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Encyclopedia > Electrostatics
Electromagnetism
Electricity · Magnetism
Electrostatics
 · Electric charge · Coulomb’s law · Electric field · Electric flux · Gauss’ law · Electric potential · Electrostatic induction · Electric dipole moment ·
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Paper shavings attracted by a charged CD
Paper shavings attracted by a charged CD

Electrostatics is the branch of science that deals with the phenomena arising from what seems to be stationary electric charges. Since ancient history it is known that some materials attract light particles after rubbing. The greek word for amber, ήλεκτρον (electron), gave name for many areas of natural science. Electrostatic phenomena arise from the forces that electric charges carry out on each other. Such forces are described by Coulomb's law. Electrostatic phenomena include such as simple as the attraction of plastic wrap to your hand after you remove it from a package to apparently spontaneous explosion of grain silos, to damage of electronic components during manufacturing, to the operation of photocopiers. Electrostatics involves the buildup of charge on the surface of objects due to contact with other surfaces. Although charge exchange happens whenever any two surfaces contact and separate, the effects of charge exchange are usually only noticed when at least one of the surfaces has a high resistance to electrical flow. This is because the charges that transfer to or from the highly resistive surface are more or less trapped there for a long enough time for their effects to be observed. These charges then remain on the object until they either bleed off to ground or are quickly neutralized by a discharge: e.g., the familiar phenomenon of a static 'shock' is caused by the neutralization of charge built up in the body from contact with nonconductive surfaces. This box:      Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... Image File history File links Solenoid. ... Electricity (from New Latin Ä“lectricus, amberlike) is a general term for a variety of phenomena resulting from the presence and flow of electric charge. ... For other senses of this word, see magnetism (disambiguation). ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Coulombs torsion balance Coulombs law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows: This is analogous to Newtons third law of motion in mechanics. ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... In physics, Gausss law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. ... This box:      At a point in space, the electric potential is the potential energy per unit of charge that is associated with a static (time-invariant) electric field. ... Electrostatic induction is a method by which an electrically charged object can be used to create an electrical charge in a second object, without contact between the two objects. ... This article is about the electromagnetic phenomenon. ... Magnetostatics is the study of static magnetic fields. ... This box:      Electric current is the flow (movement) of electric charge. ... For the indie-pop band, see The Magnetic Fields. ... Magnetic flux, represented by the Greek letter Φ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. ... A bar magnet. ... 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. ... In physics, free space is a concept of electromagnetic theory, corresponding roughly to the vacuum, the baseline state of the electromagnetic field, or the replacement for the electromagnetic aether. ... Lorentz force. ... Electromotive force (emf) is the amount of energy gained per unit charge that passes through a device in the opposite direction to the electric field existing across that device. ... For magnetic induction, see Magnetic field. ... This box:      Faradays law of induction describes an important basic law of electromagnetism, which is involved in the working of transformers, inductors, and many forms of electrical generators. ... Displacement current is a quantity related to changing electric field. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... This box:      Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. ... This box:      The Liénard-Wiechert potential describes the electromagnetic effect of a moving charge. ... In physics, the Maxwell stress tensor is the stress tensor of an electromagnetic field. ... As the circular plate moves down through a small region of constant magnetic field directed into the page, eddy currents are induced in the plate. ... A simple electric circuit made up of a voltage source and a resistor. ... Conduction is the movement of electrically charged particles through a transmission medium (electrical conductor). ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. ... An electric current i flowing around a circuit produces a magnetic field and hence a magnetic flux Φ through the circuit. ... Electrical impedance, or simply impedance, is a measure of opposition to a sinusoidal alternating electric current. ... A resonator is a device or part that vibrates (or oscillates) with waves. ... This box:      This page is about waveguides for electromagnetic wave propagation at microwave and radio wave frequencies. ... In special relativity, in order to more clearly express the fact that Maxwells equations (in vacuum) take the same form in any inertial coordinate system, the vacuum Maxwells equations are written in terms of four-vectors and tensors in the manifestly covariant form (cgs units): , and where is... This box:      The electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field of a physical system in Maxwells theory of electromagnetism. ... In physics, the electromagnetic stress-energy tensor is the portion of the stress-energy tensor due to the electromagnetic field. ... In special and general relativity, the four-current is the Lorentz covariant four-vector that replaces the electromagnetic current density where c is the speed of light, ρ the charge density, and j the conventional current density. ... The electromagnetic four-potential is a four-vector defined in SI units (and gaussian units in parentheses) as in which φ is the electrical potential, and is the magnetic potential, a vector potential. ... André-Marie Ampère (January 20, 1775 – June 10, 1836), was a French physicist and mathematician who is generally credited as one of the main discoverers of electromagnetism. ... Charles Augustin de Coulomb (born June 14, 1736, Angoulême, France - died August 23, 1806, Paris, France) was a French physicist. ... Michael Faraday, FRS (September 22, 1791 – August 25, 1867) was an English chemist and physicist (or natural philosopher, in the terminology of that time) who contributed to the fields of electromagnetism and electrochemistry. ... Oliver Heaviside (May 18, 1850 – February 3, 1925) was a self-taught English electrical engineer, mathematician, and physicist who adapted complex numbers to the study of electrical circuits, developed techniques for applying Laplace transforms to the solution of differential equations, reformulated Maxwells field equations in terms of electric and... Joseph Henry Joseph Henry (December 17, 1797 – May 13, 1878) was a Scottish-American scientist who served as the first Secretary of the Smithsonian Institution. ... Heinrich Rudolf Hertz (February 22, 1857 - January 1, 1894) was the German physicist and mechanician for whom the hertz, an SI unit, is named. ... Hendrik Lorentz by Jan Veth Hendrik Antoon Lorentz (born July 18, 1853 in Arnhem, Netherlands; died February 4, 1928 in Haarlem, Netherlands) 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. ... James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematician and theoretical physicist. ... Nikola Tesla (Serbian Cyrillic: ) (10 July 1856 – 7 January 1943) was an inventor, physicist, mechanical and electrical engineer. ... Wilhelm Eduard Weber (October 24, 1804 - June 23, 1891) was a noted physicist. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... A phenomenon (plural: phenomena) is an observable event, especially something special (literally something that can be seen from the Greek word phainomenon = observable). ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... Ancient redirects here. ... The triboelectric effect is a type of contact electrification in which certain materials become electrically charged after they come into contact with another different material and are then separated (such as through rubbing). ... For other uses, see Amber (disambiguation). ... For other uses, see Electron (disambiguation). ... This article is about the physical quantity. ... This box:      Coulombs torsion balance Coulombs law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form as follows: The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each... An open surface with X-, Y-, and Z-contours shown. ... Electrical resistance is a measure of the degree to which an electrical component opposes the passage of current. ... Look up Discharge in Wiktionary, the free dictionary. ...


The force F imposed by a charge Q on a probe q is proportional to the charge of the probe. That is, it can be described by the equation F=q·E, what defines the electric field E. The word proportionality may have one of a number of meanings: In mathematics, proportionality is a mathematical relation between two quantities. ... In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ...

Contents

The electrostatic approximation

The validity of the electrostatic approximation rests on the assumption that the electric field is irrotational: In fluid mechanics, an irrotational vector field is a vector field whose curl is zero. ...

vec{nabla}timesvec{E} = 0.

From Faraday's law, this assumption implies the absence or near-absence of time-varying magnetic fields: This box:      Faradays law of induction describes an important basic law of electromagnetism, which is involved in the working of transformers, inductors, and many forms of electrical generators. ...

{partialvec{B}overpartial t} = 0.

In other words, electrostatics does not require the absence of magnetic fields or electric currents. Rather, if magnetic fields or electric currents do exist, they must not change with time, or in the worst-case, they must change with time only very slowly. In some problems, both electrostatics and magnetostatics may be required for accurate predictions, but the coupling between the two can still be ignored. Magnetostatics is the study of static magnetic fields. ...


Electrostatic potential

Because the electric field is irrotational, it is possible to express the electric field as the gradient of a scalar function, called the electrostatic potential (also known as the voltage). An electric field, E, points from regions of high potential, φ, to regions of low potential, expressed mathematically as For other uses, see Gradient (disambiguation). ... Electric potential is the potential energy per unit charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. ... International safety symbol Caution, risk of electric shock (ISO 3864), colloquially known as high voltage symbol. ...

vec{E} = -vec{nabla}phi.

Fundamental concepts

Coulomb's law

Electric Potential is the amount of work done per unit charge, in bringing an unit positive charge from infinity to that point. The fundamental equation of electrostatics is Coulomb's law, which describes the force between two point charges The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each charge and inversely proportional to the square of the distance between the charges.Q1 and Q2: An equation is a mathematical statement, in symbols, that two things are the same (or equivalent). ... This box:      Coulombs torsion balance Coulombs law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated in scalar form as follows: The magnitude of the electrostatic force between two point electric charges is directly proportional to the product of the magnitudes of each... A point charge is an idealized model of a particle which has an electric charge. ...

F = frac{Q_1Q_2}{4pivarepsilon_0 r^2} ,

where ε0 is the electric constant, a defined value: The electric constant () is the permittivity of vacuum, a physical constant, defined by: where: - magnetic constant - speed of light In SI units, the value is exactly expressed by: = 2. ...

 varepsilon_0  stackrel{mathrm{def}}{=} frac {1}{mu_0 {c_0}^2} = 8.854 187 817 times 10^{-12} in A2s4 kg-1m−3 or C2N−1m−2 or F m−1.

For other uses, see Ampere (disambiguation). ... This article is about the unit of time. ... The coulomb (symbol: C) is the SI unit of electric charge. ... For other uses, see Newton (disambiguation). ... Examples of various types of capacitors. ...

The electric field

The electric field (in units of volts per meter) is defined as the force (in newtons) per unit charge (in coulombs). From this definition and Coulomb's law, it follows that the magnitude of the electric field E created by a single point charge Q is In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... Josephson junction array chip developed by NIST as a standard volt. ... For other uses, see Newton (disambiguation). ... The coulomb (symbol: C) is the SI unit of electric charge. ...

E = frac{Q}{4pivarepsilon_0 r^2}.

Gauss's law

Gauss' law states that "the total electric flux through a closed surface is proportional to the total electric charge enclosed within the surface". The constant of proportionality is the permittivity of free space. In physics, Gausss law gives the relation between the electric flux flowing out a closed surface and the charge enclosed in the surface. ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... This article is in need of attention. ...


Mathematically, Gauss's law takes the form of an integral equation:

oint_Svarepsilon_0vec{E} cdotmathrm{d}vec{A} = int_Vrhocdotmathrm{d}V.

Alternatively, in differential form, the equation becomes

vec{nabla}cdotvarepsilon_0vec{E} = rho.

Poisson's equation

The definition of electrostatic potential, combined with the differential form of Gauss's law (above), provides a relationship between the potential φ and the charge density ρ:

{nabla}^2 phi = - {rhoovervarepsilon_0}.

This relationship is a form of Poisson's equation. Where {varepsilon_0} is Vacuum permittivity. In mathematics, Poissons equation is a partial differential equation with broad utility in electrostatics, mechanical engineering and theoretical physics. ...


Laplace's equation

In the absence of unpaired electric charge, the equation becomes

{nabla}^2 phi = 0,

which is Laplace's equation. In mathematics, Laplaces equation is a partial differential equation named after its discoverer, Pierre-Simon Laplace. ...


Triboelectric series

Main article: Triboelectric effect

The triboelectric effect is a type of contact electrification in which certain materials become electrically charged when coming into contact with another, different, material, and are then separated. The polarity and strength of the charges produced differ according to the materials, surface roughness, temperature, strain, and other properties. It is therefore not very predictable, and only broad generalizations can be made. Amber, for example, can acquire an electric charge by friction with a material like wool. This property, first recorded by Thales of Miletus, suggested the word "electricity", from the Greek word for amber, èlectròn. Other examples of materials that can acquire a significant charge when rubbed together include glass rubbed with silk, and hard rubber rubbed with fur. The triboelectric effect is a type of contact electrification in which certain materials become electrically charged after they come into contact with another different material and are then separated (such as through rubbing). ... The triboelectric effect is a type of contact electrification in which certain materials become electrically charged after they come into contact with another different material and are then separated (such as through rubbing). ... For the French electronics and defence contractor, see Thales Group Thales (in Greek: Θαλης) of Miletus (circa 635 BC - 543 BC), also known as Thales the Milesian, was a pre-Socratic Greek philosopher and one of the Seven Sages of Greece. ...


Electrostatic generators

The presence of surface charge imbalance means that the objects will exhibit attractive or repulsive forces. This surface charge imbalance, which yields static electricity, can be generated by touching two differing surfaces together and then separating them due to the phenomena of contact electrification and the triboelectric effect. Rubbing two nonconductive objects generates a great amount of static electricity. This is not just the result of friction; two nonconductive surfaces can become charged by just being placed one on top of the other. Since most surfaces have a rough texture, it takes longer to achieve charging through contact than through rubbing. Rubbing objects together increases amount of adhesive contact between the two surfaces. Usually insulators, e.g., substances that do not conduct electricity, are good at both generating, and holding, a surface charge. Some examples of these substances are rubber, plastic, glass, and pith. Conductive objects only rarely generate charge imbalance except, for example, when a metal surface is impacted by solid or liquid nonconductors. The charge that is transferred during contact electrification is stored on the surface of each object. Static electric generators, devices which produce very high voltage at very low current and used for classroom physics demonstrations, rely on this effect. An electrostatic generator, or electrostatic machine, is a mechanical device that produces static electricity, or electricity at high voltage and low continuous current. ... Surface charge is the electric charge present on an interface, for instance on the surface of a semiconductor material. ... In the late-18th century, scientists developed sensitive instruments for detecting electrification, otherwise known as electrostatic charge imbalance. ... The triboelectric effect is a type of contact electrification in which certain materials become electrically charged after they come into contact with another different material and are then separated (such as through rubbing). ... Insulators are materials which prevent the flow of heat (thermal insulators) or electric charge (electrical insulators). ... This does not cite any references or sources. ... For other uses, see Plastic (disambiguation). ... This article is about the material. ... The centre dark spot (about 1 mm diameter) in this yew wood is the pith Elderberry shoot cut longitudinally to show the broad, solid pith (rough-textured, white) inside the wood (smooth, yellow-tinged). ... In science and engineering, conductors are materials that contain movable charges of electricity. ... An electrostatic generator, or electrostatic machine, is a mechanical device that produces static electricity, or electricity at high voltage and low continuous current. ...


Note that the presence of electric current does not detract from the electrostatic forces nor from the sparking, from the corona discharge, or other phenomena. Both phenomena can exist simultaneously in the same system. This box:      Electric current is the flow (movement) of electric charge. ... In electricity, a corona discharge is an electrical discharge brought on by the ionization of a fluid surrounding a conductor, which occurs when the potential gradient exceeds a certain value, in situations where sparking (also known as arcing) is not favoured. ...

See also: Friction machines, Wimshurst machines, and Van de Graaf generators.

An electrostatic generator is a mechanical device can produce continous current. ... Wimshurst machine with two Leyden jars. ... A Van de Graaff generator For the band with a similar name, see Van der Graaf Generator. ...

Charge neutralization

Natural electrostatic phenomena are most familiar as an occasional annoyance in seasons of low humidity, but can be destructive and harmful in some situations (e.g. electronics manufacturing). When working in direct contact with integrated circuit electronics (especially delicate MOSFETs), or in the presence of flammable gas, care must be taken to avoid accumulating and suddenly discharging a static charge (see electrostatic discharge). The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET) is a device used to amplify or switch electronic signals. ... Electrostatic discharge (ESD) is the sudden and momentary electric current that flows between two objects at different electrical potentials. ...


Charge induction

Charge induction occurs when a negatively charged object repels electrons from the surface of a second object. This creates a region in the second object that is more positively charged. An attractive force is then exerted between the objects. For example, when a balloon is rubbed, the balloon will stick to the wall as an attractive force is exerted by two oppositely charged surfaces (the surface of the wall gains an electric charge due to charge induction, as the free electrons at the surface of the wall are repelled by the negative balloon, creating a positive wall surface, which is subsequently attracted to the surface of the balloon). You can explore the effect with a simulation of the balloon and static electricity.


'Static' electricity

Main article: Static electricity

Before the year 1832, when Michael Faraday published the results of his experiment on the identity of electricities, physicists thought "static electricity" was somehow different from other electrical charges. Michael Faraday proved that the electricity induced from the magnet, voltaic electricity produced by a battery, and static electricity are all the same. Static electricity is a class of phenomena involving the net charge present on an object; typically referring to charged object with voltages of sufficient magnitude to produce visible attraction, repulsion, and sparks. ... Image File history File linksMetadata Download high resolution version (2048x3072, 3589 KB) This is a rotated version of Lightning over Oradea Romania. ... Image File history File linksMetadata Download high resolution version (2048x3072, 3589 KB) This is a rotated version of Lightning over Oradea Romania. ... Not to be confused with lighting. ... Location of Oradea Coordinates: , Country County Status County capital Government  - Mayor Petru Filip (Democratic Party) Area  - County capital 111. ... Michael Faraday, FRS (September 22, 1791 – August 25, 1867) was an English chemist and physicist (or natural philosopher, in the terminology of that time) who contributed to the fields of electromagnetism and electrochemistry. ...


Static electricity is usually caused when certain materials are rubbed against each other, like wool on plastic or the soles of shoes on carpet. The process causes electrons to be pulled from the surface of one material and relocated on the surface of the other material.


A static shock occurs when the surface of the second material, negatively charged with electrons, touches a positively-charged conductor. Or Vice-Versa.


Static electricity is commonly used in xerography, air filters, and some automotive paints. Static electricity is a build up of electric charges on two objects that have become separated from each other. Small electrical components can easily be damaged by static electricity. Component manufactures use a number of antistatic devices to avoid this. Chester F. Carlson Xerography (or Electrophotography) is a photocopying technique developed by Chester Carlson in 1938 and patented on October 6, 1942. ... Air filter in an Opel Astra car, top side=clean side Air filter in an Opel Astra car, bottom side=dust side Automotive air filter clogged with dust and debris. ...


Static electricity and chemical industry

When different materials are brought together and then separated, an accumulation of electric charge can occur which leaves one material positively charged while the other becomes negatively charged. The mild shock that you receive when touching a grounded object after walking on carpet is an example of excess electrical charge accumulating in your body from frictional charging between your shoes and the carpet. The resulting charge build-up within your body can generate a strong electrical discharge. Although experimenting with static electricity may be fun, similar sparks create severe hazards in those industries dealing with flammable substances, where a small electrical spark may ignite explosive mixtures with devastating consequences.


A similar charging mechanism can occur within low conductivity fluids flowing through pipelines - a process called flow electrification. Fluids which have low electrical conductivity (below 50 pico siemens/cm, where pico siemens/cm is a measure of electrical conductivity), are called accumulators. Fluids having conductivities above 50 pico siemens/cm are called non-accumulators. In non-accumulators, charges recombine as fast as they are separated and hence electrostatic charge generation is not significant. In the petrochemical industry, 50 pico siemens/cm is the recommended minimum value of electrical conductivity for adequate removal of charge from a fluid.


An important concept for insulating fluids is the static relaxation time. This is similar to the time constant (tau) within an RC circuit. For insulating materials, it is the ratio of the static dielectric constant divided by the electrical conductivity of the material. For hydrocarbon fluids, this is sometimes approximated by dividing the number 18 by the electrical conductivity of the fluid. Thus a fluid that has an electrical conductivity of 1 pico siemens /cm will have an estimated relaxation time of about 18 seconds. The excess charge within a fluid will be almost completely dissipated after 4 to 5 times the relaxation time, or 90 seconds for the fluid in the above example. resistor-capacitor circuit (RC circuit), or RC filter or RC network, is one of the simplest analogue electronic filters. ... The relative dielectric constant of a material under given conditions is a measure of the extent to which it concentrates electrostatic lines of flux. ...


Charge generation increases at higher fluid velocities and larger pipe diameters, becoming quite significant in pipes 8 inches (200 mm) or larger. Static charge generation in these systems is best controlled by limiting fluid velocity. The British standard BS PD CLC/TR 50404:2003 (formerly BS-5958-Part 2) Code of Practice for Control of Undesirable Static Electricity prescribes velocity limits. Because of its large impact on dielectric constant, the recommended velocity for hydrocarbon fluids containing water should be limited to 1 m/s.


Bonding and earthing are the usual ways by which charge buildup can be prevented. For fluids with electrical conductivity below 10 pico siemens/cm, bonding and earthing are not adequate for charge dissipation, and anti-static additives may be required.


Applicable Standards


1.BS PD CLC/TR 50404:2003 Code of Practice for Control of Undesirable Static Electricity


2.NFPA 77 (2007) Recommended Practice on Static Electricity


3.API RP 2003 (1998) Protection Against Ignitions Arising Out of Static, Lightning, and Stray Currents


See also

General

This box:      Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... In physics, the electrostatic force is the force arising between static (that is, non-moving) electric charges. ... Sodium and chlorine bonding ionically to form sodium chloride. ... Electronegativity is a measure of the ability of an atom or molecule to attract electrons in the context of a chemical bond. ... Electrostatic discharge (ESD) is the sudden and momentary electric current that flows between two objects at different electrical potentials. ... Electrostatic induction is a method by which an electrically charged object can be used to create an electrical charge in a second object, without contact between the two objects. ...

References

  • Faraday, Michael (1839). Experimental Researches in Electricity. London: Royal Inst.  e-book, available at Project Gutenberg.
  • Halliday, David; Robert Resnick; Kenneth S. Krane (1992). Physics. New York: John Wiley & Sons. ISBN 0-471-80457-6. 
  • Griffiths, David J. (1999). Introduction to Electrodynamics. Upper Saddle River, NJ: Prentice Hall. ISBN 0-13-805326-X. 
  • Hermann A. Haus and James R. Melcher (1989). Electromagnetic Fields and Energy. Englewood Cliffs, NJ: Prentice-Hall. ISBN 0-13-249020-X. 

Project Gutenberg, abbreviated as PG, is a volunteer effort to digitize, archive and distribute cultural works. ... David J. Griffiths is a U.S. physicist and educator. ...

External links and further reading

General
Essays
Books
  • William Cecil Dampier, "The theory of experimental electricity". Cambridge [Eng.] University press, 1905 (Cambridge physical series). xi, 334 p. illus., diagrs. 23 cm. LCCN 05040419 //r33
  • William Thomson Kelvin, Reprint of Papers on Electrostatics and Magnetism By William Thomson Kelvin, Macmillan 1872
  • Alexander McAulay Utility of Quaternions in Physics. Electrostatics—General Problem. Macmillan 1893
  • Alexander Russell, A Treatise on the Theory of Alternating Currents. Electrostatics. University Press 1904
The Right Honourable William Thomson, 1st Baron Kelvin, GCVO, OM, PC, PRS (26 June 1824–17 December 1907) was a Scottish-Irish mathematical physicist and engineer, an outstanding leader in the physical sciences of the 19th century. ... In mathematics, the quaternions are a non-commutative extension of the complex numbers. ...

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