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In
electromagnetism In physics, electromagnetism is an interaction that occurs between particles with electric charge. It is the second-strongest of the four fundamental interactions, after the strong force, and it is the dominant force in the interactions of a ...
, charge density is the amount of
electric charge Electric charge is the physical property of matter that causes charged matter to experience a force when placed in an electromagnetic field. Electric charge can be ''positive'' or ''negative'' (commonly carried by protons and electrons respe ...
per unit
length Length is a measure of distance. In the International System of Quantities, length is a quantity with dimension distance. In most systems of measurement a base unit for length is chosen, from which all other units are derived. In the Interna ...
,
surface area The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc ...
, or
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...
. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system in
coulomb The coulomb (symbol: C) is the unit of electric charge in the International System of Units (SI). In the present version of the SI it is equal to the electric charge delivered by a 1 ampere constant current in 1 second and to elementary char ...
s per cubic
meter The metre (British spelling) or meter (American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its pref ...
(C⋅m−3), at any point in a volume. Surface charge density (σ) is the quantity of charge per unit area, measured in coulombs per square meter (C⋅m−2), at any point on a surface charge distribution on a two dimensional surface. Linear charge density (λ) is the quantity of charge per unit length, measured in coulombs per meter (C⋅m−1), at any point on a line charge distribution. Charge density can be either positive or negative, since electric charge can be either positive or negative. Like
mass density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
, charge density can vary with position. In classical electromagnetic theory charge density is idealized as a ''
continuous Continuity or continuous may refer to: Mathematics * Continuity (mathematics), the opposing concept to discreteness; common examples include ** Continuous probability distribution or random variable in probability and statistics ** Continuous ...
''
scalar Scalar may refer to: *Scalar (mathematics), an element of a field, which is used to define a vector space, usually the field of real numbers * Scalar (physics), a physical quantity that can be described by a single element of a number field such ...
function of position \boldsymbol, like a fluid, and \rho(\boldsymbol), \sigma(\boldsymbol), and \lambda(\boldsymbol) are usually regarded as continuous charge distributions, even though all real charge distributions are made up of discrete charged particles. Due to the conservation of electric charge, the charge density in any volume can only change if an
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
of charge flows into or out of the volume. This is expressed by a
continuity equation A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. S ...
which links the rate of change of charge density \rho(\boldsymbol) and the
current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
\boldsymbol(\boldsymbol). Since all charge is carried by
subatomic particle In physical sciences, a subatomic particle is a particle that composes an atom. According to the Standard Model of particle physics, a subatomic particle can be either a composite particle, which is composed of other particles (for example, a pr ...
s, which can be idealized as points, the concept of a ''continuous'' charge distribution is an approximation, which becomes inaccurate at small length scales. A charge distribution is ultimately composed of individual charged particles separated by regions containing no charge. For example, the charge in an electrically charged metal object is made up of
conduction electron In solid-state physics, the valence band and conduction band are the bands closest to the Fermi level, and thus determine the electrical conductivity of the solid. In nonmetals, the valence band is the highest range of electron energies i ...
s moving randomly in the metal's
crystal lattice In geometry and crystallography, a Bravais lattice, named after , is an infinite array of discrete points generated by a set of discrete translation operations described in three dimensional space by : \mathbf = n_1 \mathbf_1 + n_2 \mathbf_2 + n ...
.
Static electricity Static electricity is an imbalance of electric charges within or on the surface of a material or between materials. The charge remains until it is able to move away by means of an electric current or electrical discharge. Static electricity is na ...
is caused by surface charges consisting of
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
s on the surface of objects, and the
space charge Space charge is an interpretation of a collection of electric charges in which excess electric charge is treated as a continuum of charge distributed over a region of space (either a volume or an area) rather than distinct point-like charges. Thi ...
in a
vacuum tube A vacuum tube, electron tube, valve (British usage), or tube (North America), is a device that controls electric current flow in a high vacuum between electrodes to which an electric voltage, potential difference has been applied. The type kn ...
is composed of a cloud of free electrons moving randomly in space. The charge carrier density in a conductor is equal to the number of mobile
charge carrier In physics, a charge carrier is a particle or quasiparticle that is free to move, carrying an electric charge, especially the particles that carry electric charges in electrical conductors. Examples are electrons, ions and holes. The term is used ...
s (
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s,
ion An ion () is an atom or molecule with a net electrical charge. The charge of an electron is considered to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be positive by conve ...
s, etc.) per unit volume. The charge density at any point is equal to the charge carrier density multiplied by the elementary charge on the particles. However, because the
elementary charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
on an electron is so small (1.6⋅10−19 C) and there are so many of them in a macroscopic volume (there are about 1022 conduction electrons in a cubic centimeter of copper) the continuous approximation is very accurate when applied to macroscopic volumes, and even microscopic volumes above the nanometer level. At even smaller scales, of atoms and molecules, due to the
uncertainty principle In quantum mechanics, the uncertainty principle (also known as Heisenberg's uncertainty principle) is any of a variety of mathematical inequalities asserting a fundamental limit to the accuracy with which the values for certain pairs of physic ...
of
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, a charged particle does not ''have'' a precise position but is represented by a
probability distribution In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon i ...
, so the charge of an individual particle is not concentrated at a point but is 'smeared out' in space and acts like a true continuous charge distribution. This is the meaning of 'charge distribution' and 'charge density' used in
chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
and
chemical bonding A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
. An electron is represented by a ''
wavefunction A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
'' \psi(\boldsymbol) whose square is proportional to the probability of finding the electron at any point \boldsymbol in space, so , \psi(\boldsymbol), ^2 is proportional to the charge density of the electron at any point. In
atom Every atom is composed of a nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, liquid, gas, and ...
s and
molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioch ...
s the charge of the electrons is distributed in clouds called orbitals which surround the atom or molecule, and are responsible for
chemical bonds A chemical bond is a lasting attraction between atoms or ions that enables the formation of molecules and crystals. The bond may result from the electrostatic force between oppositely charged ions as in ionic bonds, or through the sharing of ...
.


Definitions


Continuous charges

Following are the definitions for continuous charge distributions. The linear charge density is the ratio of an infinitesimal electric charge ''dQ'' (SI unit: C) to an infinitesimal
line element In geometry, the line element or length element can be informally thought of as a line segment associated with an infinitesimal displacement vector in a metric space. The length of the line element, which may be thought of as a differential arc l ...
, \lambda_q = \frac\,, similarly the surface charge density uses a
surface area The surface area of a solid object is a measure of the total area that the surface of the object occupies. The mathematical definition of surface area in the presence of curved surfaces is considerably more involved than the definition of arc ...
element ''dS'' \sigma_q = \frac\,, and the volume charge density uses a
volume Volume is a measure of occupied three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). The de ...
element ''dV'' \rho_q =\frac \, , Integrating the definitions gives the total charge ''Q'' of a region according to
line integral In mathematics, a line integral is an integral where the function to be integrated is evaluated along a curve. The terms ''path integral'', ''curve integral'', and ''curvilinear integral'' are also used; ''contour integral'' is used as well, alt ...
of the linear charge density ''λ''''q''(r) over a line or 1d curve ''C'', Q = \int_L \lambda_q(\mathbf) \, d\ell similarly a
surface integral In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can be thought of as the double integral analogue of the line integral. Given a surface, one may ...
of the surface charge density σ''q''(r) over a surface ''S'', Q = \int_S \sigma_q(\mathbf) \, dS and a
volume integral In mathematics (particularly multivariable calculus), a volume integral (∭) refers to an integral over a 3-dimensional domain; that is, it is a special case of multiple integrals. Volume integrals are especially important in physics for many ap ...
of the volume charge density ''ρ''''q''(r) over a volume ''V'', Q = \int_V \rho_q(\mathbf) \, dV where the subscript ''q'' is to clarify that the density is for electric charge, not other densities like
mass density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematically ...
,
number density The number density (symbol: ''n'' or ''ρ''N) is an intensive quantity used to describe the degree of concentration of countable objects (particles, molecules, phonons, cells, galaxies, etc.) in physical space: three-dimensional volumetric number ...
,
probability density In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...
, and prevent conflict with the many other uses of ''λ'', ''σ'', ''ρ'' in electromagnetism for
wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, tro ...
,
electrical resistivity and conductivity Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current. A low resistivity indicates a material that readily allows ...
. Within the context of electromagnetism, the subscripts are usually dropped for simplicity: ''λ'', ''σ'', ''ρ''. Other notations may include: ''ρ'', ''ρs'', ''ρv'', ''ρL'', ''ρS'', ''ρV'' etc. The total charge divided by the length, surface area, or volume will be the average charge densities: \langle\lambda_q \rangle = \frac\,,\quad \langle\sigma_q\rangle = \frac\,,\quad\langle\rho_q\rangle = \frac\,.


Free, bound and total charge

In
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
materials, the total charge of an object can be separated into "free" and "bound" charges. Bound charges set up electric dipoles in response to an applied
electric field An electric field (sometimes E-field) is the physical field that surrounds electrically charged particles and exerts force on all other charged particles in the field, either attracting or repelling them. It also refers to the physical field fo ...
E, and polarize other nearby dipoles tending to line them up, the net accumulation of charge from the orientation of the dipoles is the bound charge. They are called bound because they cannot be removed: in the dielectric material the charges are the
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
s bound to the nuclei. Free charges are the excess charges which can move into electrostatic equilibrium, i.e. when the charges are not moving and the resultant electric field is independent of time, or constitute
electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical conductor or space. It is measured as the net rate of flow of electric charge through a surface or into a control volume. The moving pa ...
s.


Total charge densities

In terms of volume charge densities, the total charge density is: \rho = \rho_\text + \rho_\text\,. as for surface charge densities: \sigma = \sigma_\text + \sigma_\text\,. where subscripts "f" and "b" denote "free" and "bound" respectively.


Bound charge

The bound surface charge is the charge piled up at the surface of the
dielectric In electromagnetism, a dielectric (or dielectric medium) is an electrical insulator that can be polarised by an applied electric field. When a dielectric material is placed in an electric field, electric charges do not flow through the mate ...
, given by the dipole moment perpendicular to the surface: q_b = \frac where s is the separation between the point charges constituting the dipole, \mathbf is the
electric dipole moment The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The ...
, \mathbf is the unit normal vector to the surface. Taking
infinitesimal In mathematics, an infinitesimal number is a quantity that is closer to zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referr ...
s: d q_b = \frac\cdot\mathbf and dividing by the differential surface element ''dS'' gives the bound surface charge density: \sigma_b = \frac = \frac \cdot\mathbf = \frac \cdot\mathbf = \mathbf \cdot\mathbf\,. where P is the
polarization density In classical electromagnetism, polarization density (or electric polarization, or simply polarization) is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is ...
, i.e. density of
electric dipole moment The electric dipole moment is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI unit for electric dipole moment is the coulomb-meter (C⋅m). The ...
s within the material, and ''dV'' is the differential
volume element In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form :dV ...
. Using the
divergence theorem In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the ''flux'' of a vector field through a closed surface to the ''divergence'' of the field in the vol ...
, the bound volume charge density within the material is q_b = \int \rho_b \, dV = -\oint_S \mathbf \cdot \hat\mathbf \, dS = -\int \nabla \cdot \mathbf \, dV hence: \rho_b = - \nabla\cdot\mathbf\,. The negative sign arises due to the opposite signs on the charges in the dipoles, one end is within the volume of the object, the other at the surface. A more rigorous derivation is given below.


Free charge density

The free charge density serves as a useful simplification in
Gauss's law In physics and electromagnetism, Gauss's law, also known as Gauss's flux theorem, (or sometimes simply called Gauss's theorem) is a law relating the distribution of electric charge to the resulting electric field. In its integral form, it sta ...
for electricity; the volume integral of it is the free charge enclosed in a charged object - equal to the net
flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...
of the
electric displacement field In physics, the electric displacement field (denoted by D) or electric induction is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "D" stands for "displacement", as in ...
D emerging from the object: : See
Maxwell's equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
and
constitutive relation In physics and engineering, a constitutive equation or constitutive relation is a relation between two physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance, and app ...
for more details.


Homogeneous charge density

For the special case of a
homogeneous Homogeneity and heterogeneity are concepts often used in the sciences and statistics relating to the uniformity of a substance or organism. A material or image that is homogeneous is uniform in composition or character (i.e. color, shape, siz ...
charge density ''ρ''0, independent of position i.e. constant throughout the region of the material, the equation simplifies to: Q = V \rho_0.


Proof

Start with the definition of a continuous volume charge density: Q = \int_V \rho_q(\mathbf) \, dV. Then, by definition of homogeneity, ''ρ''''q''(r) is a constant denoted by ''ρ''''q'', 0 (to differ between the constant and non-constant densities), and so by the properties of an integral can be pulled outside of the integral resulting in: Q = \rho_ \int_V \,dV = \rho_0 V so, Q = V \rho_. The equivalent proofs for linear charge density and surface charge density follow the same arguments as above.


Discrete charges

For a single point charge ''q'' at position r0 inside a region of 3d space ''R'', like an
electron The electron ( or ) is a subatomic particle with a negative one elementary electric charge. Electrons belong to the first generation of the lepton particle family, and are generally thought to be elementary particles because they have no kn ...
, the volume charge density can be expressed by the
Dirac delta function In mathematics, the Dirac delta distribution ( distribution), also known as the unit impulse, is a generalized function or distribution over the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire ...
: \rho_q(\mathbf) = q \delta(\mathbf - \mathbf_0) where r is the position to calculate the charge. As always, the integral of the charge density over a region of space is the charge contained in that region. The delta function has the ''sifting property'' for any function ''f'': \int_R d^3 \mathbf f(\mathbf)\delta(\mathbf - \mathbf_0) = f(\mathbf_0) so the delta function ensures that when the charge density is integrated over ''R'', the total charge in ''R'' is ''q'': Q =\int_R d^3 \mathbf \, \rho_q =\int_R d^3 \mathbf \, q \delta(\mathbf - \mathbf_0) = q \int_R d^3 \mathbf \, \delta(\mathbf - \mathbf_0) = q This can be extended to ''N'' discrete point-like charge carriers. The charge density of the system at a point r is a sum of the charge densities for each charge ''qi'' at position r''i'', where : \rho_q(\mathbf)=\sum_^N\ q_i\delta(\mathbf - \mathbf_i) The delta function for each charge ''qi'' in the sum, ''δ''(r − r''i''), ensures the integral of charge density over ''R'' returns the total charge in ''R'': Q = \int_R d^3 \mathbf \sum_^N\ q_i\delta(\mathbf - \mathbf_i) = \sum_^N\ q_i \int_R d^3 \mathbf \delta(\mathbf - \mathbf_i) = \sum_^N\ q_i If all charge carriers have the same charge ''q'' (for electrons ''q'' = −''e'', the
electron charge The elementary charge, usually denoted by is the electric charge carried by a single proton or, equivalently, the magnitude of the negative electric charge carried by a single electron, which has charge −1 . This elementary charge is a fundame ...
) the charge density can be expressed through the number of charge carriers per unit volume, ''n''(r), by \rho_q(\mathbf) = q n(\mathbf)\,. Similar equations are used for the linear and surface charge densities.


Charge density in special relativity

In
special relativity In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws o ...
, the length of a segment of wire depends on
velocity Velocity is the directional speed of an object in motion as an indication of its rate of change in position as observed from a particular frame of reference and as measured by a particular standard of time (e.g. northbound). Velocity is a ...
of observer because of
length contraction Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length, which is the length as measured in the object's own rest frame. It is also known as Lorentz contraction or Lorentz–FitzGerald ...
, so charge density will also depend on velocity.
Anthony French Anthony Philip French (November 19, 1920 – February 3, 2017) was a British professor of physics at the Massachusetts Institute of Technology. He was born in Brighton, England. French was a graduate of Cambridge University, receiving his ...
has described how the
magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to ...
force of a current-bearing wire arises from this relative charge density. He used (p 260) a
Minkowski diagram A spacetime diagram is a graphical illustration of the properties of space and time in the special theory of relativity. Spacetime diagrams allow a qualitative understanding of the corresponding phenomena like time dilation and length contractio ...
to show "how a neutral current-bearing wire appears to carry a net charge density as observed in a moving frame." When a charge density is measured in a moving
frame of reference In physics and astronomy, a frame of reference (or reference frame) is an abstract coordinate system whose origin, orientation, and scale are specified by a set of reference points― geometric points whose position is identified both mathema ...
it is called proper charge density. It turns out the charge density ''ρ'' and
current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
J transform together as a
four-current In special and general relativity, the four-current (technically the four-current density) is the four-dimensional analogue of the electric current density. Also known as vector current, it is used in the geometric context of ''four-dimensional spa ...
vector under
Lorentz transformations In physics, the Lorentz transformations are a six-parameter family of linear transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation i ...
.


Charge density in quantum mechanics

In
quantum mechanics Quantum mechanics is a fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including quantum chemistry, ...
, charge density ''ρ''''q'' is related to
wavefunction A wave function in quantum physics is a mathematical description of the quantum state of an isolated quantum system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements mad ...
''ψ''(r) by the equation \rho_q(\mathbf) = q , \psi(\mathbf r), ^2 where ''q'' is the charge of the particle and is the
probability density function In probability theory, a probability density function (PDF), or density of a continuous random variable, is a function whose value at any given sample (or point) in the sample space (the set of possible values taken by the random variable) can ...
i.e. probability per unit volume of a particle located at r. When the wavefunction is normalized - the average charge in the region r ∈ ''R'' is Q= \int_R q , \psi(\mathbf r), ^2 \, d^3 \mathbf where ''d''3r is the integration measure over 3d position space.


Application

The charge density appears in the
continuity equation A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. S ...
for electric current, and also in
Maxwell's Equations Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. ...
. It is the principal source term of the
electromagnetic field An electromagnetic field (also EM field or EMF) is a classical (i.e. non-quantum) field produced by (stationary or moving) electric charges. It is the field described by classical electrodynamics (a classical field theory) and is the classical c ...
; when the charge distribution moves, this corresponds to a
current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
. The charge density of molecules impacts chemical and separation processes. For example, charge density influences metal-metal bonding and
hydrogen bonding In chemistry, a hydrogen bond (or H-bond) is a primarily electrostatic force of attraction between a hydrogen (H) atom which is covalently bound to a more electronegative "donor" atom or group (Dn), and another electronegative atom bearing a l ...
. For separation processes such as
nanofiltration Nanofiltration is a membrane filtration process used most often to soften and disinfect water. Overview Nanofiltration is a membrane filtration-based method that uses nanometer sized pores through which particles smaller than 10 nanometers pa ...
, the charge density of ions influences their rejection by the membrane.


See also

*
Continuity equation A continuity equation or transport equation is an equation that describes the transport of some quantity. It is particularly simple and powerful when applied to a conserved quantity, but it can be generalized to apply to any extensive quantity. S ...
relating charge density and
current density In electromagnetism, current density is the amount of charge per unit time that flows through a unit area of a chosen cross section. The current density vector is defined as a vector whose magnitude is the electric current per cross-sectional ar ...
*
Ionic potential Ionic potential is the ratio of the electrical charge (''z'') to the radius (''r'') of an ion. \text = \frac = \frac As such, this ratio is a measure of the charge density at the surface of the ion; usually the denser the charge, the stronger ...
*
Charge density wave A charge density wave (CDW) is an ordered quantum fluid of electrons in a linear chain compound or layered crystal. The electrons within a CDW form a standing wave pattern and sometimes collectively carry an electric current. The electrons in such ...


References

* * * * *{{cite book, author=C.B. Parker, edition=2nd, title=McGraw Hill Encyclopaedia of Physics, year=1994, publisher=VHC publishers, isbn=978-0-07-051400-3, url=https://archive.org/details/mcgrawhillencycl1993park


External links



- Spatial charge distributions Density Electric charge es:Carga eléctrica#Densidad de carga eléctrica