In physics, the electromagnetic dual concept is based on the idea that, in the static case,

electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions o ...

has two separate facets: electric fields and

magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and t ...

s. Expressions in one of these will have a directly analogous, or dual, expression in the other. The reason for this can ultimately be traced to

special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The law ...

where applying the

Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...

to the electric field will transform it into a magnetic field. These are special cases of duality in mathematics. * The electric field (E) is the dual of the

(H). * The

electric displacement field In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as i ...

(D) is the dual of the

magnetic flux density A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...

(B). *

Faraday's law of induction Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf)—a phenomenon known as electromagnetic indu ...

is the dual of Ampère's circuital law. *

Gauss's law In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it sta ...

for electric field is the dual of

Gauss's law for magnetism In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics. It states that the magnetic field has divergence equal to zero, in other words, that it is a solenoidal vector field. It ...

. * The

electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work energy needed to move a unit of electric charge from a reference point to the specific point in ...

is the dual of the magnetic potential. *

Permittivity In electromagnetism, the absolute permittivity, often simply called permittivity and denoted by the Greek letter ''ε'' ( epsilon), is a measure of the electric polarizability of a dielectric. A material with high permittivity polarizes more i ...

is the dual of permeability. *

Electrostriction Electrostriction (cf. magnetostriction) is a property of all electrical non-conductors, or dielectrics, that causes them to change their shape under the application of an electric field. Explanation Electrostriction is a property of all dielectr ...

is the dual of

magnetostriction Magnetostriction (cf. electrostriction) is a property of magnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation of materials' magnetization due to the applied magnetic field chang ...

. *

Piezoelectricity Piezoelectricity (, ) is the electric charge that accumulates in certain solid materials—such as crystals, certain ceramics, and biological matter such as bone, DNA, and various proteins—in response to applied mechanical stress. The word ' ...

is the dual of

piezomagnetism Piezomagnetism is a phenomenon observed in some antiferromagnetic and ferrimagnetic crystals. It is characterized by a linear coupling between the system's magnetic polarization and mechanical strain. In a piezomagnetic material, one may induce a ...

. *

Ferroelectricity Ferroelectricity is a characteristic of certain materials that have a spontaneous electric polarization that can be reversed by the application of an external electric field. All ferroelectrics are also piezoelectric and pyroelectric, with the a ...

is the dual of

ferromagnetism Ferromagnetism is a property of certain materials (such as iron) which results in a large observed magnetic permeability, and in many cases a large magnetic coercivity allowing the material to form a permanent magnet. Ferromagnetic materials a ...

. * An

electrostatic motor An electrostatic motor or capacitor motor is a type of electric motor based on the attraction and repulsion of electric charge. An alternative type of electrostatic motor is the spacecraft electrostatic ion drive thruster where forces and motion ...

is the dual of a

magnetic motor An electric motor is an electrical machine that converts electrical energy into mechanical energy. Most electric motors operate through the interaction between the motor's magnetic field and electric current in a wire winding to generate forc ...

; *

Electret An electret (formed as a portmanteau of ''electr-'' from "electricity" and ''-et'' from "magnet") is a dielectric material that has a quasi-permanent electric charge or dipole polarisation. An electret generates internal and external electric f ...

s are the dual of

permanent magnets A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel ...

; * The

Faraday effect The Faraday effect or Faraday rotation, sometimes referred to as the magneto-optic Faraday effect (MOFE), is a physical magneto-optical phenomenon. The Faraday effect causes a polarization rotation which is proportional to the projection of the ...

is the dual of the

Kerr effect The Kerr effect, also called the quadratic electro-optic (QEO) effect, is a change in the refractive index of a material in response to an applied electric field. The Kerr effect is distinct from the Pockels effect in that the induced index cha ...

; * The Aharonov–Casher effect is the dual to the

Aharonov–Bohm effect The Aharonov–Bohm effect, sometimes called the Ehrenberg–Siday–Aharonov–Bohm effect, is a quantum mechanical phenomenon in which an electrically charged particle is affected by an electromagnetic potential (φ, A), despite being confine ...

; * The hypothetical

magnetic monopole In particle physics, a magnetic monopole is a hypothetical elementary particle that is an isolated magnet with only one magnetic pole (a north pole without a south pole or vice versa). A magnetic monopole would have a net north or south "magneti ...

is the dual of

electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respecti ...

See also