# Electric charge

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See also: Electricity and Maxwell's equations

## Introduction

Electric charge is an isolatable form of charge, a broad term that includes more than electric charge. Electric charge underlies the phenomena of electricity and electromagnetism, and manifests itself as integer multiples of the elementary charge often denoted by e and with a value in SI units of 1.602 176 565 x 10-19 C.[1] Moving electric charges constitute an electric current, and electric charges and currents are the sources of the electromagnetic field that determines the forces acting upon charges. In quantum electrodynamics, these forces are mediated by photons, uncharged, energetic particles exchanged by interacting charges and currents.[2]

Electric charge is observed as integer multiples of the elementary charge, with magnitude equal to that of the electron. In the Standard Model of strong, weak, and electromagnetic interactions, a relativistic quantum field theory that describes interactions between quarks and leptons, quarks have fractional charges that are multiples of 1/3 of an electron charge.[3] However, quarks have never been observed as "free" fractional charges.[4]

Electric charge is conserved, that is, the total amount of electric charge does not change, although it can be partitioned differently among electrically charged objects.

Classically, two types of electromagnetic charge are known, electric charge and magnetic. The distinguishing property of electric charge is that electric charges can be isolated, while an isolated magnetic charge, or magnetic monopole, never has been observed.[5][6][7][8] Electric charges interact with magnetic charges only when in relative motion one to the other.

Whatever constitutes electric charge, it exists with two separate qualities, or polarities, assigned the names 'positive' and 'negative', or 'plus' and 'minus'. Charged particles, though spatially separate, exhibit mutual attraction (if of opposite charge type) or repulsion (if of the same type).

Given that the terms 'positive' and 'negative' serve only as labels to distinguish the two polarities observed in the electric charge of matter, 'positivity' and 'negativity' do not themselves imply anything about the fundamental nature of electric charge. Other labels connoting bi-polarity, such as yin/yang, black/white, or bitter/sweet, could serve for labeling.

In the atoms of matter, protons and electrons exhibit positive and negative charge, respectively. Net positively charged matter results where there exists an excess of protons over electrons, and net negatively charged matter results where there exists an excess of electrons over protons.[9][6][7][8]

The atoms that comprise the chemical elements of the periodic table, while consisting in part of the electrically charged particles, protons and electrons, do not themselves manifest an electric charge, because protons in the nuclei and the surrounding electrons are equal in number and quantity of charge, and so are balanced, ensuring that the atoms as a whole manifest no net electric charge—a state referred to as electrical neutrality.

Net overall neutrality does not imply that no electrical forces exist between atoms, however, as their charge is distributed over their dimensions. This charge distribution can be non-uniform, leading to electrical forces due to charge dipoles or charge multipoles. The exact distribution of charge within assemblies of atoms is found using quantum mechanics and the resulting electrical forces lead to molecules and solids, as studied in chemistry and condensed matter physics.

Scientists have not determined how electric charge emerges in nature.

## Discovery and naming of electric charge

The ancient Greeks as far back as the beginning of the 6th century BCE, beginning with Thales of Miletus, had observed some of the simple phenomenology related to electric charge, Thales demonstrating it using the fossilized tree resin, amber, rubbed with cloth:[10] [11]

 That little piece of amber rubbed by Thales, some 2,500 years ago, appeared then to be very insignificant. Had the world but known, it was fraught with vast possibilities; for, in point of fact, Thales had unconsciously rediscovered Aladdin's Wonderful Lamp. As he rubbed, the Genie of electricity appeared, and demanded, "What wouldst thou have? I am ready to obey thee as the slave of the lamp, I and the other slaves of the lamp." But the question remained unanswered. Neither Thales nor the witnesses of his experiment made any request nor asked its genii to aid them. They had ears, but they heard not, and so the genie disappeared, with all that he was both willing and able to do left undone. —E.J. Houston, 1905[10]

In 600 B.C. Thales, erudite philosopher and astronomer in the thriving Ionian port of Miletus, observed the special qualities of the rare yellow orange amber, jewel-like in its hardness and transparency. If rubbed briskly with a cloth, Thales showed, amber seemed to come alive, causing light objects—like feathers, straw, or leaves—to fly toward it, cling, and then gently detach and float away. Amber was similar to a magnet in its qualities, yet it was not a lodestone. As a youth, Thales of Miletus had studied in the sacred Egyptian cities of Memphis and Thebes. Perhaps it was there, under the burning sun, that this earliest of Greek philosophers first learned from the priests about the prized amber, with its seeming possession of a soul.[11]

Thales, it appears, believed amber an animate thing, something with soul.[12]

The Greek word for amber, elektron, ultimately through Latin, electrum, gave rise to the English words, electrical and electric — words used to refer to the amber phenomenon before the publication of William Gilbert's landmark work, De magnete, in 1600, describing the results of the first systematic experimental studies of magnetic and electrical phenomena in Western science.[13][14][15]

 If one of the two materials [brought together] is rough or fibrous, it does not produce a very large contact area, and so rubbing one material upon another can augment the contact area; but this rubbing is not the cause of the electrification…If the atoms in one surface tend to embrace electrons more tightly, this surface will tend to appropriate charged particles from the other surface the instant they touch. This appropriation, in turn, causes the surfaces to become oppositely "charged," so that they acquire imbalances of opposite polarity. One surface will now possess more electrons than protons, while the other will possess more protons than electrons. If the surfaces are subsequently separated, the regions of opposite-charge imbalance will also separate. —Brian Baigre[16]

This introduction of the word elektron was brought directly into English terminology in 1891 in the form electron as a name for the elementary unit of electric charge by George Johnstone Stoney, and evolved to become the name of the charged particle we call the electron today.[17]

The word charge was first used in its electrical sense by Benjamin Franklin, in 1747, as a verb, and subsequently by him as adjective and noun:

Our spheres are fixed on iron axes, which is passed through them. At one and of the axis there is a small handle, with which you turn the sphere like a common grindstone. This we find very commodious, as the machine takes up little room, is portable, and may be enclosed in a tight box, when not in use. 'Tis true, the sphere does not turn so swift as when the great wheel is used, but swiftness we think of little importance, since a few turns will charge the phial, etc., sufficiently. [italics added] [18]

Presumably, Franklin, who, in his many writings, frequently used the word, charge, and its variant forms (charging, charged, etc.), in its non-electrical sense, had in mind the word's sense of 'loading' or 'filling' something:

charge - ORIGIN: Middle English (in the general senses ‘to load’ and ‘a load’): from Old French charger (verb), charge (noun), from late Latin carricare, carcare ‘to load,’ from Latin carrus ‘wheeled vehicle.’...Examples: load or fill (a container, gun, etc.) to the full or proper extent: will you see to it that your glasses are charged? | fill or pervade (something) with a quality or emotion: the air was charged with menace.[19]

### William Gilbert, founder of electrical science

“Although the precise beginnings of electrical science are contestable, no one doubts that William Gilbert (1540–1603), an Englishman, carried out the first sustained and influential research on electrical phenomena.”[20]

## Relation to forces

Note: The SI units are used below. The discussion is classical, that is, not quantum in nature.

The electric force upon a stationary point body with electric charge q1 due to another such body with electric charge q2 is governed by Coulomb's law:

${\displaystyle {\boldsymbol {F}}_{12}=-{\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}q_{2}}{r_{12}^{2}}}\mathbf {{\hat {u}}_{12}} \ ,}$

where r12 is their separation and û12 is a unit vector pointing from charge one to charge two. The minus sign indicates that the force F is repulsive when both charges have the same sign. The quantity ε0 is the electric constant, also called the permittivity of free space, and it is assumed that both charges are in classical vacuum.

As the separation between charges r12 is reduced toward zero, the force in Coulomb's law tends toward infinity, an observation that has led to much discussion in the history of electromagnetism regarding point charges and the structure of the electron. In quantum electrodynamics the resulting infinities are handled by a mathematical manipulation called renormalization.[21]

For stationary distributions of charge, rather than point charges, forces are found using the intermediary of the electric potential φ at any position r in free space due to electric charge density per unit volume ρ(r) located at position r. This potential can be found using Poisson's equation:

${\displaystyle \nabla ^{2}\varphi =-{\frac {\rho (\mathbf {r} )}{\varepsilon _{0}}}\ ,}$

one of the Maxwell equations. Quantity ∇2 is the Laplacian operator of vector calculus. This equation is deceptively simple in appearance and, when material bodies are present, its solution involves careful consideration of the materials and their geometries. Having found the potential by solving this equation, the force at position r is related to the potential through the electric field E at point r defined by:

${\displaystyle {\boldsymbol {E}}(\mathbf {r} )=-\nabla \varphi (\mathbf {r} )\ ,}$

where ∇ is the gradient operator of vector calculus. The field points in the direction of steepest descent from the potential at r to positions of lower potential. Using this electric field, the electric force F upon a point charge q located at r is:

${\displaystyle {\boldsymbol {F}}(\mathbf {r} )=q{\boldsymbol {E}}(\mathbf {r} )\ .}$

The force tends to move a positive charge to positions of lower potential. Here it is assumed that the introduction of q does not cause significant rearrangement of the other charges described by ρ, which would alter the potential. It is said that q is a test charge, a point charge too small to affect the force in itself.

When charges are moving relative to each other, the forces between them are much more complex. Moving electric charges constitute an electric current, generating magnetic fields and magnetic forces. See the article Liénard–Wiechert potentials.

## References

1. Elementary charge, e. NIST. Retrieved on 2012-08-20.
2. The connection between forces and exchanged particles is found for all the forces of nature, and they are called exchange forces: photon exchange for electromagnetic forces, pion exchange for nuclear forces, W bosons and Z boson for the weak force, gluon exchange for chromodynamic forces, the hypothetical graviton for gravity, and so on. For example, see James S. Trefil (2003). The nature of science: an A-Z guide to the laws and principles governing our universe. Houghton Mifflin Harcourt, p. 373. ISBN 0618319387.  and Rusty L. Myers (2006). “Table 11.3: Fundamental forces”, The basics of physics. Greenwood Publishing Group, p. 197. ISBN 0313328579.
3. Martinus Veltman (2003). Facts and mysteries in elementary particle physics. World scientific, p. 41. ISBN 981238149X.
4. Helen R. Quinn, Yossi Nir (2010). “Why don't we see the quarks?”, The Mystery of the Missing Antimatter. Princeton University Press, p. 96. ISBN 1400835712.
5. Douglas C. Giancoli. Physics for scientists and engineers with modern physics, 4rth ed. Pearson Education, p. 708. ISBN 0132273594.
6. Gibilisco S. (2005). “Chapter 2: Charge, current, voltage”, Electricity Demystified. McGraw-Hill. ISBN 0071439250.  An entry level account by Stan Gibilisco, an electronics engineer and mathematician, author of numerous technical books on electronics and mathematics.
7. Glenn Elert (1998-2010). The electric charge: Summary. The Physics Hypertextbook. Retrieved on 2011-07-27.
8. Glenn Elert (1998-2010). The electric charge: Discussion. The Physics Hypertextbook. Retrieved on 2011-07-27.
9. Douglas C. Giancoli. “§21-1 Static electricity; electric charge and its conservation”, Physics for scientists and engineers with modern physics, 4rth ed. Pearson Education, p. 560. ISBN 0132273594.
10. Houston EJ. (1905). Electricity in every-day life. P. F. Collier & Son.  Title link: Google Book Full-Text Volume 1 of 3.
11. Jonnes J. (2004). Empires of Light: Edison, Tesla, Westinghouse, and the Race to Electrify the World. Random House Digital, Inc.. ISBN 0375758844.  Title link: a Google Books extract.
12. Barnes J. (1982). The Presocratic Philosophers. Psychology Press. ISBN 9780415050791.  Title link: Google Book extract.
13. Webster's Third New International Dictionary, Unabridged: electric. Merriam-Webster, Inc.. Retrieved on 2011-07-27.
14. W Gilbert (1958). De magnete magnetisque corporibus, et de magno magnete telluro, Reprint of the Wiley 1893 translation of Gilbert's 1600 work in Latin by Dr. P. Fleury Mottelay. Courier Dover. ISBN 048626761X.
15. Steven Weinberg (2003). “Chapter 2: The discovery of the electron”, The discovery of subatomic particles, 2nd ed. Cambridge University Press, p. 11. ISBN 052182351X. “It was Gilbert who introduced the term electric (electrica in the Latin of his text), after the Greek word electron (ηλεκτρον) for amber.”
16. Baigrie BS. (2007) Electricity and magnetism: a historical perspective. Westport, Conn: Greenwood Press, ISBN 9780313333583. | Google Books preview/extract.
17. Theodore Arabatzis (2006). “§2. The birth of the term "electron"”, Representing electrons: a biographical approach to theoretical entities. University of Chicago Press, Theodore Arabatzis. 70. ISBN 0226024202.
18. Franklin B. (1769). Experiments And Observations On Electricity, Made At Philadelphia in America: To which are added, Letters and Papers On Philosophical Subjects. David Henry.  Title link: Google Books Full-Text<*See pages 311 for Franklin's 1747 letter to Peter Collinson, with Franklin's first use of 'charge'.
19. Angus Stevenson and Christine A. Lindberg, eds:New Oxford American Dictionary. Oxford University Press; Oxford Reference Online. (2010).
20. Schiffer MB, Hollenbeck KL, Bell CL (2006). Draw the Lightning Down: Benjamin Franklin and Electrical Technology in the Age of Enlightenment. University of California Press, p. 13. ISBN 0520248295.
21. For example, see Robert Oerter (2006). “The bizarre reality of QED”, The Theory of Almost Everything: The Standard Model, the Unsung Triumph of Modern Physics. Pi Press/Pearson Education Inc., pp. 118 ff. ISBN 0452287863.  Link is to Penguin edition.