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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.
In special and general relativity, the four-current (technically the four-current density) [1] is the four-dimensional analogue of the current density, with units of charge per unit time per unit area. Also known as vector current, it is used in the geometric context of four-dimensional spacetime, rather than separating time from three ...
m/s 5: L T −5: vector Current density: J →: Electric current per unit cross-section area A/m 2: L −2 I: conserved, intensive, vector Electric dipole moment: p: Measure of the separation of equal and opposite electric charges C⋅m L T I: vector Electric displacement field: D →: Strength of the electric displacement C/m 2: L −2 T I ...
Canonical quantization of the electromagnetic fields proceeds by elevating the scalar and vector potentials; φ(x), A(x), from fields to field operators. Substituting 1/ c 2 = ε 0 μ 0 into the previous Lorenz gauge equations gives:
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.
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 ...
for virtually any well-behaved function g of dimensionless argument φ, where ω is the angular frequency (in radians per second), and k = (k x, k y, k z) is the wave vector (in radians per meter). Although the function g can be and often is a monochromatic sine wave , it does not have to be sinusoidal, or even periodic.