Electric field

electricelectrostatic fieldelectrical fieldelectric field strengthfieldelectricalelectric field vectorelectric field intensityelectrostatic fieldsE
An electric field surrounds an electric charge, and exerts force on other charges in the field, attracting or repelling them.wikipedia
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Volt

VkVvolts
The SI unit for electric field strength is volt per meter (V/m).
It is also equal to the potential difference between two parallel, infinite planes spaced 1 meter apart that create an electric field of 1 newton per coulomb.

Electron

electronse − electron mass
On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding.
Since an electron has charge, it has a surrounding electric field, and if that electron is moving relative to an observer, said observer will observe it to generate a magnetic field.

Electromagnetism

electromagneticelectrodynamicselectromagnetic force
Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature.
The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light.

Magnetic field

magnetic fieldsmagneticmagnetic flux density
Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature. Electric fields are created by electric charges, or by time-varying magnetic fields. Electric fields are caused by electric charges, described by Gauss's law, or varying magnetic fields, described by Faraday's law of induction.
Magnetic fields and electric fields are interrelated, and are both components of the electromagnetic force, one of the four fundamental forces of nature.

Test particle

test chargetest particlestest mass
The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point.
In simulations with electric fields the most important characteristics of a test particle is its electric charge and its mass.

Fundamental interaction

fundamental forcesfundamental forcefundamental interactions
Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature.
The electromagnetic force, carried by the photon, creates electric and magnetic fields, which are responsible for the attraction between orbital electrons and atomic nuclei which holds atoms together, as well as chemical bonding and electromagnetic waves, including visible light, and forms the basis for electrical technology.

International System of Units

SISI unitsSI unit
The SI unit for electric field strength is volt per meter (V/m).

Gauss's law

Gauss' lawGauss lawGauss
Electric fields are caused by electric charges, described by Gauss's law, or varying magnetic fields, described by Faraday's law of induction.
In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field.

Maxwell's equations

Maxwell equationsMaxwell equationMaxwell’s equations
However, since the magnetic field is described as a function of electric field, the equations of both fields are coupled and together form Maxwell's equations that describe both fields as a function of charges and currents. Electric fields satisfy the superposition principle, because Maxwell's equations are linear.
The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields.

Electric charge

chargeelectrical chargecharged
The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. Electric fields are caused by electric charges, described by Gauss's law, or varying magnetic fields, described by Faraday's law of induction. An electric field surrounds an electric charge, and exerts force on other charges in the field, attracting or repelling them.
An electric charge has an electric field, and if the charge is moving it also generates a magnetic field.

Permittivity

dielectric functiondielectric permittivityelectric permittivity
Notice that, the vacuum electric permittivity, must be substituted with \varepsilon, permittivity, when charges are in non-empty media.
In the simplest case, the electric displacement field \mathbf{D} resulting from an applied electric field \mathbf{E} is More generally, the permittivity is a thermodynamic function of state.

Vacuum permittivity

permittivity of free spaceelectric constantvacuum electric permittivity
Notice that, the vacuum electric permittivity, must be substituted with \varepsilon, permittivity, when charges are in non-empty media. is the electric constant (also known as "the absolute permittivity of free space") in C 2 m −2 N −1
It is the capability of the vacuum to permit electric field lines.

Euclidean vector

vectorvectorsvector addition
:This is the electric field at point due to the point charge q_1; it is a vector equal to the Coulomb force per unit charge that a positive point charge would experience at the position.
Other physical vectors, such as the electric and magnetic field, are represented as a system of vectors at each point of a physical space; that is, a vector field.

Atom

atomsatomic structureatomic
On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding.
When subjected to external forces, like electrical fields, the shape of an atom may deviate from spherical symmetry.

Capacitor

capacitorscapacitivecondenser
It can be approximated by placing two conducting plates parallel to each other and maintaining a voltage (potential difference) between them; it is only an approximation because of boundary effects (near the edge of the planes, electric field is distorted because the plane does not continue).
A capacitor is a device that stores electrical energy in an electric field.

Electric potential

electrical potentialelectrostatic potentialCoulomb potential
In this case, one can define an electric potential, that is, a function \Phi such that.
This value can be calculated in either a static (time-invariant) or a dynamic (varying with time) electric field at a specific time in units of joules per coulomb (

Voltage

potential differenceVvoltages
It can be approximated by placing two conducting plates parallel to each other and maintaining a voltage (potential difference) between them; it is only an approximation because of boundary effects (near the edge of the planes, electric field is distorted because the plane does not continue).
The difference in electric potential between two points (i.e., voltage) in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points.

Coulomb's law

Coulomb forceelectrostatic forceCoulomb interaction
The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point.
By choosing one of the point charges to be the source, and the other to be the test charge, it follows from Coulomb's law that the magnitude of the electric field

Magnetic potential

magnetic vector potentialvector potentialmagnetic scalar potential
If A is the magnetic vector potential, defined so that, one can still define an electric potential \Phi such that:
Together with the electric potential φ, the magnetic vector potential can be used to specify the electric field E as well.

Electromagnetic field

electromagnetic fieldselectromagneticEMF
The total energy per unit volume stored by the electromagnetic field is
The field can be viewed as the combination of an electric field and a magnetic field.

Charge density

charge distributionelectric charge densitysurface charge density
The electric field due to a continuous distribution of charge in space (where \rho is the charge density in coulombs per cubic meter) can be calculated by considering the charge in each small volume of space dV at point as a point charge, and calculating its electric field at point
Bound charges set up electric dipoles in response to an applied electric field E, and polarize other nearby dipoles tending to line them up, the net accumulation of charge from the orientation of the dipoles is the bound charge.

Polarization density

polarizationelectric polarizationbound charge
where P is the electric polarization – the volume density of electric dipole moments, and D is the electric displacement field.
When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized.

Superposition principle

superpositionlinear superpositionsuperpose
Electric fields satisfy the superposition principle, because Maxwell's equations are linear.

Electric current

currentelectrical currentcurrents
However, since the magnetic field is described as a function of electric field, the equations of both fields are coupled and together form Maxwell's equations that describe both fields as a function of charges and currents.
With no external electric field applied, these electrons move about randomly due to thermal energy but, on average, there is zero net current within the metal.

Faraday's law of induction

Faraday's lawMaxwell–Faraday equationelectromagnetic induction
Electric fields are caused by electric charges, described by Gauss's law, or varying magnetic fields, described by Faraday's law of induction.
is the electric field and