Electrostatics is a branch of

_{0} is the _{0} are equivalently ^{2} s^{4} kg^{−1}m^{−3} or ^{2} N^{−1}m^{−2} or F m^{−1}. _{0}, k_{0}, e) are currently defined so that ''e'' is exactly defined, and ε_{0} and k_{0} are measured quantities.

Humans and sparks: The Cause, Stopping the Pain, and 'Electric People

'" ;Books *William Cecil Dampier (1905) ''The Theory of Experimental Electricity'', Cambridge University Press, (Cambridge physical series). xi, 334 p. illus., diagrs. 23 cm. LCCN 05040419 //r33 *William Thomson Kelvin (1872

Reprint of Papers on Electrostatics and Magnetism By William Thomson Kelvin

Macmillan *Alexander McAulay (1893) ''The Utility of Quaternions in Physics''

Electrostatics—General Problem

Macmillan *Alexander Russell (1904) ''A Treatise on the Theory of Alternating Currents'', Cambridge University Press

Second edition, 1914, volume 1

Second edition, 1916, volume 2

via Internet Archive

The Feynman Lectures on Physics Vol. II Ch. 4: Electrostatics

Introduction to Electrostatics: Point charges can be treated as a distribution using the Dirac delta function

] {{Authority control Electrostatics,

physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of eve ...

that studies electric charge
Electric charge is the physical property
A physical property is any property
Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of th ...

s at rest
Rest or REST may refer to:
Human resting positions
* Kneeling
Kneeling is a basic human position where one or both knees touch the ground. Kneeling is defined as “to position the body so that one or both knees rest on the floor,” according to ...

(static electricity
Static electricity is an imbalance of s within or on the surface of a material. The charge remains until it is able to move away by means of an or . Static electricity is named in contrast with , which flows through wires or other conductors and ...

).
Since classical times
Classical antiquity (also the classical era, classical period or classical age) is the period of cultural history
History (from Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece
Greece ( el, Ελλάδα, , ) ...

, it has been known that some materials, such as amber
Amber is fossil
A fossil (from Classical Latin
Classical Latin is the form of Latin language
Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was ...

, attract lightweight particles after rubbing
A rubbing (''Frottage (art), frottage'') is a reproduction of the Surface finish, texture of a surface created by placing a piece of paper or similar material over the subject and then rubbing the paper with something to deposit marks, most comm ...

. The Greek#REDIRECT Greek
Greek may refer to:
Greece
Anything of, from, or related to Greece
Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximately 10.7 million as of ...

word ''ἤλεκτρον'' (''elektron''), (amber) was thus the source of the word 'electricity
Electricity is the set of physical
Physical may refer to:
*Physical examination, a regular overall check-up with a doctor
*Physical (album), ''Physical'' (album), a 1981 album by Olivia Newton-John
**Physical (Olivia Newton-John song), "Physi ...

'. Electrostatic phenomena arise from the force
In physics
Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...

s that electric charges exert on each other. Such forces are described by Coulomb's law
between two point charge
A point particle (ideal particle or point-like particle, often spelled pointlike particle) is an idealization of particle
In the Outline of physical science, physical sciences, a particle (or corpuscule in older te ...

.
Even though electrostatically induced forces seem to be rather weak, some electrostatic forces such as the one between an electron
The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family,
and are general ...

and a proton
A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collecti ...

, that together make up a hydrogen
Hydrogen is the chemical element
Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements
In chemistry, an element is a pure substance consisting only of atoms that all have the same ...

atom
An atom is the smallest unit of ordinary matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atom ...

, is about 36 orders of magnitude
An order of magnitude is an approximation of the logarithm
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geome ...

stronger than the gravitation
Gravity (), or gravitation, is a natural phenomenon
Types of natural phenomena include:
Weather, fog, thunder, tornadoes; biological processes, decomposition, germination
seedlings, three days after germination.
Germination is th ...

al force acting between them.
There are many examples of electrostatic phenomena, from those as simple as the attraction of plastic wrap to one's hand after it is removed from a package, to the apparently spontaneous explosion of grain silos, the damage of electronic components during manufacturing, and photocopier
A photocopier (also known as a copier or copy machine, and formerly a Genericised trade mark, Xerox Machine) is a machine that makes copies of documents and other visual images onto paper or plastic film quickly and cheaply. Most modern photocopi ...

& laser printer
Laser printing is an electrostatic digital printing process. It produces high-quality text and graphics (and moderate-quality photographs) by repeatedly passing a laser beam back and forth over a negatively Electric charge, charged cylinder call ...

operation. Electrostatics involves the buildup of charge on the surface
File:Water droplet lying on a damask.jpg, Water droplet lying on a damask. Surface tension is high enough to prevent floating below the textile.
A surface, as the term is most generally used, is the outermost or uppermost layer of a physical obje ...

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 noticed only when at least one of the surfaces has a high resistance
Resistance may refer to:
Arts, entertainment, and media Comics
* Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm:
** ''Resistance'' (comics), based on the video game of the same title
** ''Th ...

to electrical flow, because the charges that transfer are 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. The familiar phenomenon of a static "shock" is caused by the neutralization of charge built up in the body from contact with insulated surfaces.
Coulomb's law

Coulomb's law states that: 'The magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.' The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive. If $r$ is the distance (inmeters
The metre (British English, Commonwealth spelling) or meter (American English, American spelling; American and British English spelling differences#-re, -er, see spelling differences) (from the French unit , from the Greek noun , "measure", and ...

) between two charges, then the force (in newton
Newton most commonly refers to:
* Isaac Newton (1642–1726/1727), English scientist
* Newton (unit), SI unit of force named after Isaac Newton
Newton may also refer to:
Arts and entertainment
* Newton (film), ''Newton'' (film), a 2017 Indian fil ...

s) between two point charges $q$ and $Q$ (in coulomb
The coulomb (symbol: C) is the International System of Units
International is an adjective (also used as a noun) meaning "between nations".
International may also refer to:
Music Albums
* International (Kevin Michael album), ''International'' ( ...

s) is:
:$F\; =\; \backslash frac\backslash frac=\; k\_0\backslash frac\backslash ,\; ,$
where εvacuum permittivity
Vacuum permittivity, commonly denoted (pronounced as "epsilon nought" or "epsilon zero") is the value of the absolute dielectric permittivity of classical vacuum. Alternatively may be referred to as the permittivity of free space, the electr ...

, or permittivity of free space:
:$\backslash varepsilon\_0\; \backslash approx\; 8.854\backslash \; 187\backslash \; 817\; \backslash times\; 10^\; \backslash ;\backslash ;\; \backslash mathrm.$
The SI units of εCoulomb's constant
The Coulomb constant, the electric force constant, or the electrostatic constant (denoted , or ) is a proportionality constant in electrostatics equations. In SI units it is equal to .Derived from ''k''e = 1/(4''πε''0) – It was named aft ...

is:
:$k\_0\; =\; \backslash frac\backslash approx\; 8.987\backslash \; 551\backslash \; 792\; \backslash times\; 10^9\; \backslash ;\backslash ;\; \backslash mathrm^.$
A single proton
A proton is a subatomic particle, symbol or , with a positive electric charge of +1''e'' elementary charge and a mass slightly less than that of a neutron. Protons and neutrons, each with masses of approximately one atomic mass unit, are collecti ...

has a charge of ''e'', and the electron
The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family,
and are general ...

has a charge of −''e'', where,
:$e\; =\; 1.602\backslash \; 176\backslash \; 634\; \backslash times\; 10^\backslash ;\backslash ;\; \backslash mathrm.$
These physical constant
A physical constant, sometimes fundamental physical constant or universal constant, is a physical quantity that is generally believed to be both universal in nature and have constant (mathematics), constant value in time. It is contrasted with a ...

s (εElectric field

Theelectric field
An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particle
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' ' ...

, $\backslash vec$, in units of newtons
The newton (symbol: N) is the International System of Units
International is an adjective (also used as a noun) meaning "between nations".
International may also refer to:
Music Albums
* International (Kevin Michael album), ''International'' ( ...

per coulomb
The coulomb (symbol: C) is the International System of Units
International is an adjective (also used as a noun) meaning "between nations".
International may also refer to:
Music Albums
* International (Kevin Michael album), ''International'' ( ...

or volt
The volt is the derived unit for electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work (physics), work energy needed to move a ...

s per meter, is a vector field
In vector calculus
Vector calculus, or vector analysis, is concerned with differentiation
Differentiation may refer to:
Business
* Differentiation (economics), the process of making a product different from other similar products
* Product ...

that can be defined everywhere, except at the location of point charges (where it diverges to infinity). It is defined as the electrostatic force $\backslash vec\backslash ,$ in newtons on a hypothetical small test charge In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass
Mass is the quantity
Quantity is a property that can exist as a multitude or magnitude, which illustrate ...

at the point due to Coulomb's Law
Coulomb's law, or Coulomb's inverse-square law, is an experimental physical law, law of physics that quantifies the amount of force between two stationary, electric charge, electrically charged particles. The electric force between charged bodi ...

, divided by the magnitude of the charge $q\backslash ,$ in coulombs
:$\backslash vec\; =$
Electric field lines
Electricity is the set of physical phenomena
A phenomenon (; plural phenomena) is an observable fact or event. The term came into its modern philosophical
Philosophy (from , ) is the study of general and fundamental questions, ...

are useful for visualizing the electric field. Field lines begin on positive charge and terminate on negative charge. They are parallel to the direction of the electric field at each point, and the density of these field lines is a measure of the magnitude of the electric field at any given point.
Consider a collection of $N$ particles of charge $Q\_i$, located at points $\backslash vec\; r\_i$ (called ''source points''), the electric field at $\backslash vec\; r$ (called the ''field point'') is:
:$\backslash vec(\backslash vec\; r)\; =\backslash frac\backslash sum\_^N\; \backslash frac\; ,$
where $\backslash vec\backslash mathcal\; R\_i\; =\; \backslash vec\; r\; -\; \backslash vec\; r\_i\; ,$ is the displacement vector from a ''source point'' $\backslash vec\; r\_i$ to the ''field point'' $\backslash vec\; r$, and $\backslash widehat\backslash mathcal\; R\_i\; =\; \backslash vec\backslash mathcal\; R\_i\; /\; \backslash left\; \backslash ,\; \backslash vec\backslash mathcal\; R\_i\; \backslash right\; \backslash ,$
is a unit vector
In mathematics
Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities and t ...

that indicates the direction of the field. For a single point charge at the origin, the magnitude of this electric field is $E\; =k\_eQ/\backslash mathcal\; R^2,$ and points away from that charge if it is positive. The fact that the force (and hence the field) can be calculated by summing over all the contributions due to individual source particles is an example of the superposition principle
The superposition principle, also known as superposition property, states that, for all linear system
In systems theory
Systems theory is the interdisciplinary study of systems, i.e. cohesive groups of interrelated, interdependent parts that ...

. The electric field produced by a distribution of charges is given by the volume charge density
In electromagnetism
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is c ...

$\backslash rho\; (\backslash vec\; r)$ and can be obtained by converting this sum into a triple integral
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

:
:$\backslash vec(\backslash vec\; r)=\; \backslash frac\; \backslash iiint\; \backslash frac\; \backslash rho\; (\backslash vec\; r\; \backslash ,\text{'})\; \backslash ,\; \backslash mathrm^3\; r\backslash ,\text{'}$
Gauss' law

Gauss' law states that "the totalelectric flux
In electromagnetism
Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is carr ...

through any closed surface in free space of any shape drawn in an electric field is proportional to the total electric charge
Electric charge is the physical property
A physical property is any property
Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on the nature of th ...

enclosed by the surface." Mathematically, Gauss's law takes the form of an integral equation:
:$\backslash oint\_S\backslash vec\; \backslash cdot\backslash mathrm\backslash vec\; =\; \backslash frac\backslash ,Q\_\backslash text\; =\; \backslash int\_V\backslash cdot\; \backslash mathrm^3\; r,$
where $\backslash mathrm^3\; r\; =\backslash mathrmx\; \backslash \; \backslash mathrmy\; \backslash \; \backslash mathrmz$ is a volume element. If the charge is distributed over a surface or along a line, replace $\backslash rho\backslash ,\backslash mathrm^3r$ by $\backslash sigma\; \backslash ,\; \backslash mathrmA$ or $\backslash lambda\; \backslash ,\; \backslash mathrm\backslash ell$. The divergence theorem
In vector calculus
Vector calculus, or vector analysis, is concerned with differentiation
Differentiation may refer to:
Business
* Differentiation (economics), the process of making a product different from other similar products
* Prod ...

allows Gauss's Law to be written in differential form:
:$\backslash vec\backslash cdot\backslash vec\; =\; .$
where $\backslash vec\; \backslash cdot$ is the .
Poisson and Laplace equations

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: :$^2\; \backslash phi\; =\; -\; .$ This relationship is a form ofPoisson's equation
Poisson's equation is an elliptic partial differential equation of broad utility in theoretical physics. For example, the solution to Poisson's equation is the potential field caused by a given electric charge or mass density distribution; with t ...

. In the absence of unpaired electric charge, the equation becomes Laplace's equation
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). ...

:
:$^2\; \backslash phi\; =\; 0,$
Electrostatic approximation

The validity of the electrostatic approximation rests on the assumption that the electric field isirrotational
In vector calculus, a conservative vector field is a vector field that is the gradient of some function (mathematics), function. Conservative vector fields have the property that the line integral is path independent; the choice of any path between ...

:
:$\backslash vec\backslash times\backslash vec\; =\; 0.$
From Faraday's law, this assumption implies the absence or near-absence of time-varying magnetic fields:
:$=\; 0.$
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
Magnetostatics is the study of magnetic fields in systems where the electric currents, currents are steady (not changing with time). It is the magnetic analogue of electrostatics, where the electric charge, charges are stationary. The magnetizati ...

may be required for accurate predictions, but the coupling between the two can still be ignored. Electrostatics and magnetostatics can both be seen as Galilean limits for electromagnetism.
Electrostatic potential

As the electric field isirrotational
In vector calculus, a conservative vector field is a vector field that is the gradient of some function (mathematics), function. Conservative vector fields have the property that the line integral is path independent; the choice of any path between ...

, it is possible to express the electric field as the gradient
In vector calculus
Vector calculus, or vector analysis, is concerned with differentiation
Differentiation may refer to:
Business
* Differentiation (economics), the process of making a product different from other similar products
* Prod ...

of a scalar function, $\backslash phi$, called the electrostatic potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work
Work may refer to:
* Work (human activity), intentional activity people perform to support the ...

(also known as the voltage
Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is the ...

). An electric field, $E$, points from regions of high electric potential to regions of low electric potential, expressed mathematically as
:$\backslash vec\; =\; -\backslash vec\backslash phi.$
The gradient theorem
The gradient theorem, also known as the fundamental theorem of calculus for line integrals, says that a line integral through a Conservative vector field, gradient field can be evaluated by evaluating the original scalar field at the endpoints of ...

can be used to establish that the electrostatic potential is the amount of work
Work may refer to:
* Work (human activity)
Work or labor is intentional activity people perform to support themselves, others, or the needs and wants of a wider community. Alternatively, work can be viewed as the human activity that cont ...

per unit charge required to move a charge from point $a$ to point $b$ with the following line integral
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...

:
:$-\backslash int\_a^b\; =\; \backslash phi\; (\backslash vec\; b)\; -\backslash phi(\backslash vec\; a).$
From these equations, we see that the electric potential is constant in any region for which the electric field vanishes (such as occurs inside a conducting object).
Electrostatic energy

A singletest particle In Theoretical physics, physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass, charge (physics), charge, or volume, size) are assumed to be negligible except for the property b ...

's potential energy, $U\_\backslash mathrm^$, can be calculated from a line integral
In mathematics
Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). It ...

of the work, $q\_n\backslash vec\; E\backslash cdot\backslash mathrm\; d\backslash vec\backslash ell$. We integrate from a point at infinity, and assume a collection of $N$ particles of charge $Q\_n$, are already situated at the points $\backslash vec\; r\_i$. This potential energy (in Joule
The joule ( ; symbol: J) is a derived unit of energy
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates ...

s) is:
:$U\_\backslash mathrm^=q\backslash phi(\backslash vec\; r)=\backslash frac\backslash sum\_^N\; \backslash frac$
where $\backslash vec\backslash mathcal\; =\; \backslash vec\; r\; -\; \backslash vec\; r\_i$ is the distance of each charge $Q\_i$ from the test charge In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass
Mass is the quantity
Quantity is a property that can exist as a multitude or magnitude, which illustrate ...

$q$, which situated at the point $\backslash vec\; r$, and $\backslash phi(\backslash vec\; r)$ is the electric potential that would be at $\backslash vec\; r$ if the test charge In physical theories, a test particle, or test charge, is an idealized model of an object whose physical properties (usually mass
Mass is the quantity
Quantity is a property that can exist as a multitude or magnitude, which illustrate ...

were not present. If only two charges are present, the potential energy is $k\_eQ\_1Q\_2/r$. The total electric potential energy
Electric potential energy, is a potential energy
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
Common types of ...

due a collection of ''N'' charges is calculating by assembling these particles :
:$U\_\backslash mathrm^\; =\; \backslash frac\backslash sum\_^N\; Q\_j\; \backslash sum\_^\; \backslash frac=\; \backslash frac\backslash sum\_^N\; Q\_i\backslash phi\_i\; ,$
where the following sum from, ''j'' = 1 to ''N'', excludes ''i'' = ''j'':
:$\backslash phi\_i\; =\; \backslash frac\; \backslash sum\_^N\; \backslash frac.$
This electric potential, $\backslash phi\_i$ is what would be measured at $\backslash vec\; r\_i$ if the charge $Q\_i$ were missing. This formula obviously excludes the (infinite) energy that would be required to assemble each point charge from a disperse cloud of charge. The sum over charges can be converted into an integral over charge density using the prescription $\backslash sum\; (\backslash cdots)\; \backslash rightarrow\; \backslash int(\backslash cdots)\backslash rho\; \backslash ,\; \backslash mathrm\; d^3r$:
:$U\_\backslash mathrm^\; =\; \backslash frac\; \backslash int\backslash rho(\backslash vec)\backslash phi(\backslash vec)\; \backslash ,\; \backslash mathrm^3\; r\; =\; \backslash frac\; \backslash int\; \backslash left,\; \backslash ^2\; \backslash ,\; \backslash mathrm^3\; r,$
This second expression for electrostatic energy
Electric potential energy, is a potential energy
In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors.
Common types of ...

uses the fact that the electric field is the negative gradient
In vector calculus
Vector calculus, or vector analysis, is concerned with differentiation
Differentiation may refer to:
Business
* Differentiation (economics), the process of making a product different from other similar products
* Prod ...

of the electric potential, as well as vector calculus identities
The following are important identities involving derivatives and integrals in vector calculus
Vector calculus, or vector analysis, is concerned with differentiation
Differentiation may refer to:
Business
* Differentiation (economics), th ...

in a way that resembles integration by parts
In calculus
Calculus, originally called infinitesimal calculus or "the calculus of infinitesimal
In mathematics, infinitesimals or infinitesimal numbers are quantities that are closer to zero than any standard real number, but are not zero. ...

. These two integrals for electric field energy seem to indicate two mutually exclusive formulas for electrostatic energy density, namely $\backslash frac\backslash rho\backslash phi$ and $\backslash fracE^2$; they yield equal values for the total electrostatic energy only if both are integrated over all space.
Electrostatic pressure

On aconductor
Conductor or conduction may refer to:
Music
* Conductor (music), a person who leads a musical ensemble like, for example, an orchestra.
* Conductor (album), ''Conductor'' (album), an album by indie rock band The Comas
* Conduction, a type of ...

, a surface charge will experience a force in the presence of an electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particle
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' ' ...

. This force is the average of the discontinuous electric field at the surface charge. This average in terms of the field just outside the surface amounts to:
:$P\; =\; \backslash frac\; E^2,$
This pressure tends to draw the conductor into the field, regardless of the sign of the surface charge.
Triboelectric series

Thetriboelectric effect
The triboelectric effect (also known as triboelectric charging) is a type of contact electrification on which certain materials become electric charge, electrically charged after they are separated from a different material with which they were in ...

is a type of contact electrification in which certain materials become electrically charged when they are brought into contact with a different material and then separated. One of the materials acquires a positive charge, and the other acquires an equal negative charge. The polarity and strength of the charges produced differ according to the materials, surface roughness, temperature, strain, and other properties. Amber, for example, can acquire an electric charge by friction with a material like wool. This property, first recorded by Thales of Miletus
Thales of Miletus ( ; el, Θαλῆς
Thales of Miletus ( ; el, Θαλῆς (ὁ Μιλήσιος), ''Thalēs''; ) was a Greek mathematician
A mathematician is someone who uses an extensive knowledge of mathematics
Mathematics (fr ...

, was the first electrical phenomenon investigated by humans. Other examples of materials that can acquire a significant charge when rubbed together include glass rubbed with silk, and hard rubber rubbed with fur.
Electrostatic generators

The presence ofsurface charge
Surface charge is a two-dimensional surface with non-zero electric charge. These electric charges are constrained on this 2-D surface, and surface charge density, measured in coulombs per square meter (C•m−2), is used to describe the charge dis ...

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
Contact electrification was an erroneous scientific theory from the Enlightenment that attempted to account for all the sources of electric charge
Electric charge is the physical property of matter that causes it to experience a force when plac ...

and the triboelectric effect
The triboelectric effect (also known as triboelectric charging) is a type of contact electrification on which certain materials become electric charge, electrically charged after they are separated from a different material with which they were in ...

. 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 the amount of adhesive contact between the two surfaces. Usually insulators
Insulator may refer to:
* Insulator (electricity)
An electrical insulator is a material in which the electron does not flow freely or the atom of the insulator have tightly bound electrons whose internal electric charge
Electric charge is th ...

, i.e., substances that do not conduct electricity, are good at both generating, and holding, a surface charge. Some examples of these substances are rubber
Rubber, also called India rubber, latex, Amazonian rubber, ''caucho'', or ''caoutchouc'', as initially produced, consists of polymer
A polymer (; Greek ''poly-
Poly, from the Greek :wikt:πολύς, πολύς meaning "many" or "much" ...

, plastic
Plastics are a wide range of syntheticA synthetic is an artificial material produced by organic chemistry, organic chemical synthesis.
Synthetic may also refer to:
In the sense of both "combination" and "artificial"
* Synthetic chemical or s ...

, glass
Glass is a non- crystalline, often transparency and translucency, transparent amorphous solid, that has widespread practical, technological, and decorative use in, for example, window panes, tableware, and optics. Glass is most often formed by ...

, and pith
Pith, or medulla, is a tissue
Tissue may refer to:
Biology
* Tissue (biology), an ensemble of similar cells that together carry out a specific function
* ''Triphosa haesitata'', a species of geometer moth found in North America
* ''Triphosa d ...

. Conductive
In physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...

objects rarely generate charge imbalance, except 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. Electrostatic generator
An electrostatic generator, or electrostatic machine, is an electromechanical generator that produces ''static electricity
Static electricity is an imbalance of electric charge
Electric charge is the physical property of matter that causes ...

s, devices which produce very high voltage at very low current and used for classroom physics demonstrations, rely on this effect.
The presence of electric current
An electric current is a stream of charged particle
In physics
Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, ...

does not detract from the electrostatic forces nor from the sparking, from the corona discharge
A corona discharge is an electrical discharge
An electric discharge is the release and transmission of electricity in an applied electric field
An electric field (sometimes E-field) is the physical field that surrounds each electric cha ...

, or other phenomena. Both phenomena can exist simultaneously in the same system.
:See also: '''', and ''Van de Graaff generator
A Van de Graaff generator is an electrostatic generator which uses a moving belt to accumulate electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Th ...

''.
Charge neutralization

The most familiar natural electrostatic phenomena, often regarded as an occasional annoyance in seasons of low humidity, isStatic electricity
Static electricity is an imbalance of electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonl ...

. Static electricity
Static electricity is an imbalance of electric charge
Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonl ...

is generally harmless, but it can be destructive and harmful in some situations (e.g. electronics manufacturing). When working in direct contact with integrated circuit electronics (especially delicate MOSFET
The metal–oxide–semiconductor field-effect transistor (MOSFET, MOS-FET, or MOS FET), also known as the metal–oxide–silicon transistor (MOS transistor, or MOS), is a type of insulated-gate field-effect transistor that is fabricated by th ...

s). In the presence of flammable gas, care must be taken to avoid accumulating and suddenly discharging a static charge (see Electrostatic discharge
Electrostatic discharge (ESD) is the sudden flow of electricity
Electricity is the set of physical
Physical may refer to:
*Physical examination, a regular overall check-up with a doctor
*Physical (album), ''Physical'' (album), a 1981 album b ...

).
Electrostatic induction

Electrostatic induction, discovered by British scientistJohn Canton
John Canton FRS (31 July 1718 – 22 March 1772) was a British physicist
A physicist is a scientist
A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of inte ...

in 1753 and Swedish professor Johan Carl Wilcke
Johan Carl Wilcke was a Swedish physicist
A physicist is a scientist
A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of interest.
In classical antiquity, ther ...

in 1762 is a redistribution of charges in an object caused by the electric field of a nearby charge. For example, if a positively charged object is brought near an uncharged metal object, the mobile negatively-charged electron
The electron is a subatomic particle (denoted by the symbol or ) whose electric charge is negative one elementary charge. Electrons belong to the first generation (particle physics), generation of the lepton particle family,
and are general ...

s in the metal will be attracted by the external charge, and move to the side of the metal facing it, creating a negative charge on the surface. When the electrons move out of an area they leave a positive charge due to the metal atoms' nuclei
''Nucleus'' (plural nuclei) is a Latin word for the seed inside a fruit. It most often refers to:
*Atomic nucleus, the very dense central region of an atom
*Cell nucleus, a central organelle of a eukaryotic cell, containing most of the cell's DNA ...

, so the side of the metal object facing away from the charge acquires a positive charge. These ''induced charges'' disappear when the external charge is removed. Induction is also responsible for the attraction of light objects, such as balloons, paper scraps and foam packing peanuts to static charges. The surface charges induced in conductive objects exactly cancel external electric fields inside the conductor, so there is no electric field inside a metal object. This is the basis for the electric field shielding action of a Faraday cage
A Faraday cage or Faraday shield is an enclosure used to block electromagnetic field
An electromagnetic field (also EM field) is a classical (i.e. non-quantum) field produced by accelerating electric charge
Electric charge is the physical ...

. Since the electric field is the gradient
In vector calculus
Vector calculus, or vector analysis, is concerned with differentiation
Differentiation may refer to:
Business
* Differentiation (economics), the process of making a product different from other similar products
* Prod ...

of the voltage, electrostatic induction is also responsible for making the electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is defined as the amount of work
Work may refer to:
* Work (human activity), intentional activity people perform to support the ...

(voltage
Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential
The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is the ...

) constant throughout a conductive object.
Static electricity

Before the year 1832, whenMichael Faraday
Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist
A scientist is a person who conducts scientific research
The scientific method is an Empirical evidence, empirical method of acquiring knowledge ...

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 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
Xerography is a dry photocopying
A photocopier (also known as a copier or copy machine, and formerly a Xerox Machine) is a machine that makes copies of documents and other visual images onto paper
Paper is a thin sheet material produce ...

, air filter
A particulate air filter is a device composed of fibrous
Fiber or fibre (from la, fibra, links=no) is a natural
Nature, in the broadest sense, is the natural, physical, material world or universe
The universe ( la, univers ...

s, and some coating processes used in manufacturing.
Static electricity is a build-up of electric charges on two objects that have become separated from each other. Small electrical components can be damaged by static electricity, and component manufacturers use a number of antistatic device
An antistatic device is any device that reduces, dampens, or otherwise inhibits electrostatic discharge, or ESD, which is the buildup or discharge of static electricity. ESD can damage electrical components such as computer hard drives, and even ign ...

s to avoid this.
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 upon 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 picosiemens per meter), are called accumulators. Fluids having conductivities above 50 pS/m are called non-accumulators. In non-accumulators, charges recombine as fast as they are separated and hence electrostatic charge generation is not significant. In thepetrochemical industry The petrochemical industry is concerned with the production and trade of petrochemicals
Petrochemicals (sometimes abbreviated as petchems) are the chemical products obtained from petroleum
Petroleum (), also known as crude oil and oil, is a ...

, 50 pS/m 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
A resistor–capacitor circuit (RC circuit), or RC filter or RC network, is an electric circuit
An electrical network is an interconnection of electrical component
An electronic component is any basic discrete device or physical entity ...

. For insulating materials, it is the ratio of the static dielectric constant
The dielectric constant (or relative permittivity) is the permittivity, electric permeability of a material expressed as a ratio with the vacuum permittivity, electric permeability of a vacuum. A dielectric is an insulating material, and the diele ...

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 pS/cm (100 pS/m) 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.
Charge generation increases at higher fluid velocities and larger pipe diameters, becoming quite significant in pipes 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 pS/m, bonding and earthing are not adequate for charge dissipation, and anti-static additives may be required.
Applicable standards

*BS PD CLC/TR 50404:2003 Code of Practice for Control of Undesirable Static Electricity *NFPA 77 (2007) Recommended Practice on Static Electricity *API RP 2003 (1998) Protection Against Ignitions Arising Out of Static, Lightning, and Stray CurrentsElectrostatic induction in commercial applications

Electrostatic induction was used in the past to build high-voltage generators known as influence machines. The main component that emerged in these times is thecapacitor
A capacitor is a device that stores electric charge in an electric field
An electric field (sometimes E-field) is the physical field that surrounds electrically-charged particle
In physics
Physics (from grc, φυσική (ἐπ ...

.
Electrostatic induction is also used for electro-mechanic precipitation or projection. In such technologies, charged particles of small sizes are collected or deposited intentionally on surfaces. Applications range from electrostatic precipitator
An electrostatic precipitator (ESP) is a filterless device that removes fine particles, like dust and smoke, from a flowing gas using the force of an induced electrostatic charge minimally impeding the flow of gases through the unit.
In contra ...

to electrostatic coating and inkjet printing
Inkjet printing is a type of computer printing that recreates a digital image by propelling droplets of ink onto paper and plastic substrates. Inkjet printers were the most commonly used type of printer in 2008, and range from small inexpensi ...

.
Electrostatic actuators have recently been attracting interest in the soft robotics
Soft robotics is a subfield of robotics
Robotics is an interdisciplinary
Interdisciplinarity or interdisciplinary studies involves the combination of two or more academic disciplines into one activity (e.g., a research project). It dra ...

research area. Electrostatic actuators can be employed as clutches for wearable devices which can exhibit mechanical impedance tuning and improved energy efficiency. Other relevant applications include but not limited to multimode hydraulically amplified electrostatic actuators for wearable haptics and robots driven by electrostatic actuator.
See also

*Electromagnetism
Electromagnetism is a branch of physics
Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in ...

*Electronegativity
Electronegativity, symbolized as '' χ'', is the tendency for an atom
An atom is the smallest unit of ordinary matter
In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume ...

*Electrostatic discharge
Electrostatic discharge (ESD) is the sudden flow of electricity
Electricity is the set of physical
Physical may refer to:
*Physical examination, a regular overall check-up with a doctor
*Physical (album), ''Physical'' (album), a 1981 album b ...

* Electrostatic separator
*Electrostatic voltmeter
*Ionic bond
*Permittivity and relative permittivity
*Elementary charge, Quantisation of charge
Footnotes

References

* * * *Further reading

;Essays *William J. Beaty (1997) "Humans and sparks: The Cause, Stopping the Pain, and 'Electric People

'" ;Books *William Cecil Dampier (1905) ''The Theory of Experimental Electricity'', Cambridge University Press, (Cambridge physical series). xi, 334 p. illus., diagrs. 23 cm. LCCN 05040419 //r33 *William Thomson Kelvin (1872

Reprint of Papers on Electrostatics and Magnetism By William Thomson Kelvin

Macmillan *Alexander McAulay (1893) ''The Utility of Quaternions in Physics''

Electrostatics—General Problem

Macmillan *Alexander Russell (1904) ''A Treatise on the Theory of Alternating Currents'', Cambridge University Press

Second edition, 1914, volume 1

Second edition, 1916, volume 2

via Internet Archive

External links

*The Feynman Lectures on Physics Vol. II Ch. 4: Electrostatics

Introduction to Electrostatics: Point charges can be treated as a distribution using the Dirac delta function

] {{Authority control Electrostatics,