The coulomb (symbol: C) is the International System of Units (SI) unit of electric charge. It is the charge (symbol: Q or q) transported by a constant current of one ampere in one second:
Thus, it is also the amount of excess charge on a capacitor of one farad charged to a potential difference of one volt:
The coulomb is equivalent to the charge of approximately 6.242×10^{18} (1.036×10^{−5} mol) protons, and −1 C is equivalent to the charge of approximately 6.242×10^{18} electrons.
A new definition, in terms of the elementary charge, will take effect on 20 May 2019.^{[2]} The new definition defines the elementary charge (the charge of the proton) as exactly 1.602176634×10^{−19} coulombs.
Coulomb  

Unit system  SI derived unit 
Unit of  Electric charge 
Symbol  C 
Named after  CharlesAugustin de Coulomb 
Conversions  
1 C in ...  ... is equal to ... 
SI base units  A⋅s 
CGS units  2997924580 statC 
Atomic units  6.24150934(14)e×10^{18}^{[1]} 
This SI unit is named after CharlesAugustin de Coulomb. As with every International System of Units (SI) unit named for a person, the first letter of its symbol is upper case (C). However, when an SI unit is spelled out in English, it is treated as a common noun and should always begin with a lower case letter (coulomb)—except in a situation where any word in that position would be capitalized, such as at the beginning of a sentence or in material using title case.^{[3]}
The SI system defines the coulomb in terms of the ampere and second: 1 C = 1 A × 1 s.^{[4]} The second is defined in terms of a frequency naturally emitted by caesium atoms.^{[5]} The ampere is defined using Ampère's force law;^{[6]} the definition relies in part on the mass of the international prototype kilogram, a metal cylinder housed in France.^{[7]} In practice, the Kibble balance is used to measure amperes with the highest possible accuracy.^{[7]}
Since the charge of one electron is known to be about 1.6021766208(98)×10^{−19} C,^{[8]} 1 C can also be considered the charge of roughly 6.241509×10^{18} electrons or +1 C the charge of that many positrons or protons, where the number is the reciprocal of 1.602177×10^{−19}.
By 1873, the British Association for the Advancement of Science had defined the volt, ohm, and farad, but not the coulomb.^{[9]} In 1881, the International Electrical Congress, now the International Electrotechnical Commission (IEC), approved the volt as the unit for electromotive force, the ampere as the unit for electric current, and the coulomb as the unit of electric charge.^{[10]} At that time, the volt was defined as the potential difference [i.e., what is nowadays called the "voltage (difference)"] across a conductor when a current of one ampere dissipates one watt of power. The coulomb (later "absolute coulomb" or "abcoulomb" for disambiguation) was part of the EMU system of units. The "international coulomb" based on laboratory specifications for its measurement was introduced by the IEC in 1908. The entire set of "reproducible units" was abandoned in 1948 and the "international coulomb" became the modern Coulomb.^{[11]}
The proposed redefinition of the ampere and other SI base units would fix the numerical value of the elementary charge to exactly 1.602176634×10^{−19} when expressed in coulombs, and therefore it would fix the value of the coulomb when expressed as a multiple of the fundamental charge (the numerical values of those quantities are the multiplicative inverses of each other).
Submultiples  Multiples  

Value  SI symbol  Name  Value  SI symbol  Name  
10^{−1} C  dC  decicoulomb  10^{1} C  daC  decacoulomb  
10^{−2} C  cC  centicoulomb  10^{2} C  hC  hectocoulomb  
10^{−3} C  mC  millicoulomb  10^{3} C  kC  kilocoulomb  
10^{−6} C  µC  microcoulomb  10^{6} C  MC  megacoulomb  
10^{−9} C  nC  nanocoulomb  10^{9} C  GC  gigacoulomb  
10^{−12} C  pC  picocoulomb  10^{12} C  TC  teracoulomb  
10^{−15} C  fC  femtocoulomb  10^{15} C  PC  petacoulomb  
10^{−18} C  aC  attocoulomb  10^{18} C  EC  exacoulomb  
10^{−21} C  zC  zeptocoulomb  10^{21} C  ZC  zettacoulomb  
10^{−24} C  yC  yoctocoulomb  10^{24} C  YC  yottacoulomb  
Common multiples are in bold face. 
See also Metric prefix.
The elementary charge, the charge of a proton (equivalently, the negative of the charge of an electron), is 1.6021766208(98)×10^{−19} C.^{[8]} With the 2019 redefinition of SI base units, as of 20 May 2019 the elementary charge in coulombs has an exact value: 1.602176634×10^{−19} C.^{[13]}
2014 CODATA recommended values
2014 CODATA recommended values
The ampere (; symbol: A), often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after AndréMarie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.
The International System of Units defines the ampere in terms of other base units by measuring the electromagnetic force between electrical conductors carrying electric current. The earlier CGS measurement system had two different definitions of current, one essentially the same as the SI's and the other using electric charge as the base unit, with the unit of charge defined by measuring the force between two charged metal plates. The ampere was then defined as one coulomb of charge per second. In SI, the unit of charge, the coulomb, is defined as the charge carried by one ampere during one second.
New definitions, in terms of invariant constants of nature, specifically the elementary charge, will take effect on 20 May 2019.
CharlesAugustin de CoulombCharlesAugustin de Coulomb (; French: [kulɔ̃]; 14 June 1736 – 23 August 1806) was a French military engineer and physicist. He is best known as the eponymous discoverer of what is now called Coulomb's law, the description of the electrostatic force of attraction and repulsion, though he also did important work on friction.
The SI unit of electric charge, the coulomb, was named in his honor in 1908.
Coulomb's law
Coulomb's law, or Coulomb's inversesquare 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 CharlesAugustin 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.
In its scalar form, the law is:
where k_{e} is Coulomb's constant (k_{e} ≈ ×10^{9} N⋅m^{2}⋅C^{−2}), q_{1} and q_{2} are the signed magnitudes of the charges, and the scalar r is the distance between the charges. The force of the interaction between the charges is attractive if the charges have opposite signs (i.e., F is negative) and repulsive if likesigned (i.e., F is positive). 9
Being an inversesquare law, the law is analogous to Isaac Newton's inversesquare law of universal gravitation, but gravitational forces are always attractive, while electrostatic forces can be attractive or repulsive. Coulomb's law can be used to derive Gauss's law, and vice versa. The two laws are equivalent, expressing the same physical law in different ways. The law has been tested extensively, and observations have upheld the law on a scale from 10^{−16} m to 10^{8} m.
Coulomb (crater)Coulomb is a lunar impact crater that lies behind the northwestern limb, on the far side of the Moon. It is located to the westsouthwest of the large crater Poczobutt, and northeast of Sarton.
The rim of this crater is mildly eroded, but still retains a welldefined edge and displays some old terracing on the wide inner walls. The exterior of the crater also retains something of an outer rampart, extending for about a third of crater diameter. The satellite crater Coulomb V lies just beyond the westnorthwest limb, while on the opposite side Coulomb J lies a short distance from the outer rim, forming a nearly symmetric pattern. The inner walls of the crater have only a few small impacts along the sides, with one near each of the aforementioned satellite craters.
Within the sloping inner walls, the crater floor is remarkably level and nearly featureless, at least in comparison to the more rugged terrain that surrounds the crater. Only a few tiny craterlets mark this interior plain, and a small crater near the southsoutheast inner wall.
Coulomb lies within the CoulombSarton Basin, a 530 km wide impact crater of PreNectarian age.
Coulomb barrierThe Coulomb barrier, named after Coulomb's law, which is in turn named after physicist CharlesAugustin de Coulomb, is the energy barrier due to electrostatic interaction that two nuclei need to overcome so they can get close enough to undergo a nuclear reaction.
Coulomb constantThe Coulomb constant, the electric force constant, or the electrostatic constant (denoted ke, k or K) is a proportionality constant in electrodynamics equations. In SI units, it is equal to approximately 8987551787.3681764 N·m2·C−2 or 8.99×109 N·m2·C−2. It was named after the French physicist CharlesAugustin de Coulomb (1736–1806) who introduced Coulomb's law.
DebyeThe debye (symbol: D) (; Dutch: [dəˈbɛiə]) is a CGS unit (a nonSI metric unit) of electric dipole moment named in honour of the physicist Peter J. W. Debye. It is defined as 1×10−18 statcoulombcentimetre. Historically the debye was defined as the dipole moment resulting from two charges of opposite sign but an equal magnitude of 10−10 statcoulomb (generally called e.s.u. (electrostatic unit) in older literature), which were separated by 1 ångström. This gave a convenient unit for molecular dipole moments.
Typical dipole moments for simple diatomic molecules are in the range of 0 to 11 D. Symmetric homoatomic species, e.g. chlorine, Cl2, have zero dipole moment, and highly ionic molecular species have a very large dipole moment, e.g. gasphase potassium bromide, KBr, with a dipole moment of 10.5 D.The debye is still used in atomic physics and chemistry because SI units are inconveniently large. The smallest SI unit of electric dipole moment is the yoctocoulombmetre, which is roughly 300,000 D. There is currently no satisfactory solution to this problem of notation without resorting to the use of scientific notation.
Electric fieldAn electric field surrounds an electric charge, and exerts force on other charges in the field, attracting or repelling them. Electric field is sometimes abbreviated as Efield. The electric field is defined mathematically as a vector field that associates to each point in space the (electrostatic or Coulomb) force per unit of charge exerted on an infinitesimal positive test charge at rest at that point. The SI unit for electric field strength is volt per meter (V/m). Newtons per coulomb (N/C) is also used as a unit of electric field strengh. Electric fields are created by electric charges, or by timevarying magnetic fields. Electric fields are important in many areas of physics, and are exploited practically in electrical technology. On an atomic scale, the electric field is responsible for the attractive force between the atomic nucleus and electrons that holds atoms together, and the forces between atoms that cause chemical bonding. Electric fields and magnetic fields are both manifestations of the electromagnetic force, one of the four fundamental forces (or interactions) of nature.
Electric potentialAn electric potential (also called the electric field potential, potential drop or the electrostatic potential) is the amount of work needed to move a unit of positive charge from a reference point to a specific point inside the field without producing an acceleration. Typically, the reference point is the Earth or a point at infinity, although any point beyond the influence of the electric field charge can be used.
According to classical electrostatics, electric potential is a scalar quantity denoted by V or occasionally φ, equal to the electric potential energy of any charged particle at any location (measured in joules) divided by the charge of that particle (measured in coulombs). By dividing out the charge on the particle a quotient is obtained that is a property of the electric field itself.
This value can be calculated in either a static (timeinvariant) or a dynamic (varying with time) electric field at a specific time in units of joules per coulomb (J C−1), or volts (V). The electric potential at infinity is assumed to be zero.
In electrodynamics, when timevarying fields are present, the electric field cannot be expressed only in terms of a scalar potential. Instead, the electric field can be expressed in terms of both the scalar electric potential and the magnetic vector potential. The electric potential and the magnetic vector potential together form a four vector, so that the two kinds of potential are mixed under Lorentz transformations.
Electric potential energyElectric potential energy, or electrostatic potential energy, is a potential energy (measured in joules) that results from conservative Coulomb forces and is associated with the configuration of a particular set of point charges within a defined system. An object may have electric potential energy by virtue of two key elements: its own electric charge and its relative position to other electrically charged objects.
The term "electric potential energy" is used to describe the potential energy in systems with timevariant electric fields, while the term "electrostatic potential energy" is used to describe the potential energy in systems with timeinvariant electric fields.
Ellison (crater)Ellison is a lunar impact crater that lies on the far side of the Moon from the Earth. It is located just beyond the northwest limb of the Moon, to the southwest of the large walled plain Poczobutt. Due west of Ellison is the crater Coulomb.
The outer rim of Ellison is roughly circular, with an inward protrusion along the southern rim and a slight outward bulge to the wetnorthwest. It has a single terrace on the northeastern inner wall, formed from the slumping of material. Instead of a central peak, there is a small crater located at the midpoint. A smaller crater is located just to the westsouthwest of this centrallylocated formation, but the flat interior floor is otherwise devoid of features of interest.
Ellison lies at the approximate margin of the CoulombSarton Basin, a 530 km wide impact crater of PreNectarian age.
ExcitonAn exciton is a bound state of an electron and an electron hole which are attracted to each other by the electrostatic Coulomb force. It is an electrically neutral quasiparticle that exists in insulators, semiconductors and in some liquids. The exciton is regarded as an elementary excitation of condensed matter that can transport energy without transporting net electric charge.An exciton can form when a photon is absorbed by a semiconductor. This excites an electron from the valence band into the conduction band. In turn, this leaves behind a positively charged electron hole (an abstraction for the location from which an electron was moved). The electron in the conduction band is then effectively attracted to this localized hole by the repulsive Coulomb forces from large numbers of electrons surrounding the hole and excited electron. This attraction provides a stabilizing energy balance. Consequently, the exciton has slightly less energy than the unbound electron and hole. The wavefunction of the bound state is said to be hydrogenic, an exotic atom state akin to that of a hydrogen atom. However, the binding energy is much smaller and the particle's size much larger than a hydrogen atom. This is because of both the screening of the Coulomb force by other electrons in the semiconductor (i.e., its dielectric constant), and the small effective masses of the excited electron and hole. The recombination of the electron and hole, i.e. the decay of the exciton, is limited by resonance stabilization due to the overlap of the electron and hole wave functions, resulting in an extended lifetime for the exciton.
The electron and hole may have either parallel or antiparallel spins. The spins are coupled by the exchange interaction, giving rise to exciton fine structure. In periodic lattices, the properties of an exciton show momentum (kvector) dependence.
The concept of excitons was first proposed by Yakov Frenkel in 1931, when he described the excitation of atoms in a lattice of insulators. He proposed that this excited state would be able to travel in a particlelike fashion through the lattice without the net transfer of charge.
FrictionFriction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction:
Dry friction is a force that opposes the relative lateral motion of two solid surfaces in contact. Dry friction is subdivided into static friction ("stiction") between nonmoving surfaces, and kinetic friction between moving surfaces. With the exception of atomic or molecular friction, dry friction generally arises from the interaction of surface features, known as asperities
Fluid friction describes the friction between layers of a viscous fluid that are moving relative to each other.Lubricated friction is a case of fluid friction where a lubricant fluid separates two solid surfaces.Skin friction is a component of drag, the force resisting the motion of a fluid across the surface of a body.
Internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation.When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into thermal energy (that is, it converts work to heat). This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to thermal energy whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear, which may lead to performance degradation or damage to components. Friction is a component of the science of tribology.
Friction is desirable and important in supplying traction to facilitate motion on land. Most land vehicles rely on friction for acceleration, deceleration and changing direction. Sudden reductions in traction can cause loss of control and accidents.
Friction is not itself a fundamental force. Dry friction arises from a combination of intersurface adhesion, surface roughness, surface deformation, and surface contamination. The complexity of these interactions makes the calculation of friction from first principles impractical and necessitates the use of empirical methods for analysis and the development of theory.
Friction is a nonconservative force  work done against friction is path dependent. In the presence of friction, some energy is always lost in the form of heat. Thus mechanical energy is not conserved.
Gauge fixingIn the physics of gauge theories, gauge fixing (also called choosing a gauge) denotes a mathematical procedure for coping with redundant degrees of freedom in field variables. By definition, a gauge theory represents each physically distinct configuration of the system as an equivalence class of detailed local field configurations. Any two detailed configurations in the same equivalence class are related by a gauge transformation, equivalent to a shear along unphysical axes in configuration space. Most of the quantitative physical predictions of a gauge theory can only be obtained under a coherent prescription for suppressing or ignoring these unphysical degrees of freedom.
Although the unphysical axes in the space of detailed configurations are a fundamental property of the physical model, there is no special set of directions "perpendicular" to them. Hence there is an enormous amount of freedom involved in taking a "cross section" representing each physical configuration by a particular detailed configuration (or even a weighted distribution of them). Judicious gauge fixing can simplify calculations immensely, but becomes progressively harder as the physical model becomes more realistic; its application to quantum field theory is fraught with complications related to renormalization, especially when the computation is continued to higher orders. Historically, the search for logically consistent and computationally tractable gauge fixing procedures, and efforts to demonstrate their equivalence in the face of a bewildering variety of technical difficulties, has been a major driver of mathematical physics from the late nineteenth century to the present.
JouleThe joule (/dʒuːl/; symbol: J) is a derived unit of energy in the International System of Units. It is equal to the energy transferred to (or work done on) an object when a force of one newton acts on that object in the direction of its motion through a distance of one metre (1 newton metre or N⋅m). It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).
In terms firstly of base SI units and then in terms of other SI units:
where kg is the kilogram, m is the metre, s is the second, N is the newton, Pa is the pascal, W is the watt, C is the coulomb, and V is the volt.
One joule can also be defined as:
Mohr–Coulomb theoryMohr–Coulomb theory is a mathematical model (see yield surface) describing the response of brittle materials such as concrete, or rubble piles, to shear stress as well as normal stress. Most of the classical engineering materials somehow follow this rule in at least a portion of their shear failure envelope. Generally the theory applies to materials for which the compressive strength far exceeds the tensile strength.In geotechnical engineering it is used to define shear strength of soils and rocks at different effective stresses.
In structural engineering it is used to determine failure load as well as the angle of fracture of a displacement fracture in concrete and similar materials. Coulomb's friction hypothesis is used to determine the combination of shear and normal stress that will cause a fracture of the material. Mohr's circle is used to determine which principal stresses that will produce this combination of shear and normal stress, and the angle of the plane in which this will occur. According to the principle of normality the stress introduced at failure will be perpendicular to the line describing the fracture condition.
It can be shown that a material failing according to Coulomb's friction hypothesis will show the displacement introduced at failure forming an angle to the line of fracture equal to the angle of friction. This makes the strength of the material determinable by comparing the external mechanical work introduced by the displacement and the external load with the internal mechanical work introduced by the strain and stress at the line of failure. By conservation of energy the sum of these must be zero and this will make it possible to calculate the failure load of the construction.
A common improvement of this model is to combine Coulomb's friction hypothesis with Rankine's principal stress hypothesis to describe a separation fracture.
Rutherford scatteringRutherford scattering is the elastic scattering of charged particles by the Coulomb interaction. It is a physical phenomenon explained by Ernest Rutherford in 1911 that led to the development of the planetary Rutherford model of the atom and eventually the Bohr model. Rutherford scattering was first referred to as Coulomb scattering because it relies only upon the static electric (Coulomb) potential, and the minimum distance between particles is set entirely by this potential. The classical Rutherford scattering process of alpha particles against gold nuclei is an example of "elastic scattering" because neither the alpha particles nor the gold nuclei are internally excited. The Rutherford formula (see below) further neglects the recoil kinetic energy of the massive target nucleus.
The initial discovery was made by Hans Geiger and Ernest Marsden in 1909 when they performed the gold foil experiment in collaboration with Rutherford, in which they fired a beam of alpha particles (helium nuclei) at foils of gold leaf only a few atoms thick. At the time of the experiment, the atom was thought to be analogous to a plum pudding (as proposed by J. J. Thomson), with the negativelycharged electrons (the plums) studded throughout a positive spherical matrix (the pudding). If the plumpudding model were correct, the positive "pudding", being more spread out than in the correct model of a concentrated nucleus, would not be able to exert such large coulombic forces, and the alpha particles should only be deflected by small angles as they pass through.
However, the intriguing results showed that around 1 in 8000 alpha particles were deflected by very large angles (over 90°), while the rest passed through with little deflection. From this, Rutherford concluded that the majority of the mass was concentrated in a minute, positivelycharged region (the nucleus) surrounded by electrons. When a (positive) alpha particle approached sufficiently close to the nucleus, it was repelled strongly enough to rebound at high angles. The small size of the nucleus explained the small number of alpha particles that were repelled in this way. Rutherford showed, using the method outlined below, that the size of the nucleus was less than about 10−14 m (how much less than this size, Rutherford could not tell from this experiment alone; see more below on this problem of lowest possible size). As a visual example, Figure 1 shows the deflection of an alpha particle by a nucleus in the gas of a cloud chamber.
Rutherford scattering is now exploited by the materials science community in an analytical technique called Rutherford backscattering.
SaintCoulombSaintCoulomb (Breton: SantKouloum) is a commune in the IlleetVilaine department in Brittany in northwestern France.
VoltageVoltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points (i.e., voltage) in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule (of work) per 1 coulomb (of charge). The official SI definition for volt uses power and current, where 1 volt = 1 watt (of power) per 1 ampere (of current). This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by ∆V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.
Electric potential differences between points can be caused by electric charge, by electric current through a magnetic field, by timevarying magnetic fields, or some combination of these three. A voltmeter can be used to measure the voltage (or potential difference) between two points in a system; often a common reference potential such as the ground of the system is used as one of the points. A voltage may represent either a source of energy (electromotive force) or lost, used, or stored energy (potential drop).
Base units  

Derived units with special names  
Other accepted units  
See also  

Base units  

Derived units with special names  
Other accepted units  
See also  

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