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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.
A proper relativistic theory with a probability density current must also share this feature. To maintain the notion of a convected density, one must generalize the Schrödinger expression of the density and current so that space and time derivatives again enter symmetrically in relation to the scalar wave function.
The net electric current I is the surface integral of the electric current density J passing through Σ: =, where dS denotes the differential vector element of surface area S, normal to surface Σ. (Vector area is sometimes denoted by A rather than S , but this conflicts with the notation for magnetic vector potential ).
Current density is the rate at which charge passes through a chosen unit area. [25]: 31 It is defined as a vector whose magnitude is the current per unit cross-sectional area. [2]: 749 As discussed in Reference direction, the direction is arbitrary. Conventionally, if the moving charges are positive, then the current density has the same sign ...
where this time is the charge density, is the current density vector, and is the current source-sink term. The current source and current sinks are where the current density emerges σ > 0 {\displaystyle \sigma >0} or vanishes σ < 0 {\displaystyle \sigma <0} , respectively (for example, the source and sink can represent the two poles of an ...
The last term, proportional to the second derivative of the unit direction vector ′, is sensitive to charge motion perpendicular to the line of sight. It can be shown that the electric field generated by this term is proportional to a t / r ′ {\displaystyle a_{t}/r'} , where a t {\displaystyle a_{t}} is the transverse acceleration in the ...
Spin density is electron density applied to free radicals. It is defined as the total electron density of electrons of one spin minus the total electron density of the electrons of the other spin. One of the ways to measure it experimentally is by electron spin resonance, [14] neutron diffraction allows direct mapping of the spin density in 3D ...
where is the charge density, which is a function of time and position, is the vacuum permittivity, is the vacuum permeability, and J is the current density vector, also a function of time and position. Inside a linear material, Maxwell's equations change by switching the permeability and permittivity of free space with the permeability and ...