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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 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 ...
The most common description of the electromagnetic field uses two three-dimensional vector fields called the electric field and the magnetic field.These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates.
[2] [3] [4] It is analogous to temporal frequency, which is defined as the number of wave cycles per unit time (ordinary frequency) or radians per unit time (angular frequency). In multidimensional systems, the wavenumber is the magnitude of the wave vector. The space of wave vectors is called reciprocal space.
where (′) is the charge density, and ′ is the distance from the volume element ′ to point in space where φ is being determined. The scalar φ will add to other potentials as a scalar. This makes it relatively easy to break complex problems down into simple parts and add their potentials.
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: vector field ...
A scalar in physics and other areas of science is also a scalar in mathematics, as an element of a mathematical field used to define a vector space.For example, the magnitude (or length) of an electric field vector is calculated as the square root of its absolute square (the inner product of the electric field with itself); so, the inner product's result is an element of the mathematical field ...
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 ).