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This polarization is the displacement current as it was originally conceived by Maxwell. Maxwell made no special treatment of the vacuum, treating it as a material medium. For Maxwell, the effect of P was simply to change the relative permittivity ε r in the relation D = ε 0 ε r E. The modern justification of displacement current is ...
The formula provides a natural generalization of the Coulomb's law for cases where the source charge is moving: = [′ ′ + ′ (′ ′) + ′] = ′ Here, and are the electric and magnetic fields respectively, is the electric charge, is the vacuum permittivity (electric field constant) and is the speed of light.
Permittivity as a function of frequency can take on real or complex values. In SI units, permittivity is measured in farads per meter (F/m or A 2 ·s 4 ·kg −1 ·m −3). The displacement field D is measured in units of coulombs per square meter (C/m 2), while the electric field E is measured in volts per meter (V/m).
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 ]
They then measured this ratio by an experiment which involved charging and discharging a Leyden jar and measuring the magnetic force from the discharge current, and found a value 3.107 × 10 8 m/s, [15] remarkably close to the speed of light, which had recently been measured at 3.14 × 10 8 m/s by Hippolyte Fizeau in 1848 and at 2.98 × 10 8 m ...
In physics, the electric displacement field (denoted by D), also called electric flux density, is a vector field that appears in Maxwell's equations. It accounts for the electromagnetic effects of polarization and that of an electric field , combining the two in an auxiliary field .
where ρ is the charge density, which can (and often does) depend on time and position, ε 0 is the electric constant, μ 0 is the magnetic constant, and J is the current per unit area, also a function of time and position. The equations take this form with the International System of Quantities.
In the electric and magnetic field formulation there are four equations that determine the fields for given charge and current distribution. A separate law of nature, the Lorentz force law, describes how the electric and magnetic fields act on charged particles and currents. By convention, a version of this law in the original equations by ...