![James Clerk Maxwell](https://upload.wikimedia.org/wikipedia/commons/5/57/James_Clerk_Maxwell.png)
In the beginning of the 19th century, many experimental and theoretical works had been accomplished in the understanding of electromagnetics. In the 1780s,
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 conventiona ...
of
electrostatics
Electrostatics is a branch of physics that studies electric charges at rest (static electricity).
Since classical times, it has been known that some materials, such as amber, attract lightweight particles after rubbing. The Greek word for amber ...
had been established. In 1825, Ampère published his
Ampère's law.
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 ...
discovered the
electromagnetic induction
Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk ...
through his experiments and conceptually, he emphasized the ''lines of forces'' in this
electromagnetic induction
Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk ...
. In 1834,
Lenz Lenz may refer to:
Places
* Lenasia, Gauteng Province, South Africa, a township often called Lenz
* Lantsch/Lenz, Canton of Grisons, Switzerland, a municipality
* Lenz, Hood River County, Oregon, an unincorporated community
* Lenz, Klamath County, ...
solved the problem of the direction of the induction, and
Neumann wrote down the equation to calculate the induced force by change of magnetic flux. However, these experimental results and rules were not well organized and sometimes confusing to scientists. A comprehensive summary of the electrodynamic principles was in urgent need at that time.
This work was done by
James C. Maxwell through a series of papers published from the 1850s through to the 1870s. In the 1850s, Maxwell was working at the
University of Cambridge
, mottoeng = Literal: From here, light and sacred draughts.
Non literal: From this place, we gain enlightenment and precious knowledge.
, established =
, other_name = The Chancellor, Masters and Schola ...
where he was impressed by Faraday's ''lines of forces'' concept. In 1856, he published his 1st paper in electromagnetism: ''On Faraday's Lines of Force''.
He tried to use the analogy of incompressible fluid flow to model the magnetic lines of forces. Later, Maxwell moved to
King's College London
King's College London (informally King's or KCL) is a public research university located in London, England. King's was established by royal charter in 1829 under the patronage of King George IV and the Duke of Wellington. In 1836, King's ...
where he actually came into regular contact with
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 induction, ...
, and became life-long friends. From 1861-1862, Maxwell published a series of 4 papers under the title of ''
On Physical Lines of Force
"On Physical Lines of Force" is a four-part paper written by James Clerk Maxwell published in 1861. In it, Maxwell derived the equations of electromagnetism in conjunction with a "sea" of "molecular vortices" which he used to model Faraday's li ...
''.
In these papers, he used mechanical models, such as rotating vortex tubes, to model the electromagnetic field. He also modeled the vacuum as a kind of insulating elastic medium to account for the stress of the magnetic lines of force given by Faraday. These works had already laid the basis of the formulation of the Maxwell's equations. Moreover, the 1862 paper already derived 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 ...
from the expression of the velocity of the electromagnetic wave in relation to the vacuum constants. The final form of Maxwell's equations was published in 1865 ''
A Dynamical Theory of the Electromagnetic Field
"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. ''(Paper read at a meeting of the Royal Society on 8 December 1864).'' In the paper, Maxwell derives an electromagnetic wav ...
'',
in which the theory is formulated in strictly mathematical form.
In 1873, Maxwell published ''
A Treatise on Electricity and Magnetism
''A Treatise on Electricity and Magnetism'' is a two-volume treatise on electromagnetism written by James Clerk Maxwell in 1873. Maxwell was revising the ''Treatise'' for a second edition when he died in 1879. The revision was completed by Wil ...
'' as a summary of his work on electromagnetism. In summary, Maxwell's equations successfully unified theories of light and electromagnetism, which is one of the great unifications in physics.
Later,
Oliver Heaviside
Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vec ...
studied Maxwell's ''
A Treatise on Electricity and Magnetism
''A Treatise on Electricity and Magnetism'' is a two-volume treatise on electromagnetism written by James Clerk Maxwell in 1873. Maxwell was revising the ''Treatise'' for a second edition when he died in 1879. The revision was completed by Wil ...
'' and employed
vector calculus
Vector calculus, or vector analysis, is concerned with differentiation and integration of vector fields, primarily in 3-dimensional Euclidean space \mathbb^3. The term "vector calculus" is sometimes used as a synonym for the broader subject ...
to synthesize Maxwell's over 20 equations into the 4 recognizable ones which modern physicists use. Maxwell's equations also inspired
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
in developing the
theory of special 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 laws ...
.
The experimental proof of Maxwell's equations was demonstrated by
Heinrich Hertz
Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's Maxwell's equations, equations of electrom ...
in a series of experiments in the 1890s.
After that, Maxwell's equations were fully accepted by scientists.
Relationships among electricity, magnetism, and the speed of light
The relationships amongst electricity, magnetism, and the speed of light can be summarized by the modern equation:
:
The left-hand side is the speed of light and the right-hand side is a quantity related to the constants that appear in the equations governing electricity and magnetism. Although the right-hand side has units of velocity, it can be inferred from measurements of electric and magnetic forces, which involve no physical velocities. Therefore, establishing this relationship provided convincing evidence that light is an electromagnetic phenomenon.
The discovery of this relationship started in 1855, when
Wilhelm Eduard Weber
Wilhelm Eduard Weber (; ; 24 October 1804 – 23 June 1891) was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph.
Biography of Wilhelm
Early years
Weber was born in Schlossstrasse in ...
and
Rudolf Kohlrausch
Rudolf Hermann Arndt Kohlrausch (November 6, 1809 in Göttingen – March 8, 1858 in Erlangen) was a German physicist.
Biography
He was a native of Göttingen, the son of the Royal Hanovarian director general of schools Friedrich Kohlrausch. He ...
determined that there was a quantity related to electricity and magnetism, "the ratio of the absolute electromagnetic unit of charge to the absolute electrostatic unit of charge" (in modern language, the value
), and determined that it should have units of velocity. They then measured this ratio by an experiment which involved charging and discharging a
Leyden jar
A Leyden jar (or Leiden jar, or archaically, sometimes Kleistian jar) is an electrical component that stores a high-voltage electric charge (from an external source) between electrical conductors on the inside and outside of a glass jar. It typi ...
and measuring the magnetic force from the discharge current, and found a value ,
[
] remarkably close to the speed of light, which had recently been measured at by
Hippolyte Fizeau
Armand Hippolyte Louis Fizeau FRS FRSE MIF (; 23 September 181918 September 1896) was a French physicist, best known for measuring the speed of light in the namesake Fizeau experiment.
Biography
Fizeau was born in Paris to Louis and Beatrice Fiz ...
in 1848 and at by
Léon Foucault
Jean Bernard Léon Foucault (, ; ; 18 September 1819 – 11 February 1868) was a French physicist best known for his demonstration of the Foucault pendulum, a device demonstrating the effect of Earth's rotation. He also made an early measurement ...
in 1850.
[ However, Weber and Kohlrausch did not make the connection to the speed of light.][ Towards the end of 1861 while working on Part III of his paper '']On Physical Lines of Force
"On Physical Lines of Force" is a four-part paper written by James Clerk Maxwell published in 1861. In it, Maxwell derived the equations of electromagnetism in conjunction with a "sea" of "molecular vortices" which he used to model Faraday's li ...
'', Maxwell travelled from Scotland to London and looked up Weber and Kohlrausch's results. He converted them into a format which was compatible with his own writings, and in doing so he established the connection to the speed of light and concluded that light is a form of electromagnetic radiation.
The term ''Maxwell's equations''
The four modern Maxwell's equations can be found individually throughout his 1861 paper, derived theoretically using a molecular vortex model of 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 ...
's "lines of force" and in conjunction with the experimental result of Weber and Kohlrausch. But it wasn't until 1884 that Oliver Heaviside
Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vec ...
, concurrently with similar work by Josiah Willard Gibbs
Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in t ...
and Heinrich Hertz
Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's Maxwell's equations, equations of electrom ...
, grouped the twenty equations together into a set of only four, via vector notation. This group of four equations was known variously as the Hertz–Heaviside equations and the Maxwell–Hertz equations, but are now universally known as ''Maxwell's equations''.[
] Heaviside’s equations, which are taught in textbooks and universities as Maxwell’s equations are not exactly the same as the ones due to Maxwell, and, in fact, the latter are more easily made to conform to quantum physics.
This very subtle and paradoxical sounding situation can perhaps be most easily understood in terms of the similar situation that exists with respect to Newton’s second law of motion: In textbooks and in classrooms the law is attributed to Newton, but Newton in fact wrote his second law as , where is the time derivative of the momentum . This seems a trivial enough fact until you realize that remains true in Special 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 laws o ...
, without modification.
Maxwell's contribution to science in producing these equations lies in the correction he made to Ampère's circuital law in his 1861 paper ''On Physical Lines of Force
"On Physical Lines of Force" is a four-part paper written by James Clerk Maxwell published in 1861. In it, Maxwell derived the equations of electromagnetism in conjunction with a "sea" of "molecular vortices" which he used to model Faraday's li ...
''. He added the displacement current
In electromagnetism, displacement current density is the quantity appearing in Maxwell's equations that is defined in terms of the rate of change of , the electric displacement field. Displacement current density has the same units as electric ...
term to Ampère's circuital law and this enabled him to derive the electromagnetic wave equation
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form ...
in his later 1865 paper ''A Dynamical Theory of the Electromagnetic Field
"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. ''(Paper read at a meeting of the Royal Society on 8 December 1864).'' In the paper, Maxwell derives an electromagnetic wav ...
'' and to demonstrate the fact that light is an electromagnetic wave
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 ...
. This fact was later confirmed experimentally by Heinrich Hertz
Heinrich Rudolf Hertz ( ; ; 22 February 1857 – 1 January 1894) was a German physicist who first conclusively proved the existence of the electromagnetic waves predicted by James Clerk Maxwell's Maxwell's equations, equations of electrom ...
in 1887. The physicist Richard Feynman
Richard Phillips Feynman (; May 11, 1918 – February 15, 1988) was an American theoretical physicist, known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of the superflu ...
predicted that, "From a long view of the history of mankind, seen from, say, ten thousand years from now, there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade."
The concept of fields was introduced by, among others, Faraday. Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
wrote:
Heaviside worked to eliminate the potentials (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 ...
and magnetic potential Magnetic potential may refer to:
* Magnetic vector potential, the vector whose curl is equal to the magnetic B field
* Magnetic scalar potential
Magnetic scalar potential, ''ψ'', is a quantity in classical electromagnetism analogous to electr ...
) that Maxwell had used as the central concepts in his equations; this effort was somewhat controversial, though it was understood by 1884 that the potentials must propagate at the speed of light like the fields, unlike the concept of instantaneous action-at-a-distance like the then conception of gravitational potential.[
]
''On Physical Lines of Force''
The four equations we use today appeared separately in Maxwell's 1861 paper, ''On Physical Lines of Force'':
#Equation (56) in Maxwell's 1861 paper is Gauss's law for magnetism
In physics, Gauss's law for magnetism is one of the four Maxwell's equations that underlie classical electrodynamics. It states that the magnetic field has divergence equal to zero, in other words, that it is a solenoidal vector field. It is ...
, .
#Equation (112) is Ampère's circuital law, with Maxwell's addition of displacement current
In electromagnetism, displacement current density is the quantity appearing in Maxwell's equations that is defined in terms of the rate of change of , the electric displacement field. Displacement current density has the same units as electric ...
. This may be the most remarkable contribution of Maxwell's work, enabling him to derive the electromagnetic wave equation
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form ...
in his 1865 paper A Dynamical Theory of the Electromagnetic Field
"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. ''(Paper read at a meeting of the Royal Society on 8 December 1864).'' In the paper, Maxwell derives an electromagnetic wav ...
, showing that light is an electromagnetic wave. This lent the equations their full significance with respect to understanding the nature of the phenomena he elucidated. (Kirchhoff derived the telegrapher's equations
The telegrapher's equations (or just telegraph equations) are a pair of coupled, linear partial differential equations that describe the voltage and current on an electrical transmission line with distance and time. The equations come from Oliver ...
in 1857 without using displacement current
In electromagnetism, displacement current density is the quantity appearing in Maxwell's equations that is defined in terms of the rate of change of , the electric displacement field. Displacement current density has the same units as electric ...
, but he did use Poisson's equation and the equation of continuity, which are the mathematical ingredients of the displacement current
In electromagnetism, displacement current density is the quantity appearing in Maxwell's equations that is defined in terms of the rate of change of , the electric displacement field. Displacement current density has the same units as electric ...
. Nevertheless, believing his equations to be applicable only inside an electric wire, he cannot be credited with the discovery that light is an electromagnetic wave).
#Equation (115) is 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 sta ...
.
#Equation (54) expresses what Oliver Heaviside
Oliver Heaviside FRS (; 18 May 1850 – 3 February 1925) was an English self-taught mathematician and physicist who invented a new technique for solving differential equations (equivalent to the Laplace transform), independently developed vec ...
referred to as 'Faraday's law', which addresses the time-variant aspect of electromagnetic induction, but not the one induced by motion; Faraday's original flux law accounted for both. Maxwell deals with the motion-related aspect of electromagnetic induction, , in equation (77), which is the same as equation (D) in Maxwell's original equations as listed below. It is expressed today as the force law equation, , which sits adjacent to Maxwell's equations and bears the name Lorentz force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
, even though Maxwell derived it when Lorentz was still a young boy.
The difference between the and the vectors can be traced back to Maxwell's 1855 paper entitled ''On Faraday's Lines of Force'' which was read to the Cambridge Philosophical Society
The Cambridge Philosophical Society (CPS) is a scientific society at the University of Cambridge. It was founded in 1819. The name derives from the medieval use of the word philosophy to denote any research undertaken outside the fields of law ...
. The paper presented a simplified model of Faraday's work, and how the two phenomena were related. He reduced all of the current knowledge into a linked set of differential equation
In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...
s.
It is later clarified in his concept of a sea of molecular vortices that appears in his 1861 paper ''On Physical Lines of Force
"On Physical Lines of Force" is a four-part paper written by James Clerk Maxwell published in 1861. In it, Maxwell derived the equations of electromagnetism in conjunction with a "sea" of "molecular vortices" which he used to model Faraday's li ...
''. Within that context, represented pure vorticity (spin), whereas was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability
In electromagnetism, permeability is the measure of magnetization that a material obtains in response to an applied magnetic field. Permeability is typically represented by the (italicized) Greek letter ''μ''. The term was coined by William ...
to be a measure of the density of the vortex sea. Hence the relationship,
#Magnetic induction current causes a magnetic current density was essentially a rotational analogy to the linear electric current relationship,
#Electric convection current where ρ is electric charge density. was seen as a kind of magnetic current of vortices aligned in their axial planes, with being the circumferential velocity of the vortices. With representing vortex density, it follows that the product of with vorticity leads to the magnetic field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
denoted as .
The electric current equation can be viewed as a convective current of electric charge
Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse-square law
In science, an inverse-square law is any scientific law stating that a specified physical quantity is inversely proportional to the square of the distance from the source of that physical quantity. The fundamental cause for this can be understo ...
force.
The extension of the above considerations confirms that where is to , and where is to , then it necessarily follows from Gauss's law and from the equation of continuity of charge that is to i.e. parallels with , whereas parallels with .
''A Dynamical Theory of the Electromagnetic Field''
In 1865 Maxwell published "A dynamical theory of the electromagnetic field
"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. ''(Paper read at a meeting of the Royal Society on 8 December 1864).'' In the paper, Maxwell derives an electromagnetic wav ...
" in which he showed that light was an electromagnetic phenomenon. Confusion over the term "Maxwell's equations" sometimes arises because it has been used for a set of eight equations that appeared in Part III of Maxwell's 1865 paper "A dynamical theory of the electromagnetic field
"A Dynamical Theory of the Electromagnetic Field" is a paper by James Clerk Maxwell on electromagnetism, published in 1865. ''(Paper read at a meeting of the Royal Society on 8 December 1864).'' In the paper, Maxwell derives an electromagnetic wav ...
", entitled "General equations of the electromagnetic field", and this confusion is compounded by the writing of six of those eight equations as three separate equations (one for each of the Cartesian axes), resulting in twenty equations and twenty unknowns.
The eight original Maxwell's equations can be written in the modern form of Heaviside's vector notation as follows:
:
;Notation
: is the magnetizing field
A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
, which Maxwell called the ''magnetic intensity''.
: is the current density
In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
(with being the total current including displacement current).
: is the displacement field (called the ''electric displacement'' by Maxwell).
: is the free charge
In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is ...
density (called the ''quantity of free electricity'' by Maxwell).
: is the magnetic potential Magnetic potential may refer to:
* Magnetic vector potential, the vector whose curl is equal to the magnetic B field
* Magnetic scalar potential
Magnetic scalar potential, ''ψ'', is a quantity in classical electromagnetism analogous to electr ...
(called the ''angular impulse'' by Maxwell).
: is called the ''electromotive force'' by Maxwell. The term electromotive force
In electromagnetism and electronics, electromotive force (also electromotance, abbreviated emf, denoted \mathcal or ) is an energy transfer to an electric circuit per unit of electric charge, measured in volts. Devices called electrical ''transd ...
is nowadays used for voltage, but it is clear from the context that Maxwell's meaning corresponded more to the modern term electric field
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 fo ...
.
: is the 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 ...
(which Maxwell also called ''electric potential'').
: is the electrical conductivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allow ...
(Maxwell called the inverse of conductivity the ''specific resistance'', what is now called the resistivity
Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
).
Equation [], with the term, is effectively the Lorentz force
In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge moving with a velocity in an elect ...
, similarly to equation (77) of his 1861 paper (see above).
When Maxwell derives the electromagnetic wave equation
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form ...
in his 1865 paper, he uses equation [] to cater for electromagnetic induction
Electromagnetic or magnetic induction is the production of an electromotive force (emf) across an electrical conductor in a changing magnetic field.
Michael Faraday is generally credited with the discovery of induction in 1831, and James Clerk ...
rather than Faraday's law of induction
Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism predicting how a magnetic field will interact with an electric circuit to produce an electromotive force (emf)—a phenomenon known as electromagnetic inducti ...
which is used in modern textbooks. (Faraday's law itself does not appear among his equations.) However, Maxwell drops the term from equation [] when he is deriving the electromagnetic wave equation
The electromagnetic wave equation is a second-order partial differential equation that describes the propagation of electromagnetic waves through a medium or in a vacuum. It is a three-dimensional form of the wave equation. The homogeneous form ...
, as he considers the situation only from the rest frame.
"A treatise on electricity and magnetism"
In ''A Treatise on Electricity and Magnetism
''A Treatise on Electricity and Magnetism'' is a two-volume treatise on electromagnetism written by James Clerk Maxwell in 1873. Maxwell was revising the ''Treatise'' for a second edition when he died in 1879. The revision was completed by Wil ...
'', an 1873 treatise
A treatise is a formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject and its conclusions."Treat ...
on electromagnetism
In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
written by James Clerk Maxwell
James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and scientist responsible for the classical theory of electromagnetic radiation, which was the first theory to describe electricity, magnetism and ligh ...
, eleven general equations of the electromagnetic field are listed and these include the eight that are listed in the 1865 paper.
Relativity
Maxwell's equations were an essential inspiration for Einstein's development of special relativity. Possibly the most important aspect was their denial of instantaneous action at a distance. Rather, according to them, forces are propagated at the velocity of light through the electromagnetic field.[
]
Maxwell's original equations are based on the idea that light travels through a sea of molecular vortices known as the "luminiferous aether
Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), so ...
", and that the speed of light has to be respective to the reference frame of this aether. Measurements designed to measure the speed of the Earth through the aether conflicted with this notion, though.
A more theoretical approach was suggested by Hendrik Lorentz
Hendrik Antoon Lorentz (; 18 July 1853 – 4 February 1928) was a Dutch physicist who shared the 1902 Nobel Prize in Physics with Pieter Zeeman for the discovery and theoretical explanation of the Zeeman effect. He also derived the Lorentz t ...
along with George FitzGerald and Joseph Larmor
Sir Joseph Larmor (11 July 1857 – 19 May 1942) was an Irish and British physicist and mathematician who made breakthroughs in the understanding of electricity, dynamics, thermodynamics, and the electron theory of matter. His most influent ...
. Both Larmor (1897) and Lorentz (1899, 1904) derived the Lorentz transformation
In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...
(so named by Henri Poincaré
Jules Henri Poincaré ( S: stress final syllable ; 29 April 1854 – 17 July 1912) was a French mathematician, theoretical physicist, engineer, and philosopher of science. He is often described as a polymath, and in mathematics as "The ...
) as one under which Maxwell's equations were invariant. Poincaré (1900) analyzed the coordination of moving clocks by exchanging light signals. He also established the mathematical group property of the Lorentz transformation (Poincaré 1905). Sometimes this transformation is called the FitzGerald–Lorentz transformation or even the FitzGerald–Lorentz–Einstein transformation.
Albert Einstein
Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for developing the theory ...
dismissed the notion of the aether as an unnecessary one, and he concluded that Maxwell's equations predicted the existence of a fixed speed of light, ''independent'' of the velocity of the observer. Hence, he used the Maxwell's equations as the starting point for his Special Theory of Relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between Spacetime, space and time. In Albert Einstein's original treatment, the theory is based on two Postulates of ...
. In doing so, he established that the FitzGerald–Lorentz transformation is valid for all matter and space, and not just Maxwell's equations. Maxwell's equations played a key role in Einstein's groundbreaking scientific paper on special 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 laws o ...
(1905). For example, in the opening paragraph of his paper, he began his theory by noting that a description of an electric conductor moving with respect to a magnet must generate a consistent set of fields regardless of whether the force is calculated in the rest frame In special relativity, the rest frame of a particle is the frame of reference (a coordinate system attached to physical markers) in which the particle is at rest.
The rest frame of compound objects (such as a fluid, or a solid made of many vibratin ...
of the magnet or that of the conductor.[
]
The general theory of relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
has also had a close relationship with Maxwell's equations. For example, Theodor Kaluza
Theodor Franz Eduard Kaluza (; 9 November 1885 – 19 January 1954) was a German mathematician and physicist known for the Kaluza–Klein theory, involving field equations in five-dimensional space-time. His idea that fundamental forces can be ...
and Oskar Klein in the 1920s showed that Maxwell's equations could be derived by extending general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
into five physical dimension
In physics and mathematics, the dimension of a Space (mathematics), mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any Point (geometry), point within it. Thus, a Line (geometry), lin ...
s. This strategy of using additional dimensions to unify different forces remains an active area of research in 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 r ...
.
See also
* Classical electromagnetism and special relativity
The theory of special relativity plays an important role in the modern theory of classical electromagnetism. It gives formulas for how electromagnetic objects, in particular the electric and magnetic fields, are altered under a Lorentz transfor ...
* History of electromagnetic theory
* The Maxwellians
''The Maxwellians'' is a book by Bruce J. Hunt, published in 1991 by Cornell University Press; a paperback edition appeared in 1994, and the book was reissued in 2005. It chronicles the development of electromagnetic theory in the years after the ...
Notes
References
*
{{DEFAULTSORT:Maxwell's Equations
Electrodynamics
History of physics
History
History (derived ) is the systematic study and the documentation of the human activity. The time period of event before the History of writing#Inventions of writing, invention of writing systems is considered prehistory. "History" is an umbr ...