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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.
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
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 ).
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.
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 ...
Based on the properties of the cross product, this produces a vector that is perpendicular to both the velocity and magnetic field vectors. The other vector is in the same direction as the electric field. The sum of these two vectors is the Lorentz force.
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 ...
By comparison with vector wave equations, the scalar wave equation can be seen as a special case of the vector wave equations; in the Cartesian coordinate system, the scalar wave equation is the equation to be satisfied by each component (for each coordinate axis, such as the x component for the x axis) of a vector wave without sources of waves ...