Electromagnetism

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Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually exhibits electromagnetic fields such as electric fields, magnetic fields, and light, and is one of the four fundamental interactions (commonly called forces) in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation. [1] At high energy the weak force and electromagnetic force are unified as a single electroweak force.

Physics Study of the fundamental properties of matter and energy

Physics is the natural science that studies matter and its motion and behavior through space and time and that studies the related entities of energy and force. Physics is one of the most fundamental scientific disciplines, and its main goal is to understand how the universe behaves.

Electric charge physical property that quantifies an objects interaction with electric fields

Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. There are two types of electric charges; positive and negative. Like charges repel and unlike attract. An object with an absence of net charge is referred to as neutral. Early knowledge of how charged substances interact is now called classical electrodynamics, and is still accurate for problems that do not require consideration of quantum effects.

Electromagnetic field physical field produced by electrically charged objects

An electromagnetic field is a physical field produced by electrically charged objects. It affects the behavior of charged objects in the vicinity of the field. The electromagnetic field extends indefinitely throughout space and describes the electromagnetic interaction. It is one of the four fundamental forces of nature.

Contents

Lightning is an electrostatic discharge that travels between two charged regions. Lightning.0257.jpg
Lightning is an electrostatic discharge that travels between two charged regions.

Electromagnetic phenomena are defined in terms of the electromagnetic force, sometimes called the Lorentz force, which includes both electricity and magnetism as different manifestations of the same phenomenon. The electromagnetic force plays a major role in determining the internal properties of most objects encountered in daily life. Ordinary matter takes its form as a result of intermolecular forces between individual atoms and molecules in matter, and is a manifestation of the electromagnetic force. Electrons are bound by the electromagnetic force to atomic nuclei, and their orbital shapes and their influence on nearby atoms with their electrons is described by quantum mechanics. The electromagnetic force governs all chemical processes, which arise from interactions between the electrons of neighboring atoms.

Lorentz force mutual force exerted by two punctual charges in relative motion

In physics the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with a velocity v in an electric field E and a magnetic field B experiences a force of

Electricity Physical phenomena associated with the presence and flow of electric charge

Electricity is the set of physical phenomena associated with the presence and motion of matter that has a property of electric charge. In early days, electricity was considered as being not related to magnetism. Later on, many experimental results and the development of Maxwell's equations indicated that both electricity and magnetism are from a single phenomenon: electromagnetism. Various common phenomena are related to electricity, including lightning, static electricity, electric heating, electric discharges and many others.

Magnetism class of physical phenomena

Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. The most familiar effects occur in ferromagnetic materials, which are strongly attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves. Only a few substances are ferromagnetic; the most common ones are iron, nickel and cobalt and their alloys such as steel. The prefix ferro- refers to iron, because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe3O4.

There are numerous mathematical descriptions of the electromagnetic field. In classical electrodynamics, electric fields are described as electric potential and electric current. In Faraday's law, magnetic fields are associated with electromagnetic induction and magnetism, and Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents.

Mathematical descriptions of the electromagnetic field Formulations of electromagnetism

There are various mathematical descriptions of the electromagnetic field that are used in the study of electromagnetism, one of the four fundamental interactions of nature. In this article, several approaches are discussed, although the equations are in terms of electric and magnetic fields, potentials, and charges with currents, generally speaking.

An electric potential is the amount of work needed to move a unit of positive charge from a reference point to a specific point inside the field without producing an acceleration. Typically, the reference point is the Earth or a point at infinity, although any point beyond the influence of the electric field charge can be used.

Electric current flow of electric charge

An electric current is a flow of electric charge. In electric circuits this charge is often carried by electrons moving through a wire. It can also be carried by ions in an electrolyte, or by both ions and electrons such as in an ionized gas (plasma).

The theoretical implications of electromagnetism, particularly the establishment of the speed of light based on properties of the "medium" of propagation (permeability and permittivity), led to the development of special relativity by Albert Einstein in 1905.

Permeability (electromagnetism) measure of the ability of a material to support the formation of a magnetic field within itself

In electromagnetism, permeability is the measure of the ability of a material to support the formation of a magnetic field within itself otherwise known as distributed inductance in Transmission Line Theory. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the (italicized) Greek letter µ. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity.

Permittivity physical quantity, measure of the resistance to the electric field

In electromagnetism, absolute permittivity, often simply called permittivity, usually denoted by the Greek letter ε (epsilon), is the measure of capacitance that is encountered when forming an electric field in a particular medium. More specifically, permittivity describes the amount of charge needed to generate one unit of electric flux in a particular medium. Accordingly, a charge will yield more electric flux in a medium with low permittivity than in a medium with high permittivity. Permittivity is the measure of a material's ability to store an electric field in the polarization of the medium.

Special relativity Theory of interwoven space and time by Albert Einstein

In physics, special relativity is the generally accepted and experimentally well-confirmed physical theory regarding the relationship between space and time. In Albert Einstein's original pedagogical treatment, it is based on two postulates:

  1. The laws of physics are invariant in all inertial systems.
  2. The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

History of the theory

Hans Christian Orsted. Orsted.jpg
Hans Christian Ørsted.

Originally, electricity and magnetism were considered to be two separate forces. This view changed, however, with the publication of James Clerk Maxwell's 1873 A Treatise on Electricity and Magnetism in which the interactions of positive and negative charges were shown to be mediated by one force. There are four main effects resulting from these interactions, all of which have been clearly demonstrated by experiments:

James Clerk Maxwell Scottish physicist

James Clerk Maxwell was a Scottish scientist in the field of mathematical physics. His most notable achievement was to formulate the classical theory of electromagnetic radiation, bringing together for the first time electricity, magnetism, and light as different manifestations of the same phenomenon. Maxwell's equations for electromagnetism have been called the "second great unification in physics" after the first one realised by Isaac Newton.

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 William Davidson Niven for publication in 1881. A third edition was prepared by J. J. Thomson for publication in 1892.

  1. Electric charges attract or repel one another with a force inversely proportional to the square of the distance between them: unlike charges attract, like ones repel.
  2. Magnetic poles (or states of polarization at individual points) attract or repel one another in a manner similar to positive and negative charges and always exist as pairs: every north pole is yoked to a south pole.
  3. An electric current inside a wire creates a corresponding circumferential magnetic field outside the wire. Its direction (clockwise or counter-clockwise) depends on the direction of the current in the wire.
  4. A current is induced in a loop of wire when it is moved toward or away from a magnetic field, or a magnet is moved towards or away from it; the direction of current depends on that of the movement.
Andre-Marie Ampere Andre-marie-ampere2.jpg
André-Marie Ampère

While preparing for an evening lecture on 21 April 1820, Hans Christian Ørsted made a surprising observation. As he was setting up his materials, he noticed a compass needle deflected away from magnetic north when the electric current from the battery he was using was switched on and off. This deflection convinced him that magnetic fields radiate from all sides of a wire carrying an electric current, just as light and heat do, and that it confirmed a direct relationship between electricity and magnetism.

Hans Christian Ørsted Danish physicist and chemist

Hans Christian Ørsted was a Danish physicist and chemist who discovered that electric currents create magnetic fields, which was the first connection found between electricity and magnetism. Oersted's law and the oersted (Oe) are named after him.

At the time of discovery, Ørsted did not suggest any satisfactory explanation of the phenomenon, nor did he try to represent the phenomenon in a mathematical framework. However, three months later he began more intensive investigations. Soon thereafter he published his findings, proving that an electric current produces a magnetic field as it flows through a wire. The CGS unit of magnetic induction (oersted) is named in honor of his contributions to the field of electromagnetism.

James Clerk Maxwell James-clerk-maxwell3.jpg
James Clerk Maxwell

His findings resulted in intensive research throughout the scientific community in electrodynamics. They influenced French physicist André-Marie Ampère's developments of a single mathematical form to represent the magnetic forces between current-carrying conductors. Ørsted's discovery also represented a major step toward a unified concept of energy.

This unification, which was observed by Michael Faraday, extended by James Clerk Maxwell, and partially reformulated by Oliver Heaviside and Heinrich Hertz, is one of the key accomplishments of 19th century mathematical physics. [2] It has had far-reaching consequences, one of which was the understanding of the nature of light. Unlike what was proposed by the electromagnetic theory of that time, light and other electromagnetic waves are at present seen as taking the form of quantized, self-propagating oscillatory electromagnetic field disturbances called photons. Different frequencies of oscillation give rise to the different forms of electromagnetic radiation, from radio waves at the lowest frequencies, to visible light at intermediate frequencies, to gamma rays at the highest frequencies.

Ørsted was not the only person to examine the relationship between electricity and magnetism. In 1802, Gian Domenico Romagnosi, an Italian legal scholar, deflected a magnetic needle using a Voltaic pile. The factual setup of the experiment is not completely clear, so if current flew across the needle or not. An account of the discovery was published in 1802 in an Italian newspaper, but it was largely overlooked by the contemporary scientific community, because Romagnosi seemingly did not belong to this community. [3]

An earlier (1735), and often neglected, connection between electricity and magnetism was reported by a Dr. Cookson. [4] The account stated, "A tradesman at Wakefield in Yorkshire, having put up a great number of knives and forks in a large box ... and having placed the box in the corner of a large room, there happened a sudden storm of thunder, lightning, &c. ... The owner emptying the box on a counter where some nails lay, the persons who took up the knives, that lay on the nails, observed that the knives took up the nails. On this the whole number was tried, and found to do the same, and that, to such a degree as to take up large nails, packing needles, and other iron things of considerable weight ..." E. T. Whittaker suggested in 1910 that this particular event was responsible for lightning to be "credited with the power of magnetizing steel; and it was doubtless this which led Franklin in 1751 to attempt to magnetize a sewing-needle by means of the discharge of Leyden jars." [5]

Fundamental forces

Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation. Circular.Polarization.Circularly.Polarized.Light Right.Handed.Animation.305x190.255Colors.gif
Representation of the electric field vector of a wave of circularly polarized electromagnetic radiation.

The electromagnetic force is one of the four known fundamental forces. The other fundamental forces are:

All other forces (e.g., friction, contact forces) are derived from these four fundamental forces (including momentum which is carried by the movement of particles). [6]

The electromagnetic force is responsible for practically all phenomena one encounters in daily life above the nuclear scale, with the exception of gravity. Roughly speaking, all the forces involved in interactions between atoms can be explained by the electromagnetic force acting between the electrically charged atomic nuclei and electrons of the atoms. Electromagnetic forces also explain how these particles carry momentum by their movement. This includes the forces we experience in "pushing" or "pulling" ordinary material objects, which result from the intermolecular forces that act between the individual molecules in our bodies and those in the objects. The electromagnetic force is also involved in all forms of chemical phenomena.

A necessary part of understanding the intra-atomic and intermolecular forces is the effective force generated by the momentum of the electrons' movement, such that as electrons move between interacting atoms they carry momentum with them. As a collection of electrons becomes more confined, their minimum momentum necessarily increases due to the Pauli exclusion principle. The behaviour of matter at the molecular scale including its density is determined by the balance between the electromagnetic force and the force generated by the exchange of momentum carried by the electrons themselves. [7]

Classical electrodynamics

In 1600, William Gilbert proposed, in his De Magnete , that electricity and magnetism, while both capable of causing attraction and repulsion of objects, were distinct effects. Mariners had noticed that lightning strikes had the ability to disturb a compass needle. The link between lightning and electricity was not confirmed until Benjamin Franklin's proposed experiments in 1752. One of the first to discover and publish a link between man-made electric current and magnetism was Romagnosi, who in 1802 noticed that connecting a wire across a voltaic pile deflected a nearby compass needle. However, the effect did not become widely known until 1820, when Ørsted performed a similar experiment. [8] Ørsted's work influenced Ampère to produce a theory of electromagnetism that set the subject on a mathematical foundation.

A theory of electromagnetism, known as classical electromagnetism, was developed by various physicists during the period between 1820 and 1873 when it culminated in the publication of a treatise by James Clerk Maxwell, which unified the preceding developments into a single theory and discovered the electromagnetic nature of light. [9] In classical electromagnetism, the behavior of the electromagnetic field is described by a set of equations known as Maxwell's equations, and the electromagnetic force is given by the Lorentz force law. [10]

One of the peculiarities of classical electromagnetism is that it is difficult to reconcile with classical mechanics, but it is compatible with special relativity. According to Maxwell's equations, the speed of light in a vacuum is a universal constant that is dependent only on the electrical permittivity and magnetic permeability of free space. This violates Galilean invariance, a long-standing cornerstone of classical mechanics. One way to reconcile the two theories (electromagnetism and classical mechanics) is to assume the existence of a luminiferous aether through which the light propagates. However, subsequent experimental efforts failed to detect the presence of the aether. After important contributions of Hendrik Lorentz and Henri Poincaré, in 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaced classical kinematics with a new theory of kinematics compatible with classical electromagnetism. (For more information, see History of special relativity.)

In addition, relativity theory implies that in moving frames of reference, a magnetic field transforms to a field with a nonzero electric component and conversely, a moving electric field transforms to a nonzero magnetic component, thus firmly showing that the phenomena are two sides of the same coin. Hence the term "electromagnetism". (For more information, see Classical electromagnetism and special relativity and Covariant formulation of classical electromagnetism.)

Extension to nonlinear phenomena

Magnetic reconnection in the solar plasma gives rise to solar flares, a complex magnetohydrodynamical phenomenon. Sun in X-Ray.png
Magnetic reconnection in the solar plasma gives rise to solar flares, a complex magnetohydrodynamical phenomenon.

The Maxwell equations are linear, in that a change in the sources (the charges and currents) results in a proportional change of the fields. Nonlinear dynamics can occur when electromagnetic fields couple to matter that follows nonlinear dynamical laws. This is studied, for example, in the subject of magnetohydrodynamics, which combines Maxwell theory with the Navier–Stokes equations.

Quantities and units

Electromagnetic units are part of a system of electrical units based primarily upon the magnetic properties of electric currents, the fundamental SI unit being the ampere. The units are:

In the electromagnetic cgs system, electric current is a fundamental quantity defined via Ampère's law and takes the permeability as a dimensionless quantity (relative permeability) whose value in a vacuum is unity. As a consequence, the square of the speed of light appears explicitly in some of the equations interrelating quantities in this system.

Symbol [11] Name of quantityUnit nameSymbolBase units
Q electric charge coulomb CAs
I electric current ampere AA (= W/V = C/s)
J electric current density ampere per square metreA/m2A⋅m−2
U, ΔV, Δφ; E potential difference; electromotive force volt VJ/C = kgm2s3A1
R; Z; X electric resistance; impedance; reactance ohm ΩV/A = kgm2s3A2
ρ resistivity ohm metre Ωmkgm3s3A2
P electric power watt WVA = kgm2s3
C capacitance farad FC/V = kg1m2A2s4
ΦE electric flux volt metre Vmkgm3s3A1
E electric field strength volt per metre V/mN/C = kgmA1s3
D electric displacement field coulomb per square metre C/m2Asm2
ε permittivity farad per metre F/mkg1m3A2s4
χe electric susceptibility (dimensionless)11
G; Y; B conductance; admittance; susceptance siemens SΩ1 = kg1m2s3A2
κ, γ, σ conductivity siemens per metre S/mkg1m3s3A2
B magnetic flux density, magnetic induction tesla TWb/m2 = kgs2A1 = NA1m1
Φ, ΦM, ΦB magnetic flux weber WbVs = kgm2s2A1
H magnetic field strength ampere per metre A/mAm1
L, M inductance henry HWb/A = Vs/A = kgm2s2A2
μ permeability henry per metre H/mkgms2A2
χ magnetic susceptibility (dimensionless)11

Formulas for physical laws of electromagnetism (such as Maxwell's equations) need to be adjusted depending on what system of units one uses. This is because there is no one-to-one correspondence between electromagnetic units in SI and those in CGS, as is the case for mechanical units. Furthermore, within CGS, there are several plausible choices of electromagnetic units, leading to different unit "sub-systems", including Gaussian, "ESU", "EMU", and Heaviside–Lorentz. Among these choices, Gaussian units are the most common today, and in fact the phrase "CGS units" is often used to refer specifically to CGS-Gaussian units.

See also

Related Research Articles

The centimetre–gram–second system of units is a variant of the metric system based on the centimetre as the unit of length, the gram as the unit of mass, and the second as the unit of time. All CGS mechanical units are unambiguously derived from these three base units, but there are several different ways of extending the CGS system to cover electromagnetism.

Maxwells equations set of partial differential equations that describe how electric and magnetic fields are generated and altered by each other and by charges and currents

Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at the speed of light. Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to γ-rays. The equations are named after the physicist and mathematician James Clerk Maxwell, who between 1861 and 1862 published an early form of the equations that included the Lorentz force law. He also first used the equations to propose that light is an electromagnetic phenomenon.

Magnetic field spatial distribution of vectors allowing the calculation of the magnetic force on a test particle

A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.

The oersted is the unit of the auxiliary magnetic field H in the centimetre–gram–second system of units (CGS). It is equivalent to 1 dyne per maxwell.

Magnetic flux physical quantity

In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B passing through that surface. The SI unit of magnetic flux is the weber (Wb), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the magnetic flux.

Biot–Savart law Important law of classical magnetism

In physics, specifically electromagnetism, the Biot–Savart law is an equation describing the magnetic field generated by a constant electric current. It relates the magnetic field to the magnitude, direction, length, and proximity of the electric current. The Biot–Savart law is fundamental to magnetostatics, playing a role similar to that of Coulomb's law in electrostatics. When magnetostatics does not apply, the Biot–Savart law should be replaced by Jefimenko's equations. The law is valid in the magnetostatic approximation, and is consistent with both Ampère's circuital law and Gauss's law for magnetism. It is named after Jean-Baptiste Biot and Félix Savart, who discovered this relationship in 1820.

Ampères circuital law relates the integrated magnetic field around a closed loop to the electric current passing through the loop

In classical electromagnetism, Ampère's circuital law relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 paper "On Physical Lines of Force" and it is now one of the Maxwell equations, which form the basis of classical electromagnetism.

In physics, a unified field theory (UFT) is a type of field theory that allows all that is usually thought of as fundamental forces and elementary particles to be written in terms of a pair of physical and virtual fields. According to the modern discoveries in physics, forces are not transmitted directly between interacting objects, but instead are described and interrupted by intermediary entities called fields.

The tesla is a derived unit of the magnetic induction in the International System of Units.

The physical constant ε0, commonly called the vacuum permittivity, permittivity of free space or electric constant or the distributed capacitance of the vacuum, is an ideal, (baseline) physical constant, which is the value of the absolute dielectric permittivity of classical vacuum. It has an exactly defined value that can be approximated as

The physical constant μ0,, commonly called the vacuum permeability, permeability of free space, permeability of vacuum, or magnetic constant, is the magnetic permeability in a classical vacuum. Vacuum permeability is derived from production of a magnetic field by an electric current or by a moving electric charge and in all other formulas for magnetic-field production in a vacuum.

Inhomogeneous electromagnetic wave equation

In electromagnetism and applications, an inhomogeneous electromagnetic wave equation, or nonhomogeneous electromagnetic wave equation, is one of a set of wave equations describing the propagation of electromagnetic waves generated by nonzero source charges and currents. The source terms in the wave equations makes the partial differential equations inhomogeneous, if the source terms are zero the equations reduce to the homogeneous electromagnetic wave equations. The equations follow from Maxwell's equations.

Oersteds law

In electromagnetism, Ørsted's law, also spelled Oersted's law, is the physical law stating that an electric current creates a magnetic field.

History of Maxwells equations

In electromagnetism, one of the fundamental fields of physics, the introduction of Maxwell's equations was one of the most important aggregations of empirical facts in the history of physics. It took place in the nineteenth century, starting from basic experimental observations, and leading to the formulations of numerous mathematical equations, notably by Charles-Augustin de Coulomb, Hans Christian Ørsted, Carl Friedrich Gauss, Jean-Baptiste Biot, Félix Savart, André-Marie Ampère, and Michael Faraday. The apparently disparate laws and phenomena of electricity and magnetism were integrated by James Clerk Maxwell, who published an early form of the equations, which modify Ampère's circuital law by introducing a displacement current term. He showed that these equations imply that light propagates as electromagnetic waves. His laws were reformulated by Oliver Heaviside in the more modern and compact vector calculus formalism he independently developed. Increasingly powerful mathematical descriptions of the electromagnetic field were developed, continuing into the twentieth century, enabling the equations to take on simpler forms by advancing more sophisticated mathematics.

Electromagnetism is the study of interactions between particles and the electromagnetic field. It includes the study of forces between charged particles, electromagnetic fields and potential, the behavior of conductors and insulators in fields, circuits, magnetism, and electromagnetic waves. An understanding of electromagnetism is important for practical applications like electrical engineering and chemistry. In addition, concepts taught in courses on electromagnetism provide a basis for more advanced material in physics, such as quantum field theory and general relativity. This article focuses on a conceptual understanding of the topics rather than the details of the mathematics involved.

References

  1. Ravaioli, Fawwaz T. Ulaby, Eric Michielssen, Umberto (2010). Fundamentals of applied electromagnetics (6th ed.). Boston: Prentice Hall. p. 13. ISBN   978-0-13-213931-1.
  2. Darrigol, Olivier (2000). Electrodynamics from Ampère to Einstein. New York: Oxford University Press. ISBN   0198505949.
  3. Martins, Roberto de Andrade. "Romagnosi and Volta's Pile: Early Difficulties in the Interpretation of Voltaic Electricity" (PDF). In Fabio Bevilacqua and Lucio Fregonese (eds). Nuova Voltiana: Studies on Volta and his Times. vol. 3. Università degli Studi di Pavia. pp. 81–102. Archived from the original (PDF) on 2013-05-30. Retrieved 2010-12-02.CS1 maint: Uses editors parameter (link)
  4. VIII. An account of an extraordinary effect of lightning in communicating magnetism. Communicated by Pierce Dod, M.D. F.R.S. from Dr. Cookson of Wakefield in Yorkshire. Phil. Trans. 1735 39, 74-75, published 1 January 1735
  5. Whittaker, E.T. (1910). A History of the Theories of Aether and Electricity from the Age of Descartes to the Close of the Nineteenth Century. Longmans, Green and Company.
  6. Browne, "Physics for Engineering and Science," p. 160: "Gravity is one of the fundamental forces of nature. The other forces such as friction, tension, and the normal force are derived from the electric force, another of the fundamental forces. Gravity is a rather weak force... The electric force between two protons is much stronger than the gravitational force between them."
  7. Purcell, "Electricity and Magnetism, 3rd Edition," p. 546: Ch 11 Section 6, "Electron Spin and Magnetic Moment."
  8. Stern, Dr. David P.; Peredo, Mauricio (2001-11-25). "Magnetic Fields – History". NASA Goddard Space Flight Center. Retrieved 2009-11-27.
  9. Purcell, p. 436. Chapter 9.3, "Maxwell's description of the electromagnetic field was essentially complete."
  10. Purcell: p. 278: Chapter 6.1, "Definition of the Magnetic Field." Lorentz force and force equation.
  11. International Union of Pure and Applied Chemistry (1993). Quantities, Units and Symbols in Physical Chemistry , 2nd edition, Oxford: Blackwell Science. ISBN   0-632-03583-8. pp. 14–15. Electronic version.

Further reading

Web sources

Textbooks

General references

  • A. Beiser (1987). Concepts of Modern Physics (4th ed.). McGraw-Hill (International). ISBN   978-0-07-100144-1.
  • L.H. Greenberg (1978). Physics with Modern Applications. Holt-Saunders International W.B. Saunders and Co. ISBN   978-0-7216-4247-5.
  • R.G. Lerner; G.L. Trigg (2005). Encyclopaedia of Physics (2nd ed.). VHC Publishers, Hans Warlimont, Springer. pp. 12–13. ISBN   978-0-07-025734-4.
  • J.B. Marion; W.F. Hornyak (1984). Principles of Physics. Holt-Saunders International Saunders College. ISBN   978-4-8337-0195-2.
  • H.J. Pain (1983). The Physics of Vibrations and Waves (3rd ed.). John Wiley & Sons. ISBN   978-0-471-90182-2.
  • C.B. Parker (1994). McGraw Hill Encyclopaedia of Physics (2nd ed.). McGraw Hill. ISBN   978-0-07-051400-3.
  • R. Penrose (2007). The Road to Reality. Vintage books. ISBN   978-0-679-77631-4.
  • P.A. Tipler; G. Mosca (2008). Physics for Scientists and Engineers: With Modern Physics (6th ed.). W.H. Freeman and Co. ISBN   978-1-4292-0265-7.
  • P.M. Whelan; M.J. Hodgeson (1978). Essential Principles of Physics (2nd ed.). John Murray. ISBN   978-0-7195-3382-2.