# Electric charge

Last updated
Electric charge
Electric field of a positive and a negative point charge
Common symbols
q
SI unit coulomb
Other units
In SI base units C = A s
Extensive?yes
Conserved?yes
Dimension TI

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 charge: positive and negative (commonly carried by protons and electrons respectively). Like charges repel each other and unlike charges attract each other. 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.

## Contents

Electric charge is a conserved property; the net charge of an isolated system, the amount of positive charge minus the amount of negative charge, cannot change. Electric charge is carried by subatomic particles. In ordinary matter, negative charge is carried by electrons, and positive charge is carried by the protons in the nuclei of atoms. If there are more electrons than protons in a piece of matter, it will have a negative charge, if there are fewer it will have a positive charge, and if there are equal numbers it will be neutral. Charge is quantized ; it comes in integer multiples of individual small units called the elementary charge, e, about 1.602×10−19 coulombs, [1] which is the smallest charge which can exist freely (particles called quarks have smaller charges, multiples of 1/3e, but they are only found in combination, and always combine to form particles with integer charge). The proton has a charge of +e, and the electron has a charge of −e.

An electric charge has an electric field, and if the charge is moving it also generates a magnetic field. The combination of the electric and magnetic field is called the electromagnetic field, and its interaction with charges is the source of the electromagnetic force, which is one of the four fundamental forces in physics. The study of photon-mediated interactions among charged particles is called quantum electrodynamics.

The SI derived unit of electric charge is the coulomb (C) named after French physicist Charles-Augustin de Coulomb. In electrical engineering, it is also common to use the ampere-hour (Ah); in physics and chemistry, it is common to use the elementary charge (e as a unit). Chemistry also uses the Faraday constant as the charge on a mole of electrons. The lowercase symbol q often denotes charge.

## Overview

Charge is the fundamental property of forms of matter that exhibit electrostatic attraction or repulsion in the presence of other matter. Electric charge is a characteristic property of many subatomic particles. The charges of free-standing particles are integer multiples of the elementary charge e; we say that electric charge is quantized . Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge. Robert Millikan's oil drop experiment demonstrated this fact directly, and measured the elementary charge. It has been discovered that one type of particle, quarks, have fractional charges of either −1/3 or +2/3, but it is believed they always occur in multiples of integral charge; free-standing quarks have never been observed.

By convention, the charge of an electron is negative, −e, while that of a proton is positive, +e. Charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. Coulomb's law quantifies the electrostatic force between two particles by asserting that the force is proportional to the product of their charges, and inversely proportional to the square of the distance between them. The charge of an antiparticle equals that of the corresponding particle, but with opposite sign.

The electric charge of a macroscopic object is the sum of the electric charges of the particles that make it up. This charge is often small, because matter is made of atoms, and atoms typically have equal numbers of protons and electrons, in which case their charges cancel out, yielding a net charge of zero, thus making the atom neutral.

An ion is an atom (or group of atoms) that has lost one or more electrons, giving it a net positive charge (cation), or that has gained one or more electrons, giving it a net negative charge (anion). Monatomic ions are formed from single atoms, while polyatomic ions are formed from two or more atoms that have been bonded together, in each case yielding an ion with a positive or negative net charge.

Electric field induced by a positive electric charge (left) and a field induced by a negative electric charge (right).

During the formation of macroscopic objects, constituent atoms and ions usually combine to form structures composed of neutral ionic compounds electrically bound to neutral atoms. Thus macroscopic objects tend toward being neutral overall, but macroscopic objects are rarely perfectly net neutral.

Sometimes macroscopic objects contain ions distributed throughout the material, rigidly bound in place, giving an overall net positive or negative charge to the object. Also, macroscopic objects made of conductive elements, can more or less easily (depending on the element) take on or give off electrons, and then maintain a net negative or positive charge indefinitely. When the net electric charge of an object is non-zero and motionless, the phenomenon is known as static electricity. This can easily be produced by rubbing two dissimilar materials together, such as rubbing amber with fur or glass with silk. In this way, non-conductive materials can be charged to a significant degree, either positively or negatively. Charge taken from one material is moved to the other material, leaving an opposite charge of the same magnitude behind. The law of conservation of charge always applies, giving the object from which a negative charge is taken a positive charge of the same magnitude, and vice versa.

Even when an object's net charge is zero, the charge can be distributed non-uniformly in the object (e.g., due to an external electromagnetic field, or bound polar molecules). In such cases, the object is said to be polarized. The charge due to polarization is known as bound charge, while the charge on an object produced by electrons gained or lost from outside the object is called free charge. The motion of electrons in conductive metals in a specific direction is known as electric current.

## Units

The SI derived unit of quantity of electric charge is the coulomb (symbol: C). The coulomb is defined as the quantity of charge that passes through the cross section of an electrical conductor carrying one ampere for one second. [2] This unit was proposed in 1946 and ratified in 1948. [2] In modern practice, the phrase "amount of charge" is used instead of "quantity of charge". [3] The amount of charge in 1 electron (elementary charge) is approximately 1.6×10−19 C, and 1 coulomb corresponds to the amount of charge for about 6.24×1018 electrons. The lowercase symbol q is often used to denote a quantity of electricity or charge. The quantity of electric charge can be directly measured with an electrometer, or indirectly measured with a ballistic galvanometer.

After finding the quantized character of charge, in 1891 George Stoney proposed the unit 'electron' for this fundamental unit of electrical charge. This was before the discovery of the particle by J. J. Thomson in 1897. The unit is today treated as nameless, referred to as elementary charge, fundamental unit of charge, or simply as e. A measure of charge should be a multiple of the elementary charge e, even if at large scales charge seems to behave as a real quantity. In some contexts it is meaningful to speak of fractions of a charge; for example in the charging of a capacitor, or in the fractional quantum Hall effect.

The unit faraday is sometimes used in electrochemistry. One faraday of charge is the magnitude of the charge of one mole of electrons, [4] i.e. 96485.33289(59) C.

In systems of units other than SI such as cgs, electric charge is expressed as combination of only three fundamental quantities (length, mass, and time), and not four, as in SI, where electric charge is a combination of length, mass, time, and electric current. [5] [6]

## History

From ancient times, persons were familiar with four types of phenomena that today would all be explained using the concept of electric charge: (a) lightning, (b) the torpedo fish (or electric ray), (c) St Elmo's Fire, and (d) that amber rubbed with fur would attract small, light objects. [7] The first account of the amber effect is often attributed to the ancient Greek mathematician Thales of Miletus, who lived from c. 624 – c. 546 BC, but there are doubts about whether Thales left any writings; [8] his account about amber is known from an account from early 200s. [9] This account can be taken as evidence that the phenomenon was known since at least c. 600 BC, but Thales explained this phenomenon as evidence for inanimate objects having a soul. [9] In other words, there was no indication of any conception of electric charge. More generally, the ancient Greeks did not understand the connections among these four kinds of phenomena. The Greeks observed that the charged amber buttons could attract light objects such as hair. They also found that if they rubbed the amber for long enough, they could even get an electric spark to jump,[ citation needed ] but there is also a claim that no mention of electric sparks appeared until late 17th century. [10] This property derives from the triboelectric effect. In late 1100s, the substance jet, a compacted form of coal, was noted to have an amber effect, [11] and in the middle of the 1500s, Girolamo Fracastoro, discovered that diamond also showed this effect. [12] Some efforts were made by Fracastoro and others, especially Gerolamo Cardano to develop explanations for this phenomenon. [13]

In contrast to astronomy, mechanics, and optics, which had been studied quantitatively since antiquity, the start of ongoing qualitative and quantitative research into electrical phenomena can be marked with the publication of De Magnete by the English scientist William Gilbert in 1600. [14] In this book, there was a small section where Gilbert returned to the amber effect (as he called it) in addressing many of the earlier theories, [13] and coined the New Latin word electrica (from ἤλεκτρον (ēlektron), the Greek word for amber). The Latin word was translated into English as electrics. [15] Gilbert is also credited with the term electrical, while the term electricity came later, first attributed to Sir Thomas Browne in his Pseudodoxia Epidemica from 1646. [16] (For more linguistic details see Etymology of electricity.) Gilbert hypothesized that this amber effect could be explained by an effluvium (a small stream of particles that flows from the electric object, without diminishing its bulk or weight) that acts on other objects. This idea of a material electrical effluvium was influential in the 17th and 18th centuries. It was a precursor to ideas developed in the 18th century about "electric fluid" (Dufay, Nollet, Franklin) and "electric charge." [17]

Around 1663 Otto von Guericke invented what was probably the first electrostatic generator, but he did not recognize it primarily as an electrical device and only conducted minimal electrical experiments with it. [18] Other European pioneers were Robert Boyle, who in 1675 published the first book in English that was devoted solely to electrical phenomena. [19] His work was largely a repetition of Gilbert's studies, but he also identified several more "electrics", [20] and noted mutual attraction between two bodies. [19]

In 1729 Stephen Gray was experimenting with static electricity, which he generated using a glass tube. He noticed that a cork, used to protect the tube from dust and moisture, also became electrified (charged). Further experiments (e.g, extending the cork by putting thin sticks into it) showed—for the first time—that electrical effluvia (as Gray called it) could be transmitted (conducted) over a distance. Gray managed to transmit charge with twine (765 feet) and wire (865 feet). [21] Through these experiments, Gray discovered the importance of different materials, which facilitated or hindered the conduction of electrical effluvia. John Theophilus Desaguliers, who repeated many of Gray’s experiments, is credited with coining the terms conductors and insulators to refer to the effects of different materials in these experiments. [21] Gray also discovered electrical induction (i.e., where charge could be transmitted from one object to another without any direct physical contact). For example, he showed that by bringing a charged glass tube close to, but not touching, a lump of lead that was sustained by a thread, it was possible to make the lead become electrified (e.g., to attract and repel brass filings). [22] He attempted to explain this phenomenon with the idea of electrical effluvia. [23]

Gray’s discoveries introduced an important shift in the historical development of knowledge about electric charge. The fact that electrical effluvia could be transferred from one object to another, opened the theoretical possibility that this property was not inseparably connected to the bodies that were electrified by rubbing. [24] In 1733 Charles François de Cisternay du Fay, inspired by Gray's work, made a series of experiments (reported in Mémoires de l'Académie Royale des Sciences ), showing that more or less all substances could be 'electrified' by rubbing, except for metals and fluids [25] and proposed that electricity comes in two varieties that cancel each other, which he expressed in terms of a two-fluid theory. [26] When glass was rubbed with silk, du Fay said that the glass was charged with vitreous electricity, and, when amber was rubbed with fur, the amber was charged with resinous electricity. Another important two-fluid theory from this time was proposed by Jean-Antoine Nollet (1745). [27] In 1839, Michael Faraday showed that the apparent division between static electricity, current electricity, and bioelectricity was incorrect, and all were a consequence of the behavior of a single kind of electricity appearing in opposite polarities. It is arbitrary which polarity is called positive and which is called negative. Positive charge can be defined as the charge left on a glass rod after being rubbed with silk. [28]

Up until about 1745, the main explanation for electrical attraction and repulsion was the idea that electrified bodies gave off an effluvium. [29] Benjamin Franklin started electrical experiments in late 1746, [30] and by 1750 had developed a one-fluid theory of electricity, based on an experiment that showed that a rubbed glass received the same, but opposite, charge strength as the cloth used to rub the glass. [30] [31] Franklin imagined electricity as being a type of invisible fluid present in all matter; for example, he believed that it was the glass in a Leyden jar that held the accumulated charge. He posited that rubbing insulating surfaces together caused this fluid to change location, and that a flow of this fluid constitutes an electric current. He also posited that when matter contained too little of the fluid it was negatively charged, and when it had an excess it was positively charged. He identified the term positive with vitreous electricity and negative with resinous electricity after performing an experiment with a glass tube he had received from his overseas colleague Peter Collinson. The experiment had participant A charge the glass tube and participant B receive a shock to the knuckle from the charged tube. Franklin identified participant B to be positively charged after having been shocked by the tube. [32] William Watson independently arrived at the same one-fluid explanation at about the same time (1746).[ citation needed ] After Franklin's work, effluvia-based explanations were rarely put forward. [33]

It is now known that the Franklin–Watson model was fundamentally correct. There is only one kind of electrical charge, and only one variable is required to keep track of the amount of charge. [34]

Until 1800 it was only possible to study conduction of electric charge by using an electrostatic discharge. In 1800 Alessandro Volta was the first to show that charge could be maintained in continuous motion through a closed path. [35]

## The role of charge in static electricity

Static electricity refers to the electric charge of an object and the related electrostatic discharge when two objects are brought together that are not at equilibrium. An electrostatic discharge creates a change in the charge of each of the two objects.

### Electrification by friction

When a piece of glass and a piece of resin—neither of which exhibit any electrical properties—are rubbed together and left with the rubbed surfaces in contact, they still exhibit no electrical properties. When separated, they attract each other.

A second piece of glass rubbed with a second piece of resin, then separated and suspended near the former pieces of glass and resin causes these phenomena:

• The two pieces of glass repel each other.
• Each piece of glass attracts each piece of resin.
• The two pieces of resin repel each other.

This attraction and repulsion is an electrical phenomenon, and the bodies that exhibit them are said to be electrified, or electrically charged. Bodies may be electrified in many other ways, as well as by friction. The electrical properties of the two pieces of glass are similar to each other but opposite to those of the two pieces of resin: The glass attracts what the resin repels and repels what the resin attracts.

If a body electrified in any manner whatsoever behaves as the glass does, that is, if it repels the glass and attracts the resin, the body is said to be vitreously electrified, and if it attracts the glass and repels the resin it is said to be resinously electrified. All electrified bodies are either vitreously or resinously electrified.

An established convention in the scientific community defines vitreous electrification as positive, and resinous electrification as negative. The exactly opposite properties of the two kinds of electrification justify our indicating them by opposite signs, but the application of the positive sign to one rather than to the other kind must be considered as a matter of arbitrary convention—just as it is a matter of convention in mathematical diagram to reckon positive distances towards the right hand.

No force, either of attraction or of repulsion, can be observed between an electrified body and a body not electrified. [36]

## The role of charge in electric current

Electric current is the flow of electric charge through an object, which produces no net loss or gain of electric charge. The most common charge carriers are the positively charged proton and the negatively charged electron. The movement of any of these charged particles constitutes an electric current. In many situations, it suffices to speak of the conventional current without regard to whether it is carried by positive charges moving in the direction of the conventional current or by negative charges moving in the opposite direction. This macroscopic viewpoint is an approximation that simplifies electromagnetic concepts and calculations.

At the opposite extreme, if one looks at the microscopic situation, one sees there are many ways of carrying an electric current, including: a flow of electrons; a flow of electron holes that act like positive particles; and both negative and positive particles (ions or other charged particles) flowing in opposite directions in an electrolytic solution or a plasma.

Beware that, in the common and important case of metallic wires, the direction of the conventional current is opposite to the drift velocity of the actual charge carriers; i.e., the electrons. This is a source of confusion for beginners.

## Conservation of electric charge

The total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equation. More generally, the rate of change in charge density ρ within a volume of integration V is equal to the area integral over the current density J through the closed surface S = ∂V, which is in turn equal to the net current I:

${\displaystyle -{\frac {d}{dt}}\int _{V}\rho \,\mathrm {d} V=}$${\displaystyle \scriptstyle \partial V}$${\displaystyle \mathbf {J} \cdot \mathrm {d} \mathbf {S} =\int J\mathrm {d} S\cos \theta =I.}$

Thus, the conservation of electric charge, as expressed by the continuity equation, gives the result:

${\displaystyle I=-{\frac {\mathrm {d} q}{\mathrm {d} t}}.}$

The charge transferred between times ${\displaystyle t_{\mathrm {i} }}$ and ${\displaystyle t_{\mathrm {f} }}$ is obtained by integrating both sides:

${\displaystyle q=\int _{t_{\mathrm {i} }}^{t_{\mathrm {f} }}I\,\mathrm {d} t}$

where I is the net outward current through a closed surface and q is the electric charge contained within the volume defined by the surface.

## Relativistic invariance

Aside from the properties described in articles about electromagnetism, charge is a relativistic invariant. This means that any particle that has charge q, no matter how fast it goes, always has charge q. This property has been experimentally verified by showing that the charge of one helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at high speeds) is the same as two deuterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus). [37] [38] [39]

## Related Research Articles

An electric current is the rate of flow of electric charge past a point or region. An electric current is said to exist when there is a net flow of electric charge through a region. 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 electron is a subatomic particle, symbol
e
or
β
, whose electric charge is negative one elementary charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no known components or substructure. The electron has a mass that is approximately 1/1836 that of the proton. Quantum mechanical properties of the electron include an intrinsic angular momentum (spin) of a half-integer value, expressed in units of the reduced Planck constant, ħ. Being fermions, no two electrons can occupy the same quantum state, in accordance with the Pauli exclusion principle. Like all elementary particles, electrons exhibit properties of both particles and waves: they can collide with other particles and can be diffracted like light. The wave properties of electrons are easier to observe with experiments than those of other particles like neutrons and protons because electrons have a lower mass and hence a longer de Broglie wavelength for a given energy.

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 is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light. It is one of the four fundamental interactions in nature, together with the strong interaction, the weak interaction, and gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force.

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 unrelated 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.

A Leyden jar is an antique electrical component which stores a high-voltage electric charge between electrical conductors on the inside and outside of a glass jar. It typically consists of a glass jar with metal foil cemented to the inside and the outside surfaces, and a metal terminal projecting vertically through the jar lid to make contact with the inner foil. It was the original form of the capacitor.

Timeline of electromagnetism and classical optics lists, within the history of electromagnetism, the associated theories, technology, and events.

The triboelectric effect is a type of contact electrification on which certain materials become electrically charged after they are separated from a different material with which they were in contact. Rubbing the two materials each with the other increases the contact between their surfaces, and hence the triboelectric effect. Rubbing glass with fur for example, or a plastic comb through the hair, can build up triboelectricity. Most everyday static electricity is triboelectric. The polarity and strength of the charges produced differ according to the materials, surface roughness, temperature, strain, and other properties.

Sir Joseph John Thomson was a British physicist and Nobel Laureate in Physics, credited with the discovery of the electron, the first subatomic particle to be discovered.

In physics, screening is the damping of electric fields caused by the presence of mobile charge carriers. It is an important part of the behavior of charge-carrying fluids, such as ionized gases, electrolytes, and charge carriers in electronic conductors . In a fluid, with a given permittivity ε, composed of electrically charged constituent particles, each pair of particles interact through the Coulomb force as

Static electricity is an imbalance of electric charges within or on the surface of a material. The charge remains until it is able to move away by means of an electric current or electrical discharge. Static electricity is named in contrast with current electricity, which flows through wires or other conductors and transmits energy.

Electrostatics is a branch of physics that studies electric charges at rest.

Lichtenberg figures, or "Lichtenberg Figures", are branching electric discharges that sometimes appear on the surface or in the interior of insulating materials. Lichtenberg figures are often associated with the progressive deterioration of high voltage components and equipment. The study of planar Lichtenberg figures along insulating surfaces and 3D electrical trees within insulating materials often provides engineers with valuable insights for improving the long-term reliability of high voltage equipment. Lichtenberg figures are now known to occur on or within solids, liquids, and gases during electrical breakdown.

Electrostatic induction, also known as "electrostatic influence" or simply "influence" in Europe and Latin America, is a redistribution of electric charge in an object, caused by the influence of nearby charges. In the presence of a charged body, an insulated conductor develops a positive charge on one end and a negative charge on the other end. Induction was discovered by British scientist John Canton in 1753 and Swedish professor Johan Carl Wilcke in 1762. Electrostatic generators, such as the Wimshurst machine, the Van de Graaff generator and the electrophorus, use this principle. Due to induction, the electrostatic potential (voltage) is constant at any point throughout a conductor. Electrostatic Induction is also responsible for the attraction of light nonconductive objects, such as balloons, paper or styrofoam scraps, to static electric charges. Electrostatic induction laws apply in dynamic situations as far as the quasistatic approximation is valid. Electrostatic induction should not be confused with Electromagnetic induction.

An electroscope is an early scientific instrument used to detect the presence of electric charge on a body. It detects charge by the movement of a test object due to the Coulomb electrostatic force on it. The amount of charge on an object is proportional to its voltage. The accumulation of enough charge to detect with an electroscope requires hundreds or thousands of volts, so electroscopes are used with high voltage sources such as static electricity and electrostatic machines. An electroscope can only give a rough indication of the quantity of charge; an instrument that measures electric charge quantitatively is called an electrometer.

Atmospheric electricity is the study of electrical charges in the Earth's atmosphere. The movement of charge between the Earth's surface, the atmosphere, and the ionosphere is known as the global atmospheric electrical circuit. Atmospheric electricity is an interdisciplinary topic with a long history, involving concepts from electrostatics, atmospheric physics, meteorology and Earth science.

Fluid theories of electricity are outdated theories that postulated one or more electrical fluids which were thought to be responsible for many electrical phenomena in the history of electromagnetism. The "two-fluid" theory of electricity, created by Charles François de Cisternay du Fay, postulated that electricity was the interaction between two electrical 'fluids.' An alternate simpler theory was proposed by Benjamin Franklin, called the unitary, or one-fluid, theory of electricity. This theory claimed that electricity was really one fluid, which could be present in excess, or absent from a body, thus explaining its electrical charge. Franklin's theory explained how charges could be dispelled and how they could be passed through a chain of people. The fluid theories of electricity eventually became updated to include the effects of magnetism, and electrons.

In physics, charge conservation is the principle that the total electric charge in an isolated system never changes. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always conserved. Charge conservation, considered as a physical conservation law, implies that the change in the amount of electric charge in any volume of space is exactly equal to the amount of charge flowing into the volume minus the amount of charge flowing out of the volume. In essence, charge conservation is an accounting relationship between the amount of charge in a region and the flow of charge into and out of that region, given by a continuity equation between charge density and current density .

The history of electromagnetic theory begins with ancient measures to understand atmospheric electricity, in particular lightning. People then had little understanding of electricity, and were unable to explain the phenomena. Scientific understanding into the nature of electricity grew throughout the eighteenth and nineteenth centuries through the work of researchers such as Coulomb, Ampère, Faraday and Maxwell.

Coulomb's law, or Coulomb's inverse-square 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 conventionally called electrostatic force or Coulomb force. The quantity of electrostatic force between stationary charges is always described by Coulomb's law. The law was first published in 1785 by French physicist Charles-Augustin de Coulomb, and was essential to the development of the theory of electromagnetism, maybe even its starting point, because it was now possible to discuss quantity of electric charge in a meaningful way.

Electromagnetism is the study of forces between charged particles, electromagnetic fields, electric (scalar) potentials, magnetic vector potentials, 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. "2018 CODATA Value: elementary charge". The NIST Reference on Constants, Units, and Uncertainty. NIST. 20 May 2019. Retrieved 2019-05-20.
2. "CIPM, 1946: Resolution 2". BIPM.
3. International Bureau of Weights and Measures (2006), The International System of Units (SI) (PDF) (8th ed.), ISBN   92-822-2213-6, archived (PDF) from the original on 2017-08-14, p. 150
4. Gambhir, RS; Banerjee, D; Durgapal, MC (1993). Foundations of Physics, Vol. 2. New Dehli: Wiley Eastern Limited. p. 51. ISBN   9788122405231 . Retrieved 10 October 2018.
5. Carron, Neal J. (21 May 2015). "Babel of units: The evolution of units systems in classical electromagnetism". p. 5. arXiv: [physics.hist-ph].
6. Purcell, Edward M.; David J. Morin (2013). Electricity and Magnetism (3rd ed.). Cambridge University Press. p. 766. ISBN   9781107014022.
7. Roller, Duane; Roller, D.H.D. (1954). . Cambridge, MA: Harvard University Press. p.  1.
8. O'Grady, Patricia F. (2002). Thales of Miletus: The Beginnings of Western Science and Philosophy. Ashgate. p. 8. ISBN   978-1351895378.
9. Roller, Duane; Roller, D.H.D. (1953). "The Prenatal History of Electrical Science". American Journal of Physics. 21 (5): 348. Bibcode:1953AmJPh..21..343R. doi:10.1119/1.1933449.
10. Roller, Duane; Roller, D.H.D. (1953). "The Prenatal History of Electrical Science". American Journal of Physics. 21 (5): 351. Bibcode:1953AmJPh..21..343R. doi:10.1119/1.1933449.
11. Roller, Duane; Roller, D.H.D. (1953). "The Prenatal History of Electrical Science". American Journal of Physics. 21 (5): 353. Bibcode:1953AmJPh..21..343R. doi:10.1119/1.1933449.
12. Roller, Duane; Roller, D.H.D. (1953). "The Prenatal History of Electrical Science". American Journal of Physics. 21 (5): 356. Bibcode:1953AmJPh..21..343R. doi:10.1119/1.1933449.
13. Roche, J.J. (1998). The mathematics of measurement. London: The Athlone Press. p. 62. ISBN   978-0387915814.
14. Roller, Duane; Roller, D.H.D. (1954). . Cambridge, MA: Harvard University Press. pp.  6–7.
Heilbron, J.L. (1979). Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics. University of California Press. p. 169. ISBN   978-0-520-03478-5.
15. Brother Potamian; Walsh, J.J. (1909). Makers of electricity. New York: Fordham University Press. p.  70.
16. Baigrie, Brian (2007). Electricity and magnetism: A historical perspective. Westport, CT: Greenwood Press. p. 11.
17. Heathcote, N.H. de V. (1950). "Guericke's sulphur globe". Annals of Science. 6 (3): 304. doi:10.1080/00033795000201981.
18. Baigrie, Brian (2007). Electricity and magnetism: A historical perspective. Westport, CT: Greenwood Press. p. 20.
19. Baigrie, Brian (2007). Electricity and magnetism: A historical perspective. Westport, CT: Greenwood Press. p. 21.
20. Baigrie, Brian (2007). Electricity and magnetism: A historical perspective. Westport, CT: Greenwood Press. p. 27.
21. Baigrie, Brian (2007). Electricity and magnetism: A historical perspective. Westport, CT: Greenwood Press. p. 28.
22. Heilbron, J.L. (1979). Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics. University of California Press. p. 248. ISBN   978-0-520-03478-5.
23. Baigrie, Brian (2007). Electricity and magnetism: A historical perspective. Westport, CT: Greenwood Press. p. 35.
24. Roller, Duane; Roller, D.H.D. (1954). . Cambridge, MA: Harvard University Press. p.  40.
25. Two Kinds of Electrical Fluid: Vitreous and Resinous – 1733. Charles François de Cisternay DuFay (1698–1739) Archived 2009-05-26 at the Wayback Machine . sparkmuseum.com
26. Heilbron, J.L. (1979). Electricity in the 17th and 18th Centuries: A Study of Early Modern Physics. University of California Press. pp. 280–289. ISBN   978-0-520-03478-5.
27. Roald K. Wangsness (1986) Electromagnetic Fields (2nd Ed.). Wiley. ISBN   0-471-81186-6.
28. Heilbron, John (2003). "Leyden jar and electrophore". In Heilbron, John (ed.). The Oxford Companion to the History of Modern Science. New York: Oxford University Press. p. 459. ISBN   9780195112290.
29. Baigrie, Brian (2007). Electricity and magnetism: A historical perspective. Westport, CT: Greenwood Press. p. 38.
30. Guarnieri, Massimo (2014). "Electricity in the Age of Enligtenment". IEEE Industrial Electronics Magazine. 8 (3): 61. doi:10.1109/MIE.2014.2335431.
31. Franklin, Benjamin (1747-05-25). "Letter to Peter Collinson, May 25, 1747". Letter to Peter Collinson. Retrieved 2019-09-16.
32. Tricker, R.A.R (1965). . Oxford: Pergamon. p.  2. ISBN   9781483185361.
33. Denker, John (2007). "One Kind of Charge". www.av8n.com/physics. Archived from the original on 2016-02-05.
34. Zangwill, Andrew (2013). Modern Electrodynamics. Cambridge University Press. p. 31. ISBN   978-0-521-89697-9.
35. James Clerk Maxwell (1891) A Treatise on Electricity and Magnetism , pp. 32–33, Dover Publications
36. Jefimenko, O.D. (1999). "Relativistic invariance of electric charge" (PDF). Zeitschrift für Naturforschung A. 54 (10–11): 637–644. Bibcode:1999ZNatA..54..637J. doi:10.1515/zna-1999-10-1113 . Retrieved 11 April 2018.
37. "How can we prove charge invariance under Lorentz Transformation?". physics.stackexchange.com. Retrieved 2018-03-27.
38. Singal, A.K. (1992). "On the charge invariance and relativistic electric fields from a steady conduction current". Physics Letters A. 162 (2): 91–95. Bibcode:1992PhLA..162...91S. doi:10.1016/0375-9601(92)90982-R. ISSN   0375-9601.