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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 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 n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
A well-known one-dimensional current sheet equilibrium is the Harris sheet, which is a stationary solution to the Maxwell–Vlasov system. [6] The magnetic field profile of a Harris sheet along = is given by = ^, where is the asymptotic magnetic field strength and provides the thickness of the current sheet.
Electric charge density: ρ Q: Electric charge per unit volume C/m 3: L −3 T I: intensive Electrical conductance: G: Measure for how easily current flows through a material siemens (S = Ω −1) L −2 M −1 T 3 I 2: scalar Electrical conductivity: σ: Measure of a material's ability to conduct an electric current S/m L −3 M −1 T 3 I 2 ...
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, = /
The current 3-form can be integrated over a 3-dimensional space-time region. The physical interpretation of this integral is the charge in that region if it is spacelike, or the amount of charge that flows through a surface in a certain amount of time if that region is a spacelike surface cross a timelike interval.
where current density J D is the displacement current, and J is the current density contribution actually due to movement of charges, both free and bound. Because ∇ ⋅ D = ρ , the charge continuity issue with Ampère's original formulation is no longer a problem. [ 22 ]
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (three dimensional), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.