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Encyclopedia > Displacement current
Electrostatics Electromagnetism Electricity · Magnetism Electric charge Coulomb's law Electric field Gauss's law Electric potential Electric dipole moment Ampère's Circuital law Magnetic field Magnetic flux Biot-Savart law Magnetic dipole moment Electrical current Lorentz force law Electromotive force (EM) Electromagnetic induction Faraday-Lenz law Displacement current Maxwell's equations (EMF) Electromagnetic field (EM) Electromagnetic radiation Electrical conduction Electrical resistance Capacitance Inductance Impedance Resonant cavities Waveguides Electromagnetic tensor Electromagnetic stress-energy tensor This box: view • talk • edit

In the particular case of when it occurs in free space, it is not believed to involve the motion of electric charge as is the case with free electric current and with displacement current in dielectric materials. A dielectric, or electrical insulator, is a substance that is highly resistant to electric current. ...

Displacement current possesses the units of electric current and it has an associated changing magnetic field. It appears in James Clerk Maxwell's 1861 paper entitled On Physical Lines of Force. Magnetic field lines shown by iron filings In physics, a magnetic field is a solenoidal vector field in the space surrounding moving electric charges and magnetic dipoles, such as those in electric currents and magnets. ... James Clerk Maxwell (13 June 1831 â€“ 5 November 1879) was a Scottish mathematician and theoretical physicist. ...

## Contents

The displacement current is mathematically defined by the rate of change of the electric displacement field, D: In physics, the electric displacement field or electric flux density or electric induction is a vector field that appears in Maxwells equations. ... $mathbf{J}_mathrm{D} = frac{partial mathbf{D}}{partial t} =varepsilon frac{partial mathbf{E}}{partial t}$

(since D = εE) and where the permittivity ε = ε0 εr, Permittivity is a physical quantity that describes how an electric field affects and is affected by a dielectric medium and is determined by the ability of a material to polarize in response to an applied electric field, and thereby to cancel, partially, the field inside the material. ...

• εr is the relative permittivity of the dielectric and
• ε0 is the permittivity of free space ( 8.854 E-12 Fm-1)

In this equation the use of ε, accounts for the polarisation of the dielectric.

The scalar value of displacement current may also be expressed in terms of electric flux: In physics, a scalar is a simple physical quantity that does not depend on direction, and therefore does not depend on the choice of a coordinate system. ... In physics, Gausss law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. ... $I_mathrm{D} =varepsilon frac{dPhi_E}{dt}$

The forms in terms of $varepsilon$ are only correct for linear isotropic materials, unless you consider $varepsilon$ to be a tensor, in which case they are valid for all linear materials. Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ... In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...

For a linear isotropic dielectric, the polarisation P is given by: $mathbf{P} = varepsilon_0 chi_e mathbf{E} = varepsilon_0 (varepsilon_r - 1) mathbf{E}$

where χe is known as the electric susceptibility of the dielectric. Note that: The electric susceptibility Ï‡e of a dielectric material is a measure of how easily it polarizes in response to an electric field. ... $varepsilon = varepsilon_r varepsilon_0 = (1+chi_e)varepsilon_0$

The electric displacement field is defined as: In physics, the electric displacement field or electric flux density or electric induction is a vector field that appears in Maxwells equations. ... $mathbf{D} = varepsilon_0 mathbf{E} + mathbf{P}$

Taking the time derivative of this, we find that displacement current has two components in a dielectric: A dielectric, or electrical insulator, is a substance that is highly resistant to electric current. ... $mathbf{J}_mathrm{D} = varepsilon_0 frac{partial mathbf{E}}{partial t} + frac{partial mathbf{P}}{partial t}$

The first part is present everywhere, even in a vacuum. It is believed not to involve any actual movement of charge, but to nevertheless have an associated magnetic field, as if it were an actual current. The second part is caused by the linear polarization of the individual molecules of the dielectric material. Even though charges cannot flow freely in a dielectric, their limited but elastically self restoring movements produce a polarization current.

## Mathematical Justification

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 only applies to situations in which there is 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'. A Dynamical Theory of the Electromagnetic Field was the third of James Clerk Maxwells papers concerned with electromagnetism. ... Lasers used for visual effects during a musical performance. ... Lasers used for visual effects during a musical performance. ...

## History and interpretation

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). In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... Magnetic field lines shown by iron filings In physics, a magnetic field is a solenoidal vector field in the space surrounding moving electric charges and magnetic dipoles, such as those in electric currents and magnets. ...

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 is the cause of electric and magnetic phenomena.

It is now believed that displacement current does not 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 is 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. Results from FactBites:

 Electric current Summary (2337 words) Electric current is measured in amperes, with one ampere equal to a charge-flow of one coulomb per second. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second. It is the current that passes that determines the effect, and this depends on the nature of the contact, the condition of the body part, the current path through the body and the voltage of the source.
 Displacement current - Wikipedia, the free encyclopedia (556 words) It is not a real current (movement of charge) in a vacuum, but it has the units of current, as movement of charge does, and has an associated magnetic field. Maxwell interpreted the displacement current as a real motion of charges, even in a vacuum, where he supposed that it corresponded to motion of dipole charges in the ether. With the addition of the displacement current, Maxwell concluded that light was a form of electromagnetism (see Electromagnetic wave equation and Electromagnetic waves).
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