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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 ...
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 ]
In physics, the electric displacement field (denoted by D), also called electric flux density or electric induction, 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 .
Maxwell's addition states that magnetic fields also relate to changing electric fields, which Maxwell called displacement current. The integral form states that electric and displacement currents are associated with a proportional magnetic field along any enclosing curve.
This lent the equations their full significance with respect to understanding the nature of the phenomena he elucidated. (Kirchhoff derived the telegrapher's equations in 1857 without using displacement current, but he did use Poisson's equation and the equation of continuity, which are the mathematical ingredients of the displacement current ...
Gauss's law can be stated using either the electric field E or the electric displacement field D. This section shows some of the forms with E ; the form with D is below, as are other forms with E .
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is the displacement vector from to . Note that ε 0 {\displaystyle \varepsilon _{0}} must be replaced with ε {\displaystyle \varepsilon } , permittivity , when charges are in non-empty media. When the charges q 0 {\displaystyle q_{0}} and q 1 {\displaystyle q_{1}} have the same sign this force is positive, directed away from the other charge ...