Displacement current

Electromagnetism

Electrodynamics
· Free space · Lorentz force law · EMF · Electromagnetic induction · Faraday’s law · Displacement current · Maxwell’s equations · EM field · Electromagnetic radiation · Liénard-Wiechert Potentials · Maxwell tensor · Eddy current ·

This box: view • talk • edit

Displacement current is a quantity related to a changing electric field. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation Electromotive force ( emf, \mathcal{E} is a term used to characterize electrical devices such as Voltaic cells thermoelectric devices electrical Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric The electromagnetic field is a physical field produced by electrically charged objects. Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. The Liénard-Wiechert potential describes the electromagnetic effect of a moving Electric charge. The Maxwell Stress Tensor (also known as Maxwell's Stress Tensor is used to calculate the stresses on objects in magnetic or electrical fields An eddy current (also known as Foucault current) is an electrical phenomenon discovered by French physicist Léon Foucault in It occurs in the vacuum or other dielectric and is not a physical current in the sense that no physical charge is transported. A dielectric is a nonconducting substance ie an insulator. The term was coined by William Whewell in response to a request from Michael Faraday. 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. James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. In Classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère, relates the integrated Magnetic field around a closed

1 Explanation
2 Simplifications
3 History and interpretation
4 See also

Explanation

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

$\mathbf{J}_\mathrm{D} = \frac{\partial \mathbf{D}} {\partial t}\ ,$

where D is the electric displacement field that enters Maxwell's equations. In Physics, the electric displacement field (also called electrical field/flux density is a Vector field \mathbf{D} that appears in Maxwell's equations In Physics, the electric displacement field (also called electrical field/flux density is a Vector field \mathbf{D} that appears in Maxwell's equations In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric The electric displacement field is defined as:

$\mathbf{D} = \varepsilon_0 \mathbf{E} + \mathbf{P}$

Taking the time derivative of this, we find that displacement current has two components in a dielectric:

$\mathbf{J}_\mathrm{D} = \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} + \frac{\partial \mathbf{P}}{\partial t}$

The first part is present everywhere, even in a vacuum. In Physics, the electric displacement field (also called electrical field/flux density is a Vector field \mathbf{D} that appears in Maxwell's equations A dielectric is a nonconducting substance ie an insulator. The term was coined by William Whewell in response to a request from Michael Faraday. 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.

Simplifications

In the case of a very simple dielectric material the constitutive relation holds:

$\mathbf{D} = \epsilon \mathbf{E} \ ,$

where the permittivity ε = ε₀ ε_r,

ε_r is the relative permittivity of the dielectric and
ε₀ is the electric constant. 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 Vacuum permittivity, referred to by international standards organizations as the electric constant, and denoted by the symbol ε0 is a fundamental Physical

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:

$I_\mathrm{D} =\varepsilon \frac{d\Phi_E}{dt}$

The forms in terms of $\varepsilon$ are only correct for linear isotropic materials. In Physics, a scalar is a simple Physical quantity that is not changed by Coordinate system rotations or translations (in Newtonian mechanics or In Electromagnetism, electric flux is Flux of the Electric field. Isotropy is uniformity in all directions Precise definitions depend on the subject area More generally $\varepsilon$ may be a tensor, may depend upon the electric field itself, and may exhibit time dependence (dispersion). History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually

For a linear isotropic dielectric, the polarization P is given by:

$\mathbf{P} = \varepsilon_0 \chi_e \mathbf{E} = \varepsilon_0 (\varepsilon_r - 1) \mathbf{E}$

where $χ e$ is known as the electric susceptibility of the dielectric. Polarization ( ''Brit'' polarisation) is a property of Waves that describes the orientation of their oscillations The electric susceptibility χe of a Dielectric material is a measure of how easily it polarizes in response to an Electric field. Note that:

$\varepsilon = \varepsilon_r \varepsilon_0 = (1+\chi_e)\varepsilon_0$

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 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. A Dynamical Theory of the Electromagnetic Field which was written in the year 1864 is the third of James Clerk Maxwell 's papers concerned with Electromagnetism The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of Electromagnetic waves through a medium The Electromagnetic wave equation is very closely related to the 'Telegraphy Equation'. The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of Electromagnetic waves through a medium

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 (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges

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.

Contents

Explanation

Simplifications

History and interpretation

See also