Classical electrodynamics (or classical electromagnetism) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell. It provides an excellent description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible (see quantum electrodynamics). Jump to: navigation, search This article needs to be cleaned up to conform to a higher standard of quality. ... Alternative meaning: Nineteenth Century (periodical) (18th century — 19th century — 20th century — more centuries) As a means of recording the passage of time, the 19th century was that century which lasted from 1801-1900 in the sense of the Gregorian calendar. ... Jump to: navigation, search James Clerk Maxwell (June 13, 1831–November 5, 1879) was a Scottish mathematical physicist, born in Edinburgh. ... In general English usage, length (symbols: l, L) is but one particular instance of distance – an objects length is how long the object is – but in the physical sciences and engineering, the word length is in some contexts used synonymously with distance. Height is vertical distance; width (or breadth... Fig. ... Jump to: navigation, search This article may be too technical for most readers to understand. ...

Lorentz force

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The electromagnetic field exerts the following force (often called the Lorentz force) on charged particles: Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ...

where all boldfaced quantities are vectors: F is the force that a charge q experiences, E is the electric field at q's location, v is q's velocity, B is the strength of the magnetic field at q's position. Jump to: navigation, search In mathematics, and in particular in vectorial analysis a vector is an arrow pointing from one point to another. ... Jump to: navigation, search In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ... Jump to: navigation, search Current flowing through a wire produces a magnetic field (M) around the wire. ...

This description of the force between charged particles, unlike Coulomb's force law, does not break down under relativity and in fact, the magnetic force is seen as part of the relativistic interaction of fast moving charges that Coulomb's law neglects. Jump to: navigation, search It has been suggested that this article or section be merged into Electrostatic force. ... Jump to: navigation, search Wikisource has original text related to this article: Relativity: The Special and General Theory Albert Einsteins theory of relativity is a set of two scientific theories in physics: special relativity and general relativity. ...

The Electric Field E

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The electric field E is defined such that, on a stationary charge: Jump to: navigation, search In physics, an electric field or E-field is an effect produced by an electric charge that exerts a force on charged objects in its vicinity. ...

where q₀ is what is known as a test charge. The size of the charge doesn't really matter, as long as it is small enough as to not influence the electric field by its mere presence. What is plain from this definition, though, is that the unit of E is N/C, or newtons per coulomb. This unit is equal to V/m (volts per meter), see below. This article is about the SI unit of force. ... The coulomb (symbol: C) is the SI unit of electric charge. ... The volt is the SI derived unit for electric potential and voltage (derived from the ampere and watt). ... The metre, or meter (symbol: m) is the SI base unit of length. ...

The above definition seems a little bit circular but, in electrostatics, where charges are not moving, Coulomb's law works fine. So what we end up with is:

where n is the number of charges, q_i is the amount of charge associated with the 'i'th charge, r_i is the position of the 'i'th charge, r is the position where the electric field is being determined, and ε₀ is a universal constant called the permittivity of free space. The permittivity of a medium is an intensive physical quantity that describes how an electric field affects and is affected by the medium. ...

Note: the above is just Coulomb's law, divided by q₁, added up more multiple charges.

Changing the summation to an integral yields the following:

where ρ is the charge density as a function of position, r_unit is the unit vector pointing from dV to the point in space E is being calculated at, and r is the distance from the point E is being calculated at to the point charge.

Both of the above equations are cumbersome, especially if one wants to calculate E as a function of position. There is, however, a scalar function called the electrical potential that can help. Electric potential, also called voltage (the units for which are the volt), which is defined thus: Electrical potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential or the electric potential, typically measured in volts. ...

where φ_E is the electric potential, and s is the path over which the integral is being taken.

Unfortunately, this definition has a caveat. From Maxwell's equations, it is clear that is not always zero, and hence the scalar potential alone is insufficient to define the electric field exactly. As a result, one must resort to adding a correction factor, which is generally done by subtracting the time derivative of the A vector potential. Whenever the charges are quasistatic, however, this condition will be essentially met, so there will be few problems. (As a side note, by using the appropriate gauge transformations, one can define V to be zero and define E entirely as the negative time derivative of A, however, this is rarely done because a) it's a hassle and more importantly, b) it no longer satisfies the requirements of the Lorenz gauge and hence is no longer relativistically invariant).

From the definition of charge, it is trivial to show that the electric potential of a point charge as a function of position is:

where q is the point charge's charge, r is the position, and r_q is the position of the point charge. The potential for a general distribution of charge ends up being:

where ρ is the charge density as a function of position, and r is the distance from the volume element dV.

Note well that φ is a scalar, which means that it will add to other potential fields as a scalar. This makes it relatively easy to break complex problems down in to simple parts and add their potentials. Taking the definition of φ backwards, we see that the electric field is just the negative gradient of the potential. Or:

From this formula it is clear that E can be expressed in V/m (volts per meter).

Electromagnetic waves

A changing electromagnetic field propagates away from its origin in the form of a wave. These waves travel in vacuum at the speed of light and exist in a wide spectrum of wavelengths. Examples of the dynamic fields of electromagnetic radiation (in order of increasing frequency): radio waves, microwaves, light (infrared, visible light and ultraviolet), x-rays and gamma rays. In the field of particle physics this electromagnetic radiation is the manifestation of the electromagnetic interaction between charged particles. Jump to: navigation, search A wave is a disturbance that propagates in a periodically repeating fashion, often transferring energy. ... Cherenkov effect in a swimming pool nuclear reactor. ... Jump to: navigation, search The electromagnetic spectrum is the range of all possible electromagnetic radiation. ... Jump to: navigation, search The wavelength is the distance between repeating units of a wave pattern. ... Jump to: navigation, search Electromagnetic radiation can be conceptualized as a self propagating transverse oscillating wave of electric and magnetic fields. ... Jump to: navigation, search This page is about the radiation; for the appliance, see microwave oven. ... Jump to: navigation, search Prism splitting light Light is electromagnetic radiation with a wavelength that is visible to the eye (visible light) or, in a technical or scientific setting, electromagnetic radiation of any wavelength. ... Jump to: navigation, search Image of a small dog taken in mid-infrared (thermal) light (false color) Infrared (IR) radiation is electromagnetic radiation of a wavelength longer than visible light, but shorter than microwave radiation. ... The optical spectrum (light or visible spectrum) is the portion of the electromagnetic spectrum that is visible to the human eye. ... Jump to: navigation, search Ultraviolet (UV) radiation is electromagnetic radiation of a wavelength shorter than that of the visible region, but longer than that of soft X-rays. ... In the NATO phonetic alphabet, X-ray represents the letter X. An X-ray picture (radiograph) taken by Röntgen An X-ray is a form of electromagnetic radiation with a wavelength approximately in the range of 5 pm to 10 nanometers (corresponding to frequencies in the range 30 PHz... This article is about electromagnetic radiation. ... Particles erupt from the collision point of two relativistic (100 GeV) gold ions in the STAR detector of the Relativistic Heavy Ion Collider. ... Electromagnetic interaction is a fundamental force of nature and is felt by charged leptons and quarks. ...

General Field Equations

As simple and satisfying as Coulomb's equation may be, it is not entirely correct in the context of classical electromagnetism. Problems arise because changes in charge distributions require a non zero amount of time to be "felt" elsewhere (required by special relativity).

For the fields of general charge distributions, the retarded potentials can be computed and differentiated accordingly to yield Jefimenko's Equations.

Retarded potentials can also be derived for point charges, and the equations are known as the Liénard-alfred e neumann-Wiechert potentials. These can then be differentiated accordingly to obtain the complete field equations for a moving point particle. Though the equations are aesthetically unpleasant, they bring a satisfying closure to classical electrodynamics.