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The SI derived unit of electric charge is the coulomb (C) named after French physicist Charles-Augustin de Coulomb. In electrical engineering it is also common to use the ampere-hour (Ah). In physics and chemistry it is common to use the elementary charge ("e" as a unit). Chemistry also uses the Faraday constant as the charge on a mole of electrons. The lowercase symbol "q" often denotes charge. |
Charge is the fundamental property of matter that exhibit electrostatic attraction or repulsion in the presence of other matter with charge. Electric charge is a characteristic property of many subatomic particles. The charges of free-standing particles are integer multiples of the elementary charge "e"; we say that electric charge is "quantized". Michael Faraday, in his electrolysis experiments, was the first to note the discrete nature of electric charge. Robert Millikan's oil drop experiment demonstrated this fact directly, and measured the elementary charge. It has been discovered that one type of particle, quarks, have fractional charges of either − or +, but it is believed they always occur in multiples of integral charge; free-standing quarks have never been observed. |
By convention, the charge of an electron is negative, "−e", while that of a proton is positive, "+e". Charged particles whose charges have the same sign repel one another, and particles whose charges have different signs attract. Coulomb's law quantifies the electrostatic force between two particles by asserting that the force is proportional to the product of their charges, and inversely proportional to the square of the distance between them. The charge of an antiparticle equals that of the corresponding particle, but with opposite sign. |
The electric charge of a macroscopic object is the sum of the electric charges of the particles that make it up. This charge is often small, because matter is made of atoms, and atoms typically have equal numbers of protons and electrons, in which case their charges cancel out, yielding a net charge of zero, thus making the atom neutral. |
An "ion" is an atom (or group of atoms) that has lost one or more electrons, giving it a net positive charge (cation), or that has gained one or more electrons, giving it a net negative charge (anion). "Monatomic ions" are formed from single atoms, while "polyatomic ions" are formed from two or more atoms that have been bonded together, in each case yielding an ion with a positive or negative net charge. |
During the formation of macroscopic objects, constituent atoms and ions usually combine to form structures composed of neutral "ionic compounds" electrically bound to neutral atoms. Thus macroscopic objects tend toward being neutral overall, but macroscopic objects are rarely perfectly net neutral. |
Even when an object's net charge is zero, the charge can be distributed non-uniformly in the object (e.g., due to an external electromagnetic field, or bound polar molecules). In such cases, the object is said to be polarized. The charge due to polarization is known as bound charge, while the charge on an object produced by electrons gained or lost from outside the object is called "free charge". The motion of electrons in conductive metals in a specific direction is known as electric current. |
The SI derived unit of quantity of electric charge is the coulomb (symbol: C). The coulomb is defined as the quantity of charge that passes through the cross section of an electrical conductor carrying one ampere for one second. This unit was proposed in 1946 and ratified in 1948. In modern practice, the phrase "amount of charge" is used instead of "quantity of charge". The lowercase symbol "q" is often used to denote a quantity of electricity or charge. The quantity of electric charge can be directly measured with an electrometer, or indirectly measured with a ballistic galvanometer. |
The amount of charge in 1 electron (elementary charge) is defined as a fundamental constant in the SI system of units, (effective from 20 May 2019). The value for elementary charge, when expressed in the SI unit for electric charge (coulomb), is "exactly" . |
After finding the quantized character of charge, in 1891 George Stoney proposed the unit 'electron' for this fundamental unit of electrical charge. This was before the discovery of the particle by J. J. Thomson in 1897. The unit is today referred to as , , or simply as . A measure of charge should be a multiple of the elementary charge "e", even if at large scales charge seems to behave as a real quantity. In some contexts it is meaningful to speak of fractions of a charge; for example in the charging of a capacitor, or in the fractional quantum Hall effect. |
The unit faraday is sometimes used in electrochemistry. One faraday of charge is the magnitude of the charge of one mole of electrons, i.e. 96485.33289(59) C. |
In systems of units other than SI such as cgs, electric charge is expressed as combination of only three fundamental quantities (length, mass, and time), and not four, as in SI, where electric charge is a combination of length, mass, time, and electric current. |
In late 1100s, the substance jet, a compacted form of coal, was noted to have an amber effect, and in the middle of the 1500s, Girolamo Fracastoro, discovered that diamond also showed this effect. Some efforts were made by Fracastoro and others, especially Gerolamo Cardano to develop explanations for this phenomenon. |
Around 1663 Otto von Guericke invented what was probably the first electrostatic generator, but he did not recognize it primarily as an electrical device and only conducted minimal electrical experiments with it. Other European pioneers were Robert Boyle, who in 1675 published the first book in English that was devoted solely to electrical phenomena. His work was largely a repetition of Gilbert's studies, but he also identified several more "electrics", and noted mutual attraction between two bodies. |
Up until about 1745, the main explanation for electrical attraction and repulsion was the idea that electrified bodies gave off an effluvium. |
It is now known that the Franklin model was fundamentally correct. There is only one kind of electrical charge, and only one variable is required to keep track of the amount of charge. |
Until 1800 it was only possible to study conduction of electric charge by using an electrostatic discharge. In 1800 Alessandro Volta was the first to show that charge could be maintained in continuous motion through a closed path. |
In 1833, Michael Faraday sought to remove any doubt that electricity is identical, regardless of the source by which it is produced. He discussed a variety of known forms, which he characterized as common electricity (e.g., static electricity, piezoelectricity, magnetic induction), voltaic electricity (e.g., electric current from a voltaic pile), and animal electricity (e.g., bioelectricity). |
In 1838, Faraday raised a question about whether electricity was a fluid or fluids or a property of matter, like gravity. He investigated whether matter could be charged with one kind of charge independently of the other. He came to the conclusion that electric charge was a relation between two or more bodies, because he could not charge one body without having an opposite charge in another body. |
In 1838, Faraday also put forth a theoretical explanation of electric force, while expressing neutrality about whether it originates from one, two, or no fluids. He focused on the idea that the normal state of particles is to be nonpolarized, and that when polarized, they seek to return to their natural, nonpolarized state. |
In developing a field theory approach to electrodynamics (starting in the mid-1850s), James Clerk Maxwell stops considering electric charge as a special substance that accumulates in objects, and starts to understand electric charge as a consequence of the transformation of energy in the field. This pre-quantum understanding considered magnitude of electric charge to be a continuous quantity, even at the microscopic level. |
The role of charge in static electricity. |
Static electricity refers to the electric charge of an object and the related electrostatic discharge when two objects are brought together that are not at equilibrium. An electrostatic discharge creates a change in the charge of each of the two objects. |
When a piece of glass and a piece of resin—neither of which exhibit any electrical properties—are rubbed together and left with the rubbed surfaces in contact, they still exhibit no electrical properties. When separated, they attract each other. |
A second piece of glass rubbed with a second piece of resin, then separated and suspended near the former pieces of glass and resin causes these phenomena: |
This attraction and repulsion is an "electrical phenomenon", and the bodies that exhibit them are said to be "electrified", or "electrically charged". Bodies may be electrified in many other ways, as well as by friction. The electrical properties of the two pieces of glass are similar to each other but opposite to those of the two pieces of resin: The glass attracts what the resin repels and repels what the resin attracts. |
If a body electrified in any manner whatsoever behaves as the glass does, that is, if it repels the glass and attracts the resin, the body is said to be "vitreously" electrified, and if it attracts the glass and repels the resin it is said to be "resinously" electrified. All electrified bodies are either vitreously or resinously electrified. |
An established convention in the scientific community defines vitreous electrification as positive, and resinous electrification as negative. The exactly opposite properties of the two kinds of electrification justify our indicating them by opposite signs, but the application of the positive sign to one rather than to the other kind must be considered as a matter of arbitrary convention—just as it is a matter of convention in mathematical diagram to reckon positive distances towards the right hand. |
No force, either of attraction or of repulsion, can be observed between an electrified body and a body not electrified. |
The role of charge in electric current. |
Electric current is the flow of electric charge through an object, which produces no net loss or gain of electric charge. The most common charge carriers are the positively charged proton and the negatively charged electron. The movement of any of these charged particles constitutes an electric current. In many situations, it suffices to speak of the "conventional current" without regard to whether it is carried by positive charges moving in the direction of the conventional current or by negative charges moving in the opposite direction. This macroscopic viewpoint is an approximation that simplifies electromagnetic concepts and calculations. |
At the opposite extreme, if one looks at the microscopic situation, one sees there are many ways of carrying an electric current, including: a flow of electrons; a flow of electron holes that act like positive particles; and both negative and positive particles (ions or other charged particles) flowing in opposite directions in an electrolytic solution or a plasma. |
Beware that, in the common and important case of metallic wires, the direction of the conventional current is opposite to the drift velocity of the actual charge carriers; i.e., the electrons. This is a source of confusion for beginners. |
The total electric charge of an isolated system remains constant regardless of changes within the system itself. This law is inherent to all processes known to physics and can be derived in a local form from gauge invariance of the wave function. The conservation of charge results in the charge-current continuity equation. More generally, the rate of change in charge density "ρ" within a volume of integration "V" is equal to the area integral over the current density J through the closed surface "S" = ∂"V", which is in turn equal to the net current "I": |
Thus, the conservation of electric charge, as expressed by the continuity equation, gives the result: |
The charge transferred between times formula_2 and formula_3 is obtained by integrating both sides: |
where "I" is the net outward current through a closed surface and "q" is the electric charge contained within the volume defined by the surface. |
Aside from the properties described in articles about electromagnetism, charge is a relativistic invariant. This means that any particle that has charge "q" has the same charge regardless of how fast it is travelling. This property has been experimentally verified by showing that the charge of one helium nucleus (two protons and two neutrons bound together in a nucleus and moving around at high speeds) is the same as two deuterium nuclei (one proton and one neutron bound together, but moving much more slowly than they would if they were in a helium nucleus). |
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge. There are also many approximate conservation laws, which apply to such quantities as mass, parity, lepton number, baryon number, strangeness, hypercharge, etc. These quantities are conserved in certain classes of physics processes, but not in all. |
A local conservation law is usually expressed mathematically as a continuity equation, a partial differential equation which gives a relation between the amount of the quantity and the "transport" of that quantity. It states that the amount of the conserved quantity at a point or within a volume can only change by the amount of the quantity which flows in or out of the volume. |
From Noether's theorem, each conservation law is associated with a symmetry in the underlying physics. |
Conservation laws as fundamental laws of nature. |
Conservation laws are considered to be fundamental laws of nature, with broad application in physics, as well as in other fields such as chemistry, biology, geology, and engineering. |
Most conservation laws are exact, or absolute, in the sense that they apply to all possible processes. Some conservation laws are partial, in that they hold for some processes but not for others. |
One particularly important result concerning conservation laws is Noether's theorem, which states that there is a one-to-one correspondence between each one of them and a differentiable symmetry of nature. For example, the conservation of energy follows from the time-invariance of physical systems, and the conservation of angular momentum arises from the fact that physical systems behave the same regardless of how they are oriented in space. |
A partial listing of physical conservation equations due to symmetry that are said to be exact laws, or more precisely "have never been proven to be violated:" |
There are also approximate conservation laws. These are approximately true in particular situations, such as low speeds, short time scales, or certain interactions. |
In continuum mechanics, the most general form of an exact conservation law is given by a continuity equation. For example, conservation of electric charge "q" is |
where ∇⋅ is the divergence operator, "ρ" is the density of "q" (amount per unit volume), j is the flux of "q" (amount crossing a unit area in unit time), and "t" is time. |
If we assume that the motion u of the charge is a continuous function of position and time, then |
In one space dimension this can be put into the form of a homogeneous first-order quasilinear hyperbolic equation: |
where the dependent variable "y" is called the "density" of a "conserved quantity", and "A"("y") is called the "current Jacobian", and the subscript notation for partial derivatives has been employed. The more general inhomogeneous case: |
is not a conservation equation but the general kind of balance equation describing a dissipative system. The dependent variable "y" is called a "nonconserved quantity", and the inhomogeneous term "s"("y","x","t") is the-"source", or dissipation. For example, balance equations of this kind are the momentum and energy Navier-Stokes equations, or the entropy balance for a general isolated system. |
In the one-dimensional space a conservation equation is a first-order quasilinear hyperbolic equation that can be put into the "advection" form: |
where the dependent variable "y"("x","t") is called the density of the "conserved" (scalar) quantity, and "a"("y") is called the current coefficient, usually corresponding to the partial derivative in the conserved quantity of a current density of the conserved quantity "j"("y"): |
In this case since the chain rule applies: |
the conservation equation can be put into the current density form: |
In a space with more than one dimension the former definition can be extended to an equation that can be put into the form: |
where the "conserved quantity" is "y"(r,"t"), formula_11 denotes the scalar product, "∇" is the nabla operator, here indicating a gradient, and "a"("y") is a vector of current coefficients, analogously corresponding to the divergence of a vector current density associated to the conserved quantity j("y"): |
This is the case for the continuity equation: |
Here the conserved quantity is the mass, with density "ρ"(r,"t") and current density "ρ"u, identical to the momentum density, while u(r,"t") is the flow velocity. |
In the general case a conservation equation can be also a system of this kind of equations (a vector equation) in the form: |
where y is called the "conserved" (vector) quantity, ∇ y is its gradient, 0 is the zero vector, and A(y) is called the Jacobian of the current density. In fact as in the former scalar case, also in the vector case A(y) usually corresponding to the Jacobian of a current density matrix J(y): |
and the conservation equation can be put into the form: |
For example, this the case for Euler equations (fluid dynamics). In the simple incompressible case they are: |
It can be shown that the conserved (vector) quantity and the current density matrix for these equations are respectively: |
Conservation equations can be also expressed in integral form: the advantage of the latter is substantially that it requires less smoothness of the solution, which paves the way to weak form, extending the class of admissible solutions to include discontinuous solutions. By integrating in any space-time domain the current density form in 1-D space: |
and by using Green's theorem, the integral form is: |
In a similar fashion, for the scalar multidimensional space, the integral form is: |
where the line integration is performed along the boundary of the domain, in an anticlockwise manner. |
Moreover, by defining a test function "φ"(r,"t") continuously differentiable both in time and space with compact support, the weak form can be obtained pivoting on the initial condition. In 1-D space it is: |
Note that in the weak form all the partial derivatives of the density and current density have been passed on to the test function, which with the former hypothesis is sufficiently smooth to admit these derivatives. |
In physics, charge conservation is the principle that the total electric charge in an isolated system never changes. The net quantity of electric charge, the amount of positive charge minus the amount of negative charge in the universe, is always "conserved". Charge conservation, considered as a physical conservation law, implies that the change in the amount of electric charge in any volume of space is exactly equal to the amount of charge flowing into the volume minus the amount of charge flowing out of the volume. In essence, charge conservation is an accounting relationship between the amount of charge in a region and the flow of charge into and out of that region, given by a continuity equation between charge density formula_1 and current density formula_2. |
This does not mean that individual positive and negative charges cannot be created or destroyed. Electric charge is carried by subatomic particles such as electrons and protons. Charged particles can be created and destroyed in elementary particle reactions. In particle physics, charge conservation means that in reactions that create charged particles, equal numbers of positive and negative particles are always created, keeping the net amount of charge unchanged. Similarly, when particles are destroyed, equal numbers of positive and negative charges are destroyed. This property is supported without exception by all empirical observations so far. |
Although conservation of charge requires that the total quantity of charge in the universe is constant, it leaves open the question of what that quantity is. Most evidence indicates that the net charge in the universe is zero; that is, there are equal quantities of positive and negative charge. |
Charge conservation was first proposed by British scientist William Watson in 1746 and American statesman and scientist Benjamin Franklin in 1747, although the first convincing proof was given by Michael Faraday in 1843. |
Mathematically, we can state the law of charge conservation as a continuity equation: |
where formula_4 is the electric charge accumulation rate in a specific volume at time , formula_5 is the amount of charge flowing into the volume and formula_6 is the amount of charge flowing out of the volume; both amounts are regarded as generic functions of time. |
The integrated continuity equation between two time values reads: |
The general solution is obtained by fixing the initial condition time formula_8, leading to the integral equation: |
The condition formula_10 corresponds to the absence of charge quantity change in the control volume: the system has reached a steady state. From the above condition, the following must hold true: |
therefore, formula_5 and formula_6 are equal (not necessarily constant) over time, then the overall charge inside the control volume does not change. This deduction could be derived directly from the continuity equation, since at steady state formula_14 holds, and implies formula_15. |
In electromagnetic field theory, vector calculus can be used to express the law in terms of charge density (in coulombs per cubic meter) and electric current density (in amperes per square meter). This is called the charge density continuity equation |
The term on the left is the rate of change of the charge density at a point. The term on the right is the divergence of the current density at the same point. The equation equates these two factors, which says that the only way for the charge density at a point to change is for a current of charge to flow into or out of the point. This statement is equivalent to a conservation of four-current. |
The net current into a volume is |
where is the boundary of oriented by outward-pointing normals, and is shorthand for , the outward pointing normal of the boundary . Here is the current density (charge per unit area per unit time) at the surface of the volume. The vector points in the direction of the current. |
From the Divergence theorem this can be written |
Charge conservation requires that the net current into a volume must necessarily equal the net change in charge within the volume. |
The total charge "q" in volume "V" is the integral (sum) of the charge density in "V" |
Since this is true for every volume, we have in general |
Charge conservation can also be understood as a consequence of symmetry through Noether's theorem, a central result in theoretical physics that asserts that each conservation law is associated with a symmetry of the underlying physics. The symmetry that is associated with charge conservation is the global gauge invariance of the electromagnetic field. This is related to the fact that the electric and magnetic fields are not changed by different choices of the value representing the zero point of electrostatic potential formula_24. However the full symmetry is more complicated, and also involves the vector potential formula_25. The full statement of gauge invariance is that the physics of an electromagnetic field are unchanged when the scalar and vector potential are shifted by the gradient of an arbitrary scalar field formula_26: |
In quantum mechanics the scalar field is equivalent to a phase shift in the wavefunction of the charged particle: |
so gauge invariance is equivalent to the well known fact that changes in the phase of a wavefunction are unobservable, and only changes in the magnitude of the wavefunction result in changes to the probability function formula_29. This is the ultimate theoretical origin of charge conservation. |
Gauge invariance is a very important, well established property of the electromagnetic field and has many testable consequences. The theoretical justification for charge conservation is greatly strengthened by being linked to this symmetry. For example, gauge invariance also requires that the photon be massless, so the good experimental evidence that the photon has zero mass is also strong evidence that charge is conserved. |
Even if gauge symmetry is exact, however, there might be apparent electric charge non-conservation if charge could leak from our normal 3-dimensional space into hidden extra dimensions. |
Simple arguments rule out some types of charge nonconservation. For example, the magnitude of the elementary charge on positive and negative particles must be extremely close to equal, differing by no more than a factor of 10−21 for the case of protons and electrons. Ordinary matter contains equal numbers of positive and negative particles, protons and electrons, in enormous quantities. If the elementary charge on the electron and proton were even slightly different, all matter would have a large electric charge and would be mutually repulsive. |
The best experimental tests of electric charge conservation are searches for particle decays that would be allowed if electric charge is not always conserved. No such decays have ever been seen. |
The best experimental test comes from searches for the energetic photon from an electron decaying into a neutrino and a single photon: |
but there are theoretical arguments that such single-photon decays will never occur even if charge is not conserved. |
Charge disappearance tests are sensitive to decays without energetic photons, other unusual charge violating processes such as an electron spontaneously changing into a positron, |
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