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Encyclopedia > Electric field
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

The electric field is a vector with SI units of newtons per coulomb (N C-1) or, equivalently, volts per meter (V m-1). The direction of the field at a point is defined by the direction of the electric force exerted on a positive test charge placed at that point. The strength of the field is defined by the ratio of the electric force on a charge at a point to the magnitude of the charge placed at that point. Electric fields contain electrical energy with energy density proportional to the square of the field intensity. The electric field is to charge as acceleration is to mass and force density is to volume. A vector going from A to B. In physics and in vector calculus, a spatial vector, or simply vector, is a concept characterized by a magnitude and a direction. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... The newton (symbol: N) is the SI unit of force. ... The coulomb (symbol: C) is the SI unit of electric charge. ... Josephson junction array chip developed by NIST as a standard volt. ... The metre, or meter (symbol: m) is the SI base unit of length. ... Electrical energy can refer to several closely related things. ... Energy density is the amount of energy stored in a given system or region of space per unit volume or per unit mass, depending on the context. ... Acceleration is the time rate of change of velocity, and at any point on a velocity-time graph, it is given by the slope of the tangent to that point basicly. ... In fluid mechanics, the force density has the physical dimensions of force per unit volume. ...

A moving charge has not just an electric field but also a magnetic field, and in general the electric and magnetic fields are not completely separate phenomena; what one observer perceives as an electric field, another observer in a different frame of reference perceives as a mixture of electric and magnetic fields. For this reason, one speaks of "electromagnetism" or "electromagnetic fields." In quantum mechanics, disturbances in the electromagnetic fields are called photons, and the energy of photons is quantized. Magnetic field lines shown by iron filings In physics, a magnetic field is a solenoidal vector field in the space surrounding moving electric charges, such as those in electric currents and bar magnets. ... In modern physics the photon is the elementary particle responsible for electromagnetic phenomena. ...

Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge.

The electric field is defined as the proportionality constant between charge and force (in other words, the force per unit of test charge): $mathbf{E} = frac{mathbf{F}}{q}$

where $mathbf{F}$ is the electric force given by Coulomb's law,
q is the charge of a "test charge",

However, note that this equation is only true in the case of electrostatics, that is to say, when there is nothing moving. The more general case of moving charges causes this equation to become the Lorentz force equation. Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... Electrostatics (also known as Static Electricity) is the branch of physics that deals with the forces exerted by a static (i. ... Lorentz force. ...

## Coulomb's law

The electric field surrounding a point charge is given by Coulomb's law: Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... $mathbf{E} =frac{1}{4 pi varepsilon_0}frac{Q}{r^2}mathbf{hat{r}} .......... (1)$

where

Q is the charge of the particle creating the electric field,
r is the distance from the particle with charge Q to the E-field evaluation point, $mathbf{hat{r}}$ is the Unit vector pointing from the particle with charge Q to the E-field evaluation point, $varepsilon_0$ is the Permittivity of free space.

Coulomb's law is actually a special case of Gauss's Law, a more fundamental description of the relationship between the distribution of electric charge in space and the resulting electric field. Gauss's law is one of Maxwell's equations, a set of four laws governing electromagnetics. In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) whose length, (or magnitude) is 1. ... 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. ... Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... In physics and mathematical analysis, Gausss law is the electrostatic application of the generalized Gausss theorem giving the equivalence relation between any flux, e. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ...

## Properties (in electrostatics)

According to Equation (1) above, electric field is dependent on position. The electric field due to any single charge falls off as the square of the distance from that charge. Image File history File links EfieldTwoOppositePointCharges. ... Image File history File links EfieldTwoOppositePointCharges. ...

Electric fields follow the superposition principle. If more than one charge is present, the total electric field at any point is equal to the vector sum of the respective electric fields that each object would create in the absence of the others. In linear algebra, the principle of superposition states that, for a linear system, a linear combination of solutions to the system is also a solution to the same linear system. ... A vector in physics and engineering typically refers to a quantity that has close relationship to the spatial coordinates, informally described as an object with a magnitude and a direction. The word vector is also now used for more general concepts (see also vector and generalizations below), but in this... $mathbf{E}_{rm total} = sum_i mathbf{E}_i = mathbf{E}_1 + mathbf{E}_2 + mathbf{E}_3 ldots ,!$

If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula results: $mathbf{E} = frac{1}{4pivarepsilon_0} intfrac{rho}{r^2} mathbf{hat{r}},mathrm{d}V$

where

ρ is the charge density, or the amount of charge per unit volume.

The electric field at a point is equal to the negative gradient of the electric potential there. In symbols, Charge density is the amount of electric charge per unit volume. ... The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. ... For other uses, see Gradient (disambiguation). ... This article or section does not cite any references or sources. ... $mathbf{E} = -mathbf{nabla}phi$

where

φ(x,y,z) is the scalar field representing the electric potential at a given point.

If several spatially distributed charges generate such an electric potential, e.g. in a solid, an electric field gradient may also be defined. In mathematics and physics, a scalar field associates a scalar to every point in space. ... This article or section does not cite any references or sources. ... For other uses, see Solid (disambiguation). ... Mathematically, the electric field gradient (EFG) is the hessian matrix (the matrix of the second derivatives) of the electrical potential V: It is an important structural property of a crystalline solid, where it is defined at the location of a nucleus. ...

Considering the permittivity $varepsilon$ of a material, which may differ from the permittivity of free space $varepsilon_{0}$, the electric displacement field is: 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. ... In physics, the electric displacement field or electric flux density is a vector-valued field that appears in Maxwells equations. ... $mathbf{D} = varepsilon mathbf{E}$

## Energy in the electric field

Main article: Electrical energy

The electric field stores energy. The energy density of the electric field is given by Electrical energy can refer to several closely related things. ... $u = frac{1}{2} varepsilon |mathbf{E}|^2$

where $varepsilon$ is the permittivity of the medium in which the field exists $mathbf{E}$ is the electric field vector.

The total energy stored in the electric field in a given volume V is therefore 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. ... $int_{V} frac{1}{2} varepsilon |mathbf{E}|^2 , mathrm{d}V$

where

dV is the differential volume element.

## Parallels between electrostatics and gravity

Coulomb's law, which describes the interaction of electric charges: Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... $mathbf{F} = frac{1}{4 pi varepsilon_0}frac{Qq}{r^2}mathbf{hat{r}} = qmathbf{E}$

is similar to the Newtonian gravitation law: $mathbf{F} = Gfrac{Mm}{r^2}mathbf{hat{r}} = mmathbf{g}$

This suggests similarities between the electric field E and the gravitational field g, so sometimes mass is called "gravitational charge".

Similarities between electrostatic and gravitational forces:

1. Both act in a vacuum.
2. Both are central and conservative.
3. Both obey an inverse-square law (both are inversely proprotional to square of r).
4. Both propagate with finite speed c.

Differences between electrostatic and gravitational forces:

1. Electrostatic forces are much greater than gravitational forces (by about 1036 times).
2. Gravitational forces are attractive for like charges, whereas electrostatic forces are repulsive for like charges.
3. There are no negative gravitational charges (no negative mass) while there are both positive and negative electric charges. This difference combined with previous implies that gravitational forces are always attractive, while electrostatic forces may be either attractive or repulsive.
4. Electric charges are invariant under Lorentz transformations while gravitational charges (relativistic mass) are not.

Exotic matter is a hypothetical concept of particle physics. ... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Charge invariance refers to the fixed electric charge of a particle, regardless of speed. ...

## Time-varying fields

Charges do not only produce electric fields. As they move, they generate magnetic fields, and if the magnetic field changes, it generates electric fields. This "secondary" electric field can be computed using Faraday's law of induction, Magnetic field lines shown by iron filings In physics, a magnetic field is a solenoidal vector field in the space surrounding moving electric charges, such as those in electric currents and bar magnets. ... Faradays law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop. ... $mathbf{nabla} times mathbf{E} = -frac{partial mathbf{B}} {partial t}$

where $mathbf{nabla} times mathbf{E}$ indicates the curl of the electric field, $-frac{partial mathbf{B}} {partial t}$ represents the vector rate of decrease of magnetic field with time.

This means that a magnetic field changing in time produces a curled electric field, possibly also changing in time. The situation in which electric or magnetic fields change in time is no longer electrostatics, but rather electrodynamics or electromagnetics. In vector calculus, curl is a vector operator that shows a vector fields rate of rotation: the direction of the axis of rotation and the magnitude of the rotation. ... Magnetic field lines shown by iron filings In physics, a magnetic field is a solenoidal vector field in the space surrounding moving electric charges, such as those in electric currents and bar magnets. ... Magnetic field lines shown by iron filings In physics, a magnetic field is a solenoidal vector field in the space surrounding moving electric charges, such as those in electric currents and bar magnets. ... Electrostatics (also known as Static Electricity) is the branch of physics that deals with the forces exerted by a static (i. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... Electrostatics (also known as Static Electricity) is the branch of physics that deals with the forces exerted by a static (i. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ... In electromagnetism, Maxwells equations are a set of equations first presented as a distinct group in the later half of the nineteenth century by James Clerk Maxwell. ... It has been suggested that this article or section be merged with magnet. ... This article is a stub Overview A teltron tube is used to fire electrons. ... Results from FactBites:

 Problem Set - Electric Fields - Physics 106 (0 words) The number of electric field lines per unit area crossing a surface at a right angle to the surface equals the electric field at the surface. Find the electric field for (a) r ≤ R, (b) r ≥ R. (c) Sketch a graph of E as a function of r. A proton of charge +e and mass m is placed in an electric field E. Find (a) the acceleration of the proton and (b) the velocity and displacement of the proton in time t after entering the field.
 Electric field (223 words) Electric field is defined as the electric force per unit charge. The electric field is radially outward from a positive charge and radially in toward a negative point charge. A positive number is taken to be an outward field; the field of a negative charge is toward it.
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