On Physical Lines of Force
Encyclopedia
On Physical Lines of Force is a famous four-part paper written by James Clerk Maxwell
published between 1861 and 1862. In it, Maxwell derived the equations of electromagnetism
in conjunction with a "sea" of "molecular
vortices
" which he used to model Faraday's lines of force. Maxwell made an analogy between the density of this medium and the magnetic permeability, as well as an analogy between the transverse elasticity and the dielectric constant, and using the results of a prior experiment by Wilhelm Eduard Weber
and Rudolf Kohlrausch
performed in 1856, he established a connection between the speed of light and the speed of propagation of waves in this medium.
The paper ushered in a new era of classical electrodynamics and catalyzed further progress in the mathematical field of vector calculus. Because of this, it is considered one of the most historically significant publications in the field of physics and of science in general, comparable with Einstein's Annus Mirabilis papers
and Newton's Principia Mathematica.
and Rudolf Kohlrausch
performed an experiment with a Leyden jar
and established the ratio of electric charge
as measured statically
to the same electric charge as measured electrodynamically. Maxwell used this ratio in Isaac Newton
's equation for the speed of sound
, as applied using the density and transverse elasticity of his sea of molecular vortices. He obtained a value which was very close to the speed of light
, as recently measured directly by Hippolyte Fizeau
. Maxwell then wrote
It was also in this 1861 paper that Maxwell first introduced the displacement current
term which is now included in Ampère's circuital law. But it wasn't until his next paper in 1864, A Dynamical Theory of the Electromagnetic Field
that Maxwell used this displacement current term to derive the electromagnetic wave equation
.
, as laid down in a publication by Oliver Heaviside
in 1884, had all appeared in Maxwell's 1861 paper. Heaviside however presented these equations in modern vector format using the nabla operator
(∇) devised by William Rowan Hamilton
in 1837,
Of Maxwell's work, Albert Einstein
wrote:
Other physicists were equally impressed with Maxwell's work, such as Richard Feynman
who commented:
James Clerk Maxwell
James Clerk Maxwell of Glenlair was a Scottish physicist and mathematician. His most prominent achievement was formulating classical electromagnetic theory. This united all previously unrelated observations, experiments and equations of electricity, magnetism and optics into a consistent theory...
published between 1861 and 1862. In it, Maxwell derived the equations of electromagnetism
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
in conjunction with a "sea" of "molecular
Molecule
A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...
vortices
Vortex
A vortex is a spinning, often turbulent,flow of fluid. Any spiral motion with closed streamlines is vortex flow. The motion of the fluid swirling rapidly around a center is called a vortex...
" which he used to model Faraday's lines of force. Maxwell made an analogy between the density of this medium and the magnetic permeability, as well as an analogy between the transverse elasticity and the dielectric constant, and using the results of a prior experiment by Wilhelm Eduard Weber
Wilhelm Eduard Weber
Wilhelm Eduard Weber was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph.-Early years:...
and Rudolf Kohlrausch
Rudolf Kohlrausch
Rudolf Hermann Arndt Kohlrausch was a German physicist.-Biography:He was a native of Göttingen, the son of educator Heinrich Friedrich Theodor Kohlrausch...
performed in 1856, he established a connection between the speed of light and the speed of propagation of waves in this medium.
The paper ushered in a new era of classical electrodynamics and catalyzed further progress in the mathematical field of vector calculus. Because of this, it is considered one of the most historically significant publications in the field of physics and of science in general, comparable with Einstein's Annus Mirabilis papers
Annus Mirabilis Papers
The Annus Mirabilis papers are the papers of Albert Einstein published in the Annalen der Physik scientific journal in 1905. These four articles contributed substantially to the foundation of modern physics and changed views on space, time, and matter...
and Newton's Principia Mathematica.
Motivations
In 1856, Wilhelm Eduard WeberWilhelm Eduard Weber
Wilhelm Eduard Weber was a German physicist and, together with Carl Friedrich Gauss, inventor of the first electromagnetic telegraph.-Early years:...
and Rudolf Kohlrausch
Rudolf Kohlrausch
Rudolf Hermann Arndt Kohlrausch was a German physicist.-Biography:He was a native of Göttingen, the son of educator Heinrich Friedrich Theodor Kohlrausch...
performed an experiment with a Leyden jar
Leyden jar
A Leyden jar, or Leiden jar, is a device that "stores" static electricity between two electrodes on the inside and outside of a jar. It was invented independently by German cleric Ewald Georg von Kleist on 11 October 1745 and by Dutch scientist Pieter van Musschenbroek of Leiden in 1745–1746. The...
and established the ratio of electric charge
Electric charge
Electric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
as measured statically
Electrostatics
Electrostatics is the branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges....
to the same electric charge as measured electrodynamically. Maxwell used this ratio in Isaac Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...
's equation for the speed of sound
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
, as applied using the density and transverse elasticity of his sea of molecular vortices. He obtained a value which was very close to the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
, as recently measured directly by Hippolyte Fizeau
Hippolyte Fizeau
Armand Hippolyte Louis Fizeau was a French physicist.-Biography:Fizeau was born in Paris. His earliest work was concerned with improvements in photographic processes. Following suggestions by François Arago, Léon Foucault and Fizeau collaborated in a series of investigations on the interference of...
. Maxwell then wrote
"we can scarcely avoid the inference that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena"
It was also in this 1861 paper that Maxwell first introduced the displacement current
Displacement current
In electromagnetism, displacement current is a quantity that is defined in terms of the rate of change of electric displacement field. Displacement current has the units of electric current density, and it has an associated magnetic field just as actual currents do. However it is not an electric...
term which is now included in Ampère's circuital law. But it wasn't until his next paper in 1864, A Dynamical Theory of the Electromagnetic Field
A Dynamical Theory of the Electromagnetic Field
"A Dynamical Theory of the Electromagnetic Field" is the third of James Clerk Maxwell's papers regarding electromagnetism, published in 1865. It is the paper in which the original set of four Maxwell's equations first appeared...
that Maxwell used this displacement current term to derive the electromagnetic wave equation
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...
.
Impact
The four modern Maxwell's equationsMaxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
, as laid down in a publication by Oliver Heaviside
Oliver Heaviside
Oliver Heaviside was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, invented mathematical techniques to the solution of differential equations , reformulated Maxwell's field equations in terms of electric and...
in 1884, had all appeared in Maxwell's 1861 paper. Heaviside however presented these equations in modern vector format using the nabla operator
Nabla symbol
right|thumb|256px|The [[harp]], the instrument after which the nabla symbol is namedNabla is the symbol \nabla . The name comes from the Greek word for a Hebrew harp, which had a similar shape. Related words also exist in Aramaic and Hebrew. The symbol was first used by William Rowan Hamilton in...
(∇) devised by William Rowan Hamilton
William Rowan Hamilton
Sir William Rowan Hamilton was an Irish physicist, astronomer, and mathematician, who made important contributions to classical mechanics, optics, and algebra. His studies of mechanical and optical systems led him to discover new mathematical concepts and techniques...
in 1837,
Of Maxwell's work, Albert Einstein
Albert Einstein
Albert Einstein was a German-born theoretical physicist who developed the theory of general relativity, effecting a revolution in physics. For this achievement, Einstein is often regarded as the father of modern physics and one of the most prolific intellects in human history...
wrote:
"Imagine [Maxwell's] feelings when the differential equations he had formulated proved to him that electromagnetic fields spread in the form of polarised waves, and at the speed of light! To few men in the world has such an experience been vouchsafed... it took physicists some decades to grasp the full significance of Maxwell's discovery, so bold was the leap that his genius forced upon the conceptions of his fellow-workers."
Other physicists were equally impressed with Maxwell's work, such as Richard Feynman
Richard Feynman
Richard Phillips Feynman was an American physicist known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics and the physics of the superfluidity of supercooled liquid helium, as well as in particle physics...
who commented:
"From a long view of the history of the world—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 electromagnetism. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade."
See also
- A Dynamical Theory of the Electromagnetic FieldA Dynamical Theory of the Electromagnetic Field"A Dynamical Theory of the Electromagnetic Field" is the third of James Clerk Maxwell's papers regarding electromagnetism, published in 1865. It is the paper in which the original set of four Maxwell's equations first appeared...
- A Treatise on Electricity and MagnetismA Treatise on Electricity and MagnetismA Treatise on Electricity and Magnetism is a two volume treatise on electromagnetism written by James Clerk Maxwell in 1873.-See also:* On Physical Lines of Force* A Dynamical Theory of the Electromagnetic Field-External links:...
- Maxwell's equationsMaxwell's equationsMaxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...