Displacement current
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This article is about electric displacement current. For magnetic displacement
current, see Magnetic current § Magnetic displacement current.
In electromagnetism, displacement current density is the
quantity ∂D/∂t appearing in Maxwell's equations that is defined in terms of the
rate of change of D, the electric displacement field. Displacement current
density has the same units as electric current density, and it is a source of
the magnetic field just as actual current is. However it is not an electric current
of moving charges, but a time-varying electric field. In physical materials (as
opposed to vacuum), there is also a contribution from the slight motion of
charges bound in atoms, called dielectric polarization.
The idea was conceived by James Clerk Maxwell in his 1861 paper On Physical
Lines of Force, Part III in connection with the displacement of electric particles
in a dielectric medium. Maxwell added displacement current to the electric
current term in Ampère's Circuital Law. In his 1865 paper A Dynamical Theory
of the Electromagnetic Field Maxwell used this amended version of Ampère's
Circuital Law to derive the electromagnetic wave equation. This derivation is
now generally accepted as a historical landmark in physics by virtue of uniting
electricity, magnetism and optics into one single unified theory. The
displacement current term is now seen as a crucial addition that completed
Maxwell's equations and is necessary to explain many phenomena, most
particularly the existence of electromagnetic waves.
Explanation[edit]
The electric displacement field is defined as:
where:
ε0 is the permittivity of free space;
E is the electric field intensity; and
P is the polarization of the medium.
Differentiating this equation with respect to time defines the displacement
current density, which therefore has two components in a dielectric: (see also
[1]
the "displacement current" section of the article "current density")
, The first term on the right hand side is present in material media and in free
space. It doesn't necessarily come from any actual movement of charge, but it
does have an associated magnetic field, just as a current does due to charge
motion. Some authors apply the name displacement current to the first term by
itself. [2]
The second term on the right hand side, called polarization current density,
comes from the change in polarization of the individual molecules of the
dielectric material. Polarization results when, under the influence of an
applied electric field, the charges in molecules have moved from a position of
exact cancellation. The positive and negative charges in molecules separate,
causing an increase in the state of polarization P. A changing state of
polarization corresponds to charge movement and so is equivalent to a
current, hence the term "polarization current". Thus,
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 in the relation D = ε ε E.
r 0 r
The modern justification of displacement current is explained below.
Isotropic dielectric case[edit]
In the case of a very simple dielectric material the constitutive relation holds:
where the permittivity is the product of:
ε0, the permittivity of free space, or the electric constant; and
εr , the relative permittivity of the dielectric.
In the equation above, the use of ε accounts for the polarization (if any) of the
dielectric material.
The scalar value of displacement current may also be expressed in terms
of electric flux:
Jump to navigationJump to search
This article is about electric displacement current. For magnetic displacement
current, see Magnetic current § Magnetic displacement current.
In electromagnetism, displacement current density is the
quantity ∂D/∂t appearing in Maxwell's equations that is defined in terms of the
rate of change of D, the electric displacement field. Displacement current
density has the same units as electric current density, and it is a source of
the magnetic field just as actual current is. However it is not an electric current
of moving charges, but a time-varying electric field. In physical materials (as
opposed to vacuum), there is also a contribution from the slight motion of
charges bound in atoms, called dielectric polarization.
The idea was conceived by James Clerk Maxwell in his 1861 paper On Physical
Lines of Force, Part III in connection with the displacement of electric particles
in a dielectric medium. Maxwell added displacement current to the electric
current term in Ampère's Circuital Law. In his 1865 paper A Dynamical Theory
of the Electromagnetic Field Maxwell used this amended version of Ampère's
Circuital Law to derive the electromagnetic wave equation. This derivation is
now generally accepted as a historical landmark in physics by virtue of uniting
electricity, magnetism and optics into one single unified theory. The
displacement current term is now seen as a crucial addition that completed
Maxwell's equations and is necessary to explain many phenomena, most
particularly the existence of electromagnetic waves.
Explanation[edit]
The electric displacement field is defined as:
where:
ε0 is the permittivity of free space;
E is the electric field intensity; and
P is the polarization of the medium.
Differentiating this equation with respect to time defines the displacement
current density, which therefore has two components in a dielectric: (see also
[1]
the "displacement current" section of the article "current density")
, The first term on the right hand side is present in material media and in free
space. It doesn't necessarily come from any actual movement of charge, but it
does have an associated magnetic field, just as a current does due to charge
motion. Some authors apply the name displacement current to the first term by
itself. [2]
The second term on the right hand side, called polarization current density,
comes from the change in polarization of the individual molecules of the
dielectric material. Polarization results when, under the influence of an
applied electric field, the charges in molecules have moved from a position of
exact cancellation. The positive and negative charges in molecules separate,
causing an increase in the state of polarization P. A changing state of
polarization corresponds to charge movement and so is equivalent to a
current, hence the term "polarization current". Thus,
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 in the relation D = ε ε E.
r 0 r
The modern justification of displacement current is explained below.
Isotropic dielectric case[edit]
In the case of a very simple dielectric material the constitutive relation holds:
where the permittivity is the product of:
ε0, the permittivity of free space, or the electric constant; and
εr , the relative permittivity of the dielectric.
In the equation above, the use of ε accounts for the polarization (if any) of the
dielectric material.
The scalar value of displacement current may also be expressed in terms
of electric flux:
