Displacement current Totally Explained

Everything about Displacement Current totally explained

Displacement current is a quantity related to a changing electric field. It occurs in the vacuum or other dielectric and isn't a physical current in the sense that no physical charge is transported. It nevertheless has the units of electric current and it has an associated magnetic field. It appears in James Clerk Maxwell's 1861 paper entitled On Physical Lines of Force

, equation (112), where he added it as an additional term to the electric current term in Ampère's Circuital Law.

Explanation

The displacement current was introduced by Maxwell as the rate of change of the electric displacement, D:
ť

mathbf

where

chi_e

is known as the electric susceptibility of the dielectric. Note that:
ť

varepsilon = varepsilon_r varepsilon_0 = (1+chi_e)varepsilon_0

History and interpretation

Prior to Maxwell's work, it was thought that the magnetic field was generated solely by electric charge in motion. This idea is expressed mathematically with Ampère's Circuital Law.
   As in the case of Kirchhoff's Current law, Ampère's Circuital Law applies only to situations in which there's no variation in charge density. This fact can be seen by considering the divergence of the differential form of Ampère's Circuital Law in conjunction with the equation of continuity of charge. The divergence of a curl is always zero and hence the rate of change of charge density must necessarily be zero for Ampère's Circuital Law to hold true.
   If we substitute Gauss's law into the equation of continuity of charge in the above scenario we can see the mathematical justification for Maxwell's displacement current.
   Kirchhoff used the above interrelationships when he derived his 'Telegraphy Equation' in 1857, without any explicit mention of displacement current. Maxwell on the other hand, explicitly used displacement current in his 1864 paper A Dynamical Theory of the Electromagnetic Field, in order to derive the Electromagnetic wave equation. The Electromagnetic wave equation is very closely related to the 'Telegraphy Equation'.
   Maxwell's displacement current was postulated in part III of his 1861 paper 'On Physical Lines of Force

'.
   It appears in the preamble and then again formally at equation (111). It is the time differential of the elasticity equation. Maxwell interpreted the displacement current as a real motion of electrical particles in a sea of aethereal vortices. This interpretation has been abandoned in modern physics, although Maxwell's correction to Ampère's circuital law remains valid (a changing electric field produces a magnetic field).
   Using the concept of electrical displacement, Maxwell concluded, using Newton's equation for the speed of sound (equation 132), that light consists of transverse undulations in the same medium that's the cause of electric and magnetic phenomena.
   It is now believed that displacement current doesn't exist as a real current (movement of charge). It is defined as a quantity proportional to the time derivative of the electric field, and it's deemed to be able to exist in pure vacuum. The present day concept of displacement current therefore simply refers to the fact that a changing electric field has an associated magnetic field.

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