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The electromagnetic field is a physical field produced by electrically charged objects. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation Electromotive force ( emf, \mathcal{E} is a term used to characterize electrical devices such as Voltaic cells thermoelectric devices electrical Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of Displacement current is a quantity that arises in a changing electric field In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. The Liénard-Wiechert potential describes the electromagnetic effect of a moving Electric charge. The Maxwell Stress Tensor (also known as Maxwell's Stress Tensor is used to calculate the stresses on objects in magnetic or electrical fields An eddy current (also known as Foucault current) is an electrical phenomenon discovered by French physicist Léon Foucault in In Physics, a field is a Physical quantity associated to each point of Spacetime. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. It affects the behaviour of charged objects in the vicinity of the field.

The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of It is one of the four fundamental forces of nature (the others are gravitation, the weak interaction, and the strong interaction). In Physics, a fundamental interaction or fundamental force is a mechanism by which particles interact with each other and which cannot be explained in terms Gravitation is a natural Phenomenon by which objects with Mass attract one another The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and

The field can be viewed as the combination of an electric field and a magnetic field. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges The electric field is produced by stationary charges, and the magnetic field by moving charges (currents); these two are often described as the sources of the field. The way in which charges and currents interact with the electromagnetic field is described by Maxwell's equations and the Lorentz force law. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation

From a classical point of view, the electromagnetic field can be regarded as a smooth, continuous field, propagated in a wavelike manner, whereas from a quantum mechanical point of view, the field can be viewed as being composed of photons. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena

## Structure of the electromagnetic field

The electromagnetic field may be viewed in two distinct ways.

### Continuous structure

Classically, electric and magnetic fields are thought of as being produced by smooth motions of charged objects. For example, oscillating charges produce electric and magnetic fields that may be viewed in a 'smooth', continuous, wavelike manner. In this case, energy is viewed as being transferred continuously through the electromagnetic field between any two locations. For instance, the metal atoms in a radio transmitter appear to transfer energy continuously. Radio is the transmission of signals by Modulation of electromagnetic waves with frequencies below those of visible Light. For biologic transmitters see Transmitter substance. A transmitter is an electronic device which usually with the aid of an antenna This view is useful to a certain extent (radiation of low frequency), but problems are found at high frequencies (see ultraviolet catastrophe). The ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe was a prediction of early 20th century Classical physics that an ideal Black body at This problem leads to another view.

### Discrete structure

The electromagnetic field may be thought of in a more 'coarse' way. Experiments reveal that electromagnetic energy transfer is better described as being carried away in 'packets' or 'chunks' called photons with a fixed frequency. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena Planck's relation links the energy E of a photon to its frequency ν through the equation:

$E= \, h \, \nu$

where h is Planck's constant, named in honour of Max Planck, and ν is the frequency of the photon . The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. For example, in the photoelectric effect —the emission of electrons from metallic surfaces by electromagnetic radiation— it is found that increasing the intensity of the incident radiation has no effect, and that only the frequency of the radiation is relevant in ejecting electrons. Introduction When a Metallic surface is exposed to Electromagnetic radiation above a certain threshold Frequency, the light is absorbed and Electrons

This quantum picture of the electromagnetic field has proved very successful, giving rise to quantum electrodynamics, a quantum field theory describing the interaction of electromagnetic radiation with charged matter. Quantum electrodynamics ( QED) is a relativistic Quantum field theory of Electrodynamics. In quantum field theory (QFT the forces between particles are mediated by other particles

## Dynamics of the electromagnetic field

In the past, electrically charged objects were thought to produce two types of field associated with their charge property. An electric field is produced when the charge is stationary with respect to an observer measuring the properties of the charge and a magnetic field (as well as an electric field) is produced when the charge moves (creating an electric current) with respect to this observer. Over time, it was realized that the electric and magnetic fields are better thought of as two parts of a greater whole — the electromagnetic field.

Once this electromagnetic field has been produced from a given charge distribution, other charged objects in this field will experience a force (in a similar way that planets experience a force in the gravitational field of the Sun). If these other charges and currents are comparable in size to the sources producing the above electromagnetic field, then a new net electromagnetic field will be produced. Thus, the electromagnetic field may be viewed as a dynamic entity that causes other charges and currents to move, and which is also affected by them. These interactions are described by Maxwell's equations and the Lorentz force law. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation

## The electromagnetic field as a feedback loop

The behavior of the electromagnetic field can be resolved into four different parts of a loop: (1) the electric and magnetic fields are generated by electric charges, (2) the electric and magnetic fields interact only with each other, (3) the electric and magnetic fields produce forces on electric charges, (4) the electric charges move in space.

The feedback loop can be summarized in a list, including phenomena belonging to each part of the loop:

• charges generate fields
• the fields interact with each other
• fields act upon charges
• Lorentz force: force due to electromagnetic field
• electric force: same direction as electric field
• magnetic force: perpendicular both to magnetic field and to velocity of charge ($\star$)
• charges move

Phenomena in the list are marked with a star ($\star$) if they consist of magnetic fields and moving charges which can be reduced by suitable Lorentz transformations to electric fields and static charges. ---- Bold text Coulomb's law', developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form Displacement current is a quantity that arises in a changing electric field cURL is a Command line tool for transferring files with URL syntax. Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of Lenz's law (ˈlɛntsɨz ˌlɔː gives the direction of the induced Electromotive force (emf and current resulting from Electromagnetic induction. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric The wave equation is an important second-order linear Partial differential equation that describes the propagation of a variety of Waves such as Sound waves In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation A continuity equation is a Differential equation that describes the conservative transport of some kind of quantity In Physics, the Lorentz transformation converts between two different observers' measurements of space and time where one observer is in constant motion with respect to This means that the magnetic field ends up being (conceptually) reduced to an appendage of the electric field, i. e. something which interacts with reality only indirectly through the electric field.

## Mathematical description

There are different mathematical ways of representing the electromagnetic field. There are various mathematical descriptions of the electromagnetic field that are used in the study of Electromagnetism, one of the four Fundamental forces of nature The first one views the electric and magnetic fields as three-dimensional vector fields. In Mathematics a vector field is a construction in Vector calculus which associates a vector to every point in a (locally Euclidean space. These vector fields each have a value defined at every point of space and time and are thus often regarded as functions of the space and time coordinates. As such, they are often written as $\mathbf{E}(x, y, z, t)$ (electric field) and $\mathbf{B}(x, y, z, t)$ (magnetic field). In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges

If only the electric field ($\mathbf{E}$) is non-zero, and is constant in time, the field is said to be an electrostatic field. In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can In Physics, the space surrounding an Electric charge or in the presence of a time-varying Magnetic field has a property called an electric field (that can Similarly, if only the magnetic field ($\mathbf B$) is non-zero and is constant in time, the field is said to be a magnetostatic field. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Magnetostatics is the study of static Magnetic fields In Electrostatics the charges are stationary whereas here the currents are stationary or dc(direct However, if either the electric or magnetic field has a time-dependence, then both fields must be considered together as a coupled electromagnetic field using Maxwell's equations[1]. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric

With the advent of special relativity, physical laws became susceptible to the formalism of tensors. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually Maxwell's equations can be written in tensor form, generally viewed by physicists as a more elegant means of expressing physical laws.

The behaviour of electric and magnetic fields, whether in cases of electrostatics, magnetostatics, or electrodynamics (electromagnetic fields), is governed in a vacuum by Maxwell's equations. Classical electromagnetism (or classical electrodynamics) is a theory of Electromagnetism that was developed over the course of the 19th century most prominently In the vector field formalism, these are:

$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$ (Gauss' law)
$\nabla \cdot \mathbf{B} = 0$ (Gauss' law for magnetism)
$\nabla \times \mathbf{E} = -\frac {\partial \mathbf{B}}{\partial t}$ (Faraday's law)
$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0\varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}$ (Ampère-Maxwell law)

where ρ is the charge density, which can (and often does) depend on time and position, ε0 is the permittivity of free space, μ0 is the permeability of free space, and $\mathbf J$ is the current density vector, also a function of time and position. In Classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère, relates the integrated Magnetic field around a closed 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 In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. The units used above are the standard SI units. Inside a linear material, Maxwell's equations change by switching the permeability and permittivity of free space with the permeability and permittivity of the linear material in question. Inside other materials which possess more complex responses to electromagnetic fields, these terms are often represented by complex numbers, or tensors.

The Lorentz force law governs the interaction of the electromagnetic field with charged matter. In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation

## Properties of the field

### Reciprocal behaviour of electric and magnetic fields

The two Maxwell equations, Faraday's Law and the Ampère-Maxwell Law, illustrate a very practical feature of the electromagnetic field. Faraday's Law may be stated roughly as 'a changing magnetic field creates an electric field'. This is the principle behind the electric generator. In Electricity generation, an electrical generator is a device that converts Mechanical energy to Electrical energy, generally using Electromagnetic

The Ampère-Maxwell Law roughly states that 'a changing electric field creates a magnetic field'. Thus, this law can be applied to generate a magnetic field and run an electric motor. An electric motor uses Electrical energy to produce Mechanical energy.

### Light as an electromagnetic disturbance

Maxwell's equations take the form of an electromagnetic wave in an area that is very far away from any charges or currents (free space) - that is, where ρ and $\mathbf J$ are zero. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes It can be shown, that, under these conditions, the electric and magnetic fields satisfy the electromagnetic wave equation:

$\left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{E} \ \ = \ \ 0$
$\left( \nabla^2 - { 1 \over {c}^2 } {\partial^2 \over \partial t^2} \right) \mathbf{B} \ \ = \ \ 0$

James Clerk Maxwell was the first to obtain this relationship by his completion of Maxwell's equations with the addition of a displacement current term to Ampère's circuital law. The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of Electromagnetic waves through a medium James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric Displacement current is a quantity that arises in a changing electric field In Classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère, relates the integrated Magnetic field around a closed

## Relation to and comparison with other physical fields

Main article: Fundamental forces

Being one of the four fundamental forces of nature, it is useful to compare the electromagnetic field with the gravitational, strong and weak fields. In Physics, a fundamental interaction or fundamental force is a mechanism by which particles interact with each other and which cannot be explained in terms Gravitation is a natural Phenomenon by which objects with Mass attract one another In particle physics the strong interaction, or strong force, or color force, holds Quarks and Gluons together to form Protons and The weak interaction (often called the weak force or sometimes the weak nuclear force) is one of the four Fundamental interactions of nature The word 'force' is sometimes replaced by 'interaction'.

### Electromagnetic and gravitational fields

Sources of electromagnetic fields consist of two types of charge - positive and negative. In Physics, a charge may refer to one of many different quantities such as the Electric charge in Electromagnetism or the Color charge in This contrasts with the sources of the gravitational field, which are masses. Masses are sometimes described as gravitational charges, the important feature of them being that there is only one type (no negative masses), or, in more colloquial terms, 'gravity is always attractive'. Exotic matter is a hypothetical concept of Particle physics. It covers any material which violates one or more classical conditions or is not made of known baryonic particles

The relative strengths and ranges of the four interactions and other information are tabulated below:

TheoryInteractionmediatorRelative MagnitudeBehaviorRange
ChromodynamicsStrong interactiongluon1038110-15 m
ElectrodynamicsElectromagnetic interactionphoton10361/r2infinite
FlavordynamicsWeak interactionW and Z bosons10251/r5 to 1/r710-16 m
GeometrodynamicsGravitationgraviton1001/r2infinite