Electric field

Overview

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, an

**electric field**surrounds electrically charged particles

Electric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

and time-varying magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding. The concept of an electric field was introduced by Michael Faraday

Michael Faraday

Michael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry....

.

The electric field is a vector field

Vector field

In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...

with SI

Si

Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

units of newtons per coulomb (N C

^{−1}) or, equivalently, volt

Volt

The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

s per metre

Metre

The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

(V m

^{−1}).

Unanswered Questions

Encyclopedia

In physics

, an

and time-varying magnetic field

s. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding. The concept of an electric field was introduced by Michael Faraday

.

The electric field is a vector field

with SI

units of newtons per coulomb (N C

s per metre

(V m

of the field at a given point is defined as the force that would be exerted on a positive test charge of 1 coulomb placed at that point; the direction of the field is given by the direction of that force. Electric fields contain electrical energy with energy density

proportional to the square of the field amplitude. The electric field is to charge as gravitational acceleration

is to mass and force density

is to volume.

An electric field that changes with time, such as due to the motion of charged particles in the field, influences the local magnetic field. That is, 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 field

s". In quantum electrodynamics

, disturbances in the electromagnetic fields are called photon

s, and the energy of photons is quantized.

where

Taken literally, this equation only defines the electric field at a specific location as the force experienced by a stationary test charge at that point(with the sign of qElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

particles, adding and/or moving a source charge,Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

in the vicinity of the source distribution and measuring the force exerted on the test charges as their charge approaches zero.

This allows the electric field to be determined from the distribution of its source charges alone.

As is clear from the definition, the direction of the electric field is the same as the direction of the force it would exert on a positively-charged particle, and opposite the direction of the force on a negatively-charged particle. Since like charges repel and opposites attract (as quantified below), the electric field tends to point away from positive charges and towards negative charges.

Based on Coulomb's law

for interacting point charges, the contribution to the E-field at a point in space due to a single, discrete charge located at another point in space is given by the following:

where

The total E-field due to a quantity of point charges, , is simply the superposition

of the contribution of each individual point charge:

Alternatively, Gauss's law

allows the E-field to be calculated in terms of a continuous distribution of charge density

in space, ρ:

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.

between them; it is only an approximation because of edge effects. Ignoring such effects, the equation for the magnitude of the electric field is:

where

The negative sign arises as positive charges repel, so a positive charge will experience a force away from the positively charged plate, in the opposite direction to that in which the voltage increases.

where,

The vector

which is one of Maxwell's equations

, referred to as Faraday's law of induction

.

Where electrostatics

is the study of the fields surrounding static charges, the study of the electric fields induced by changing magnetic field comes under the domain of electrodynamics or electromagnetics.

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.

If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula results:

where 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,

where 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.

Considering the permittivity

ε of a linear material, which may differ from the permittivity of free space ε

where

of the medium in which the field exists, and

The total energy stored in the electric field in a given volume

where d

, which describes the interaction of electric charges:

is similar to Newton's law of universal gravitation

:

This suggests similarities between the electric field

Similarities between electrostatic and gravitational forces:

Differences between electrostatic and gravitational forces:

Physics

Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

, an

**electric field**surrounds electrically charged particlesElectric charge

Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

and time-varying magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

s. The electric field depicts the force exerted on other electrically charged objects by the electrically charged particle the field is surrounding. The concept of an electric field was introduced by Michael Faraday

Michael Faraday

Michael Faraday, FRS was an English chemist and physicist who contributed to the fields of electromagnetism and electrochemistry....

.

The electric field is a vector field

Vector field

In vector calculus, a vector field is an assignmentof a vector to each point in a subset of Euclidean space. A vector field in the plane for instance can be visualized as an arrow, with a given magnitude and direction, attached to each point in the plane...

with SI

Si

Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...

units of newtons per coulomb (N C

^{−1}) or, equivalently, voltVolt

The volt is the SI derived unit for electric potential, electric potential difference, and electromotive force. The volt is named in honor of the Italian physicist Alessandro Volta , who invented the voltaic pile, possibly the first chemical battery.- Definition :A single volt is defined as the...

s per metre

Metre

The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...

(V m

^{−1}). The SI base units of the electric field are kg·m·s^{−3}·A^{−1}. The strength or magnitudeField strength

In physics, the field strength of a field is the magnitude of its vector value.In theoretical physics, field strength is another name for the curvature form...

of the field at a given point is defined as the force that would be exerted on a positive test charge of 1 coulomb placed at that point; the direction of the field is given by the direction of that force. Electric fields contain electrical energy with energy density

Energy density

Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...

proportional to the square of the field amplitude. The electric field is to charge as gravitational acceleration

Acceleration

In physics, acceleration is the rate of change of velocity with time. In one dimension, acceleration is the rate at which something speeds up or slows down. However, since velocity is a vector, acceleration describes the rate of change of both the magnitude and the direction of velocity. ...

is to mass and force density

Force density

In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid...

is to volume.

An electric field that changes with time, such as due to the motion of charged particles in the field, influences the local magnetic field. That is, 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

Frame of reference

A frame of reference in physics, may refer to a coordinate system or set of axes within which to measure the position, orientation, and other properties of objects in it, or it may refer to an observational reference frame tied to the state of motion of an observer.It may also refer to both an...

perceives as a mixture of electric and magnetic fields. For this reason, one speaks of "electromagnetism

Electromagnetism

Electromagnetism is one of the four fundamental interactions in nature. The other three are the strong interaction, the weak interaction and gravitation...

" or "electromagnetic field

Electromagnetic field

An electromagnetic field is a physical field produced by moving electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction...

s". In quantum electrodynamics

Quantum electrodynamics

Quantum electrodynamics is the relativistic quantum field theory of electrodynamics. In essence, it describes how light and matter interact and is the first theory where full agreement between quantum mechanics and special relativity is achieved...

, disturbances in the electromagnetic fields are called photon

Photon

In physics, a photon is an elementary particle, the quantum of the electromagnetic interaction and the basic unit of light and all other forms of electromagnetic radiation. It is also the force carrier for the electromagnetic force...

s, and the energy of photons is quantized.

## Definition

The electric field intensity is defined as the force per unit positive charge that would be experienced by a stationary point charge, or "test charge", at a given location in the field:where

**F**is the electric forceCoulomb's lawCoulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

experienced by the test particle*q*is the charge_{t}Electric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...

of the test particleTest particleIn physical theories, a test particle is an idealized model of an object whose physical properties are assumed to be negligible except for the property being studied, which is considered to be insufficient to alter the behavior of the rest of the system...

in the electric field**E**is the electric field wherein the particle is located.

Taken literally, this equation only defines the electric field at a specific location as the force experienced by a stationary test charge at that point(with the sign of q

_{t}, positive or negative, determining the direction of the force). Given that electric fields are generated by electrically chargedElectric charge

particles, adding and/or moving a source charge,

*q*, will alter the electric field distribution. Therefore, it is important to remember that an electric field is defined with respect to a particular configuration of source charges. In practice, this is achieved by placing test particles with successively smaller electric charge_{s}Electric charge

in the vicinity of the source distribution and measuring the force exerted on the test charges as their charge approaches zero.

This allows the electric field to be determined from the distribution of its source charges alone.

As is clear from the definition, the direction of the electric field is the same as the direction of the force it would exert on a positively-charged particle, and opposite the direction of the force on a negatively-charged particle. Since like charges repel and opposites attract (as quantified below), the electric field tends to point away from positive charges and towards negative charges.

Based on Coulomb's law

Coulomb's law

Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

for interacting point charges, the contribution to the E-field at a point in space due to a single, discrete charge located at another point in space is given by the following:

where

*Q*is the charge of the particle creating the electric force,*r*is the distance from the particle with charge*Q*to the E-field evaluation point, is the unit vector pointing from the particle with charge*Q*to the E-field evaluation point,- ε
_{0}is the electric constant.

The total E-field due to a quantity of point charges, , is simply the superposition

Superposition principle

In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...

of the contribution of each individual point charge:

Alternatively, Gauss's law

Gauss's law

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. Gauss's law states that:...

allows the E-field to be calculated in terms of a continuous distribution of charge density

Charge density

The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume, respectively. It is measured in coulombs per meter , square meter , or cubic meter , respectively, and represented by the lowercase Greek letter Rho . Since there are positive as well as...

in space, ρ:

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

Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

, a set of four laws governing electromagnetics.

## Uniform fields

A uniform field is one in which the electric field is constant at every point. It can be approximated by placing two conducting plates parallel to each other and maintaining a voltageVoltage

Voltage, otherwise known as electrical potential difference or electric tension is the difference in electric potential between two points — or the difference in electric potential energy per unit charge between two points...

between them; it is only an approximation because of edge effects. Ignoring such effects, the equation for the magnitude of the electric field is:

where

*V*is the voltage difference between the plates*d*is the distance separating the plates

The negative sign arises as positive charges repel, so a positive charge will experience a force away from the positively charged plate, in the opposite direction to that in which the voltage increases.

## Time-varying fields

An electric field can be produced, not only by a static charge, but also by a changing magnetic field. The combined electric field is expressed as,where,

The vector

**B**is the magnetic flux density and the vector**A**is the magnetic vector potential. Taking the curl of the electric field equation we obtain,which is one of Maxwell's equations

Maxwell's equations

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...

, referred to as Faraday's law of induction

Faraday's law of induction

Faraday's law of induction dates from the 1830s, and is a basic law of electromagnetism relating to the operating principles of transformers, inductors, and many types of electrical motors and generators...

.

Where electrostatics

Electrostatics

Electrostatics is the branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges....

is the study of the fields surrounding static charges, the study of the electric fields induced by changing magnetic field comes under the domain of electrodynamics or electromagnetics.

## Properties (in electrostatics)

According to Coulomb's law the 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.Electric fields follow the superposition principle

Superposition principle

In physics and systems theory, the superposition principle , also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually...

. 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.

If this principle is extended to an infinite number of infinitesimally small elements of charge, the following formula results:

where is the charge density

Charge density

The linear, surface, or volume charge density is the amount of electric charge in a line, surface, or volume, respectively. It is measured in coulombs per meter , square meter , or cubic meter , respectively, and represented by the lowercase Greek letter Rho . Since there are positive as well as...

, or the amount of charge per unit volume

Volume

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance or shape occupies or contains....

.

The electric field at a point is equal to the negative gradient

Gradient

In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

of the electric potential

Electric potential

In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...

there. In symbols,

where is the scalar field

Scalar field

In mathematics and physics, a scalar field associates a scalar value to every point in a space. The scalar may either be a mathematical number, or a physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the...

representing the electric potential at a given point.

If several spatially distributed charges generate such an electric potential

Electric potential

In classical electromagnetism, the electric potential at a point within a defined space is equal to the electric potential energy at that location divided by the charge there...

, e.g. in a solid

Solid

Solid is one of the three classical states of matter . It is characterized by structural rigidity and resistance to changes of shape or volume. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire volume available to it like a...

, an electric field gradient

Electric field gradient

In atomic, molecular, and solid-state physics, the electric field gradient measures the rate of change of the electric field at an atomic nucleus generated by the electronic charge distribution and the other nuclei...

may also be defined.

Considering the permittivity

Permittivity

In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

ε of a linear material, which may differ from the permittivity of free space ε

_{0}, the electric displacement field is:## Energy in the electric field

The electric field stores energy. The energy density of the electric field is given bywhere

*ε*is the permittivityPermittivity

In electromagnetism, absolute permittivity is the measure of the resistance that is encountered when forming an electric field in a medium. In other words, permittivity is a measure of how an electric field affects, and is affected by, a dielectric medium. The permittivity of a medium describes how...

of the medium in which the field exists, and

**E**is the electric field vector.The total energy stored in the electric field in a given volume

*V*is thereforewhere d

*V*is the differential volume element.## Parallels between electrostatics and gravity

Coulomb's lawCoulomb's law

Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...

, which describes the interaction of electric charges:

is similar to Newton's law of universal gravitation

Newton's law of universal gravitation

Newton's law of universal gravitation states that every point mass in the universe attracts every other point mass with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them...

:

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:

- Both act in a vacuum.
- Both are central and conservativeConservative forceA conservative force is a force with the property that the work done in moving a particle between two points is independent of the path taken. Equivalently, if a particle travels in a closed loop, the net work done by a conservative force is zero.It is possible to define a numerical value of...

. - Both obey an inverse-square lawInverse-square lawIn physics, an inverse-square law is any physical law stating that a specified physical quantity or strength is inversely proportional to the square of the distance from the source of that physical quantity....

(both are inversely proportional to square of r). - Both propagate with finite speed c, the speed of light.
- Electric chargeCharge invarianceCharge invariance refers to the fixed electrostatic potential of a particle, regardless of speed. For example, an electron has a specific rest charge. Accelerate that electron, and the charge remains the same . The key word here is relativistic...

and relativistic mass are conserved; note, though, that rest mass is not conserved.

Differences between electrostatic and gravitational forces:

- Electrostatic forces are much greater than gravitational forces (by about 10
^{36}times). - Gravitational forces are attractive for like charges, whereas electrostatic forces are repulsive for like charges.
- There are no negative gravitational charges (no negative massNegative massIn theoretical physics, negative mass is a hypothetical concept of matter whose mass is of opposite sign to the mass of the normal matter. Such matter would violate one or more energy conditions and show some strange properties such as being repelled rather than attracted by gravity. It is used in...

) 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.

## See also

- ElectrostaticsElectrostaticsElectrostatics is the branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges....
- Classical electromagnetismClassical electromagnetismClassical electromagnetism is a branch of theoretical physics that studies consequences of the electromagnetic forces between electric charges and currents...
- MagnetismMagnetismMagnetism is a property of materials that respond at an atomic or subatomic level to an applied magnetic field. Ferromagnetism is the strongest and most familiar type of magnetism. It is responsible for the behavior of permanent magnets, which produce their own persistent magnetic fields, as well...
- Teltron TubeTeltron TubeA teltron tube is a type of cathode ray tube used to demonstrate the properties of electrons. It usually contains two electron guns, which can project two thin electron beams at right angles. The beams can be bent by applying voltages to various electrodes in the tube...

## External links

- http://www.its.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html - An applet that shows the electric field of a moving point charge.
- Fields - a chapter from an online textbook
- Learning by Simulations Interactive simulation of an electric field of up to four point charges
- Java simulations of electrostatics in 2-D and 3-D
- Electric Fields Applet - An applet that shows electric field lines as well as potential gradients.
- The inverse cube law The inverse cube law for dipoles (PDF file) by Eng. Xavier Borg
- Interactive Flash simulation picturing the electric field of user-defined or preselected sets of point charges by field vectors, field lines, or equipotential lines. Author: David Chappell