [19]
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.
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.
the total electric current density (total current per unit area), J. The universal constants appearing in the equations (the first two ones explicitly only in the SI formulation) are: the permittivity of free space, ε 0, and; the permeability of free space, μ 0, and; the speed of light, = /