An electric field (sometimes E-field) is the
physical field that surrounds electrically
charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field for a system of charged particles. Electric fields originate from electric charges and time-varying
electric current
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The movi ...
s. Electric fields and magnetic fields are both manifestations of the
electromagnetic field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
, one of the four
fundamental interactions (also called forces) of nature.
Electric fields are important in many areas of
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
, and are exploited in electrical technology. In
atomic physics
Atomic physics is the field of physics that studies atoms as an isolated system of electrons and an atomic nucleus. Atomic physics typically refers to the study of atomic structure and the interaction between atoms. It is primarily concerned wit ...
and
chemistry
Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...
, for instance, the electric field is the attractive force holding the
atomic nucleus
The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger–Marsden gold foil experiment. After the discovery of the neutron ...
and
electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
s together in atoms. It is also the force responsible for
chemical bonding between atoms that result in
molecule
A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and b ...
s.
The electric field is defined as a
vector field that associates to each point in space the electrostatic (
Coulomb) force per unit of
charge exerted on an infinitesimal positive
test charge In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be in ...
at rest at that point.
The
derived SI unit for the electric field is the
volt per
meter (V/m), which is equal to the
newton per
coulomb (N/C).
Description
The electric field is defined at each point in space as the force per unit charge that would be experienced by a
vanishingly small positive
test charge In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge, or size) are assumed to be negligible except for the property being studied, which is considered to be in ...
if held stationary at that point.
As the electric field is defined in terms of
force
In physics, a force is an influence that can change the motion of an object. A force can cause an object with mass to change its velocity (e.g. moving from a state of rest), i.e., to accelerate. Force can also be described intuitively as a ...
, and force is a
vector (i.e. having both
magnitude and
direction), it follows that an electric field is a
vector field.
[ Fields that may be defined in this manner are sometimes referred to as ]force fields
Force field may refer to:
Science
* Force field (chemistry), a set of parameter and equations for use in molecular mechanics simulations
* Force field (physics), a vector field indicating the forces exerted by one object on another
* Force field ( ...
. The electric field acts between two charges similarly to the way the gravitational field
In physics, a gravitational field is a model used to explain the influences that a massive body extends into the space around itself, producing a force on another massive body. Thus, a gravitational field is used to explain gravitational pheno ...
acts between two mass
Mass is an intrinsic property of a body. It was traditionally believed to be related to the quantity of matter in a physical body, until the discovery of the atom and particle physics. It was found that different atoms and different ele ...
es, as they both obey an inverse-square law with distance. This is the basis for Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
, which states that, for stationary charges, the electric field varies with the source charge and varies inversely with the square of the distance from the source. This means that if the source charge were doubled, the electric field would double, and if you move twice as far away from the source, the field at that point would be only one-quarter its original strength.
The electric field can be visualized with a set of lines whose direction at each point is the same as the field's, a concept introduced by Michael Faraday
Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic inducti ...
, whose term ' lines of force' is still sometimes used. This illustration has the useful property that the field's strength is proportional to the density of the lines. Field lines due to stationary charges have several important properties, including always originating from positive charges and terminating at negative charges, they enter all good conductors at right angles, and they never cross or close in on themselves.[ The field lines are a representative concept; the field actually permeates all the intervening space between the lines. More or fewer lines may be drawn depending on the precision to which it is desired to represent the field.] The study of electric fields created by stationary charges is called electrostatics.
Faraday's law describes the relationship between a time-varying magnetic field and the electric field. One way of stating Faraday's law is that the curl of the electric field is equal to the negative time derivative of the magnetic field. In the absence of time-varying magnetic field, the electric field is therefore called conservative (i.e. curl-free). This implies there are two kinds of electric fields: electrostatic fields and fields arising from time-varying magnetic fields.[ While the curl-free nature of the static electric field allows for a simpler treatment using electrostatics, time-varying magnetic fields are generally treated as a component of a unified ]electromagnetic field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
. The study of time varying magnetic and electric fields is called electrodynamics.
Mathematical formulation
Electric fields are caused by electric charges, described by 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 st ...
, and time varying magnetic fields, described by Faraday's law of induction. Together, these laws are enough to define the behavior of the electric field. 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
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
that describe both fields as a function of charges and currents.
Electrostatics
In the special case of a steady state (stationary charges and currents), the Maxwell-Faraday inductive effect disappears. The resulting two equations (Gauss's law and Faraday's law with no induction term ), taken together, are equivalent to Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
, which states that a particle with electric charge at position exerts a force on a particle with charge at position of:
where is the unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat").
The term ''direction v ...
in the direction from point to point , and is the electric constant (also known as "the absolute permittivity of free space") with the unit C2⋅m−2⋅N−1.
Note that , the vacuum electric permittivity, must be substituted with , permittivity, when charges are in non-empty media.
When the charges and have the same sign this force is positive, directed away from the other charge, indicating the particles repel each other. When the charges have unlike signs the force is negative, indicating the particles attract.
To make it easy to calculate the Coulomb force on any charge at position this expression can be divided by leaving an expression that only depends on the other charge (the ''source'' charge)
This is the ''electric field'' at point due to the point charge ; it is a vector-valued function equal to the Coulomb force per unit charge that a positive point charge would experience at the position .
Since this formula gives the electric field magnitude and direction at any point in space (except at the location of the charge itself, , where it becomes infinite) it defines a vector field.
From the above formula it can be seen that the electric field due to a point charge is everywhere directed away from the charge if it is positive, and toward the charge if it is negative, and its magnitude decreases with the inverse square of the distance from the charge.
The Coulomb force on a charge of magnitude at any point in space is equal to the product of the charge and the electric field at that point
The SI unit of the electric field is the newton per coulomb (N/C), or volt per meter (V/m); in terms of the SI base units it is kg⋅m⋅s−3⋅A−1.
Superposition principle
Due to the linearity of Maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
, electric fields satisfy the superposition principle, which states that the total electric field, at a point, due to a collection of charges is equal to the vector sum of the electric fields at that point due to the individual charges. This principle is useful in calculating the field created by multiple point charges. If charges are stationary in space at points , in the absence of currents, the superposition principle says that the resulting field is the sum of fields generated by each particle as described by Coulomb's law:
where is the unit vector
In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat").
The term ''direction v ...
in the direction from point to point .
Continuous charge distributions
The superposition principle allows for the calculation of the electric field due to a continuous distribution of charge (where is the charge density
In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system i ...
in coulombs per cubic meter). By considering the charge in each small volume of space at point as a point charge, the resulting electric field, , at point can be calculated as
where is the unit vector pointing from to . The total field is then found by "adding up" the contributions from all the increments of volume by integrating over the volume of the charge distribution :
Similar equations follow for a surface charge with continuous charge distribution where is the charge density in coulombs per square meter
and for line charges with continuous charge distribution where is the charge density in coulombs per meter.
Electric potential
If a system is static, such that magnetic fields are not time-varying, then by Faraday's law, the electric field is curl-free. In this case, one can define an 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 ...
, that is, a function such that This is analogous to the gravitational potential. The difference between the electric potential at two points in space is called the potential difference (or voltage) between the two points.
In general, however, the electric field cannot be described independently of the magnetic field. Given the magnetic vector potential, , defined so that one can still define an electric potential such that:
where is the gradient
In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...
of the electric potential and is the partial derivative of A with respect to time.
Faraday's law of induction can be recovered by taking the curl of that equation
which justifies, a posteriori, the previous form for .
Continuous vs. discrete charge representation
The equations of electromagnetism are best described in a continuous description. However, charges are sometimes best described as discrete points; for example, some models may describe electron
The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family,
and are generally thought to be elementary particles because they have n ...
s as point sources where charge density is infinite on an infinitesimal section of space.
A charge located at can be described mathematically as a charge density , where the Dirac delta function (in three dimensions) is used. Conversely, a charge distribution can be approximated by many small point charges.
Electrostatic fields
Electrostatic fields are electric fields that do not change with time. Such fields are present when systems of charged matter are stationary, or when electric currents are unchanging. In that case, Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
fully describes the field.
Parallels between electrostatic and gravitational fields
Coulomb's law, which describes the interaction of electric charges:
is similar to Newton's law of universal gravitation:
(where ).
This suggests similarities between the electric field E and the gravitational field g, or their associated potentials. Mass is sometimes called "gravitational charge".
Electrostatic and gravitational forces both are central
Central is an adjective usually referring to being in the center of some place or (mathematical) object.
Central may also refer to:
Directions and generalised locations
* Central Africa, a region in the centre of Africa continent, also known a ...
, conservative and obey an inverse-square law.
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 voltage
Voltage, also known as electric pressure, electric tension, or (electric) potential difference, is the difference in electric potential between two points. In a static electric field, it corresponds to the work needed per unit of charge to ...
(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). Assuming infinite planes, the magnitude of the electric field ''E'' is:
where Δ''V'' is the potential difference between the plates and ''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. In micro- and nano-applications, for instance in relation to semiconductors, a typical magnitude of an electric field is in the order of , achieved by applying a voltage of the order of 1 volt between conductors spaced 1 µm apart.
Electrodynamic fields
Electrodynamic fields are electric fields which do change with time, for instance when charges are in motion. In this case, a magnetic field is produced in accordance with Ampère's circuital law ( with Maxwell's addition), which, along with Maxwell's other equations, defines the magnetic field, , in terms of its curl:
where is the current density, is the vacuum permeability, and is the vacuum permittivity.
That is, both electric currents
An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
(i.e. charges in uniform motion) and the (partial) time derivative of the electric field directly contributes to the magnetic field. In addition, the Maxwell–Faraday equation states
These represent two of Maxwell's four equations and they intricately link the electric and magnetic fields together, resulting in the electromagnetic field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
. The equations represent a set of four coupled multi-dimensional partial differential equations which, when solved for a system, describe the combined behavior of the electromagnetic fields. In general, the force experienced by a test charge in an electromagnetic field is given by the Lorentz force law:
Energy in the electric field
The total energy per unit volume stored by the electromagnetic field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
is
where is the permittivity of the medium in which the field exists, its magnetic permeability, and and are the electric and magnetic field vectors.
As and fields are coupled, it would be misleading to split this expression into "electric" and "magnetic" contributions. In particular, an electrostatic field in any given frame of reference in general transforms into a field with a magnetic component in a relatively moving frame. Accordingly, decomposing the electromagnetic field into an electric and magnetic component is frame-specific, and similarly for the associated energy.
The total energy ''U'' stored in the electromagnetic field in a given volume ''V'' is
The electric displacement field
Definitive equation of vector fields
In the presence of matter, it is helpful to extend the notion of the electric field into three vector fields:
where P is the electric polarization – the volume density of electric dipole moments, and is 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 in ...
. Since E and P are defined separately, this equation can be used to define . The physical interpretation of D is not as clear as E (effectively the field applied to the material) or (induced field due to the dipoles in the material), but still serves as a convenient mathematical simplification, since Maxwell's equations can be simplified in terms of free charges and currents.
Constitutive relation
The E and D fields are related by the permittivity of the material, ''ε''.
For linear, homogeneous, isotropic
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence '' anisotropy''. ''Anisotropy'' is also used to describ ...
materials E and D are proportional and constant throughout the region, there is no position dependence:
For inhomogeneous materials, there is a position dependence throughout the material:
For anisotropic materials the and fields are not parallel, and so and are related by the permittivity tensor (a 2nd order tensor field), in component form:
For non-linear media, and are not proportional. Materials can have varying extents of linearity, homogeneity and isotropy.
Relativistic Effects on electric field
Point charge in uniform motion
The invariance of the form of Maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
under Lorentz transformation can be used to derive the electric field of a uniformly moving point charge. The charge of a particle is considered frame invariant, as supported by experimental evidence. Alternatively the electric field of uniformly moving point charges can be derived from the Lorentz transformation of four-force In the special theory of relativity, four-force is a four-vector that replaces the classical force.
In special relativity
The four-force is defined as the rate of change in the four-momentum of a particle with respect to the particle's proper ...
experienced by test charges in the source's rest frame given by Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
and assigning electric field and magnetic field by their definition given by the form of Lorentz force. However the following equation is only applicable when no acceleration is involved in the particle's history where Coulomb's law
Coulomb's inverse-square law, or simply Coulomb's law, is an experimental law of physics that quantifies the amount of force between two stationary, electrically charged particles. The electric force between charged bodies at rest is convention ...
can be considered or symmetry arguments can be used for solving Maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
in a simple manner. The electric field of such a uniformly moving point charge is hence given by:
where is the charge of the point source, is the position vector from the point source to the point in space, is the ratio of observed speed of the charge particle to the speed of light and is the angle between and the observed velocity of the charged particle.
The above equation reduces to that given by Coulomb's law for non-relativistic speeds of the point charge. Spherically symmetry is not satisfied due to breaking of symmetry in the problem by specification of direction of velocity for calculation of field. To illustrate this, field lines of moving charges are sometimes represented as unequally spaced radial lines which would appear equally spaced in a co-moving reference frame.
Propagation of disturbances in electric fields
Special theory of 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 ...
imposes the principle of locality
In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of in ...
, that requires cause and effect to be time-like separated events where the causal efficacy does not travel faster than the speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
. Maxwell's laws
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
Th ...
are found to confirm to this view since the general solutions of fields are given in terms of retarded time which indicate that electromagnetic disturbances travel at the speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
. Advanced time, which also provides a solution for maxwell's law are ignored as an unphysical solution.For the motion of a charged particle, considering for example the case of a moving particle with the above described electric field coming to an abrupt stop, the electric fields at points far from it do not immediately revert to that classically given for a stationary charge. On stopping, the field around the stationary points begin to revert to the expected state and this effect propagates outwards at the speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
while the electric field lines far away from this will continue to point radially towards an assumed moving charge. This virtual particle will never be outside the range of propagation of the disturbance in electromagnetic field
An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical ...
, since charged particles are restricted to have speeds slower than that of light, which makes it impossible to construct a gaussian surface in this region that violates gauss' 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 s ...
. Another technical difficulty that supports this is that charged particles travelling faster than or equal to speed of light no longer have a unique retarded time. Since electric field lines are continuous, an electromagnetic pulse
An electromagnetic pulse (EMP), also a transient electromagnetic disturbance (TED), is a brief burst of electromagnetic energy. Depending upon the source, the origin of an EMP can be natural or artificial, and can occur as an electromagnetic f ...
of radiation is generated that connects at the boundary of this disturbance travelling outwards at the speed of light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit fo ...
. In general, any accelerating point charge radiates electromagnetic waves however, non radiating acceleration is possible in a systems of charges.
Arbitrarily moving point charge
For arbitrarily moving point charges, propagation of potential fields such as Lorenz gauge fields at the speed of light needs to be accounted for by using Liénard–Wiechert potential
The Liénard–Wiechert potentials describe the classical electromagnetic effect of a moving electric point charge in terms of a vector potential and a scalar potential in the Lorenz gauge. Stemming directly from Maxwell's equations, these desc ...
. Since the potentials satisfy maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
, the fields derived for point charge also satisfy Maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
. The electric field is expressed as:
where is the charge of the point source, is retarded time or the time at which the source's contribution of the electric field originated, is the position vector of the particle, is a unit vector pointing from charged particle to the point in space, is the velocity of the particle divided by the speed of light, and is the corresponding Lorentz factor. The retarded time is given as solution of:
The uniqueness of solution for for given , and is valid for charged particles moving slower than speed of light. Electromagnetic radiation
In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visib ...
of accelerating charges is known to be caused by the acceleration dependent term in the electric field from which relativistic correction for Larmor formula
In electrodynamics, the Larmor formula is used to calculate the total power radiated by a nonrelativistic point charge as it accelerates. It was first derived by J. J. Larmor in 1897, in the context of the wave theory of light.
When any charge ...
is obtained.
There exist yet another set of solutions for maxwell's equation of the same form but for advanced time instead of retarded time given as a solution of:
Since the physical interpretation of this indicates that the electric field at a point is governed by the particle's state at a point of time in the future, it is considered as an unphysical solution and hence neglected. However, there have been theories exploring the advanced time solutions of maxwell's equations
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits ...
, such as Feynman Wheeler absorber theory.
The above equation, although consistent with that of uniformly moving point charges as well as its non-relativistic limit, are not corrected for quantum-mechanical effects.
Some Common Electric Field Values
*Infinite Wire having Uniform charge density has Electric Field at a distance from it as
*Infinitely large surface having charge density has Electric Field at a distance from it as
*Infinitely long cylinder having Uniform charge density that is charge contained along unit length of the cylinder has Electric Field at a distance from it as while it is everywhere inside the cylinder
*Uniformly Charged non-conducting sphere of radius , volume charge density and total charge has Electric Field at a distance from it as while the electric field at a point inside sphere from its center is given by
*Uniformly Charged conducting sphere of radius , surface charge density and total charge has Electric Field at a distance from it as while the electric field inside is
*Electric field infinitely close to a conducting surface in electrostatic equilibrium having charge density at that point is
*Uniformly Charged Ring having total charge has Electric Field at a distance along its axis as '
*Uniformly charged disc of radius and charge density has Electric Field at a distance along its axis from it as
*Electric field due to dipole of dipole moment at a distance from their center along equatorial plane is given as and the same along the axial line is approximated to for much bigger than the distance between dipoles. Further generalization is given by multipole expansion.
See also
* Classical electromagnetism
* Relativistic Electromagnetism
* Electricity
Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. Electricity is related to magnetism, both being part of the phenomenon of electromagnetism, as describe ...
* History of electromagnetic theory
The history of electromagnetic theory begins with ancient measures to understand atmospheric electricity, in particular lightning. People then had little understanding of electricity, and were unable to explain the phenomena. Scientific understan ...
* Optical field
* Magnetism
Magnetism is the class of physical attributes that are mediated by a magnetic field, which refers to the capacity to induce attractive and repulsive phenomena in other entities. Electric currents and the magnetic moments of elementary particles ...
* Teltron tube
* Teledeltos Teledeltos paper is an electrically conductive paper. It is formed by a coating of carbon on one side of a sheet of paper, giving one black and one white side. Western Union developed Teledeltos paper in the late 1940s (several decades after it ...
, a conductive paper that may be used as a simple analog computer for modelling fields
References
*
*
External links
Electric field in "Electricity and Magnetism", R Nave
– Hyperphysics, Georgia State University
Frank Wolfs's lectures
at University of Rochester
The University of Rochester (U of R, UR, or U of Rochester) is a private research university in Rochester, New York. The university grants undergraduate and graduate degrees, including doctoral and professional degrees.
The University of ...
, chapters 23 and 24
Fields
– a chapter from an online textbook
{{DEFAULTSORT:Electric Field
Electrostatics
Physical quantities
Electromagnetism