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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 o ...
, 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 Vector most often refers to: *Euclidean vector, a quantity with a magnitude and a direction *Vector (epidemiology), an agent that carries and transmits an infectious pathogen into another living organism Vector may also refer to: Mathematic ...
whose magnitude is the
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 movi ...
per cross-sectional area at a given point in space, its direction being that of the motion of the positive charges at this point. In
SI base unit The SI base units are the standard units of measurement defined by the International System of Units (SI) for the seven base quantities of what is now known as the International System of Quantities: they are notably a basic set from which al ...
s, the electric current density is measured in
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
s per
square metre The square metre ( international spelling as used by the International Bureau of Weights and Measures) or square meter (American spelling) is the unit of area in the International System of Units (SI) with symbol m2. It is the area of a square ...
.


Definition

Assume that ''A'' (SI unit: m2) is a small surface centred at a given point ''M'' and orthogonal to the motion of the charges at ''M''. If ''I'' (SI unit: A) is the
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 movi ...
flowing through ''A'', then electric current density ''j'' at ''M'' is given by the
limit Limit or Limits may refer to: Arts and media * ''Limit'' (manga), a manga by Keiko Suenobu * ''Limit'' (film), a South Korean film * Limit (music), a way to characterize harmony * "Limit" (song), a 2016 single by Luna Sea * "Limits", a 2019 ...
: :j = \lim_ \frac = \left.\frac \_, with surface ''A'' remaining centered at ''M'' and orthogonal to the motion of the charges during the limit process. The current density vector j is the vector whose magnitude is the electric current density, and whose direction is the same as the motion of the positive charges at ''M''. At a given time ''t'', if v is the velocity of the charges at ''M'', and ''dA'' is an infinitesimal surface centred at ''M'' and orthogonal to v, then during an amount of time ''dt'', only the charge contained in the volume formed by ''dA'' and will flow through ''dA''. This charge is equal to , where ''ρ'' is the
charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system i ...
at ''M'', and the electric current at ''M'' is . It follows that the current density vector can be expressed as: :\mathbf = \rho \mathbf. The
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 ...
of j over a
surface A surface, as the term is most generally used, is the outermost or uppermost layer of a physical object or space. It is the portion or region of the object that can first be perceived by an observer using the senses of sight and touch, and is ...
''S'', followed by an integral over the time duration ''t''1 to ''t''2, gives the total amount of charge flowing through the surface in that time (): :q=\int_^\iint_S \mathbf\cdot\mathbf\,dA \,dt. More concisely, this is the integral of the
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 ...
of j across ''S'' between ''t''1 and ''t''2. The
area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a shape or planar lamina, while '' surface area'' refers to the area of an op ...
required to calculate the flux is real or imaginary, flat or curved, either as a cross-sectional area or a surface. For example, for charge carriers passing through an
electrical conductor In physics and electrical engineering, a conductor is an object or type of material that allows the flow of charge (electric current) in one or more directions. Materials made of metal are common electrical conductors. Electric current is gene ...
, the area is the cross-section of the conductor, at the section considered. The
vector area In 3-dimensional geometry and vector calculus, an area vector is a vector combining an area quantity with a direction, thus representing an ''oriented area'' in three dimensions. Every bounded surface in three dimensions can be associated with ...
is a combination of the magnitude of the area through which the charge carriers pass, ''A'', and a
unit vector In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat"). The term ''direction v ...
normal to the area, \mathbf. The relation is \mathbf = A \mathbf. The differential vector area similarly follows from the definition given above: d\mathbf = dA \mathbf. If the current density j passes through the area at an angle ''θ'' to the area normal \mathbf, then :\mathbf\cdot\mathbf= j\cos\theta where ⋅ is the
dot product In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alg ...
of the unit vectors. That is, the component of current density passing through the surface (i.e. normal to it) is , while the component of current density passing tangential to the area is , but there is ''no'' current density actually passing ''through'' the area in the tangential direction. The ''only'' component of current density passing normal to the area is the cosine component.


Importance

Current density is important to the design of electrical and
electronic Electronic may refer to: *Electronics, the science of how to control electric energy in semiconductor * ''Electronics'' (magazine), a defunct American trade journal *Electronic storage, the storage of data using an electronic device *Electronic co ...
systems. Circuit performance depends strongly upon the designed current level, and the current density then is determined by the dimensions of the conducting elements. For example, as
integrated circuit An integrated circuit or monolithic integrated circuit (also referred to as an IC, a chip, or a microchip) is a set of electronic circuits on one small flat piece (or "chip") of semiconductor material, usually silicon. Large numbers of tiny ...
s are reduced in size, despite the lower current demanded by smaller devices, there is a trend toward higher current densities to achieve higher device numbers in ever smaller
chip Chromatin immunoprecipitation (ChIP) is a type of immunoprecipitation experimental technique used to investigate the interaction between proteins and DNA in the cell. It aims to determine whether specific proteins are associated with specific genom ...
areas. See
Moore's law Moore's law is the observation that the number of transistors in a dense integrated circuit (IC) doubles about every two years. Moore's law is an observation and projection of a historical trend. Rather than a law of physics, it is an empi ...
. At high frequencies, the conducting region in a wire becomes confined near its surface which increases the current density in this region. This is known as the
skin effect Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the co ...
. High current densities have undesirable consequences. Most electrical conductors have a finite, positive resistance, making them dissipate
power Power most often refers to: * Power (physics), meaning "rate of doing work" ** Engine power, the power put out by an engine ** Electric power * Power (social and political), the ability to influence people or events ** Abusive power Power may a ...
in the form of heat. The current density must be kept sufficiently low to prevent the conductor from melting or burning up, the insulating material failing, or the desired electrical properties changing. At high current densities the material forming the interconnections actually moves, a phenomenon called ''
electromigration Electromigration is the transport of material caused by the gradual movement of the ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms. The effect is important in applications where high dir ...
''. In
superconductors Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic flux fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike ...
excessive current density may generate a strong enough magnetic field to cause spontaneous loss of the superconductive property. The analysis and observation of current density also is used to probe the physics underlying the nature of solids, including not only metals, but also semiconductors and insulators. An elaborate theoretical formalism has developed to explain many fundamental observations. The current density is an important parameter in Ampère's circuital law (one of
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 ...
), which relates current density to
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 ...
. 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 law ...
theory, charge and current are combined into a
4-vector In special relativity, a four-vector (or 4-vector) is an object with four components, which transform in a specific way under Lorentz transformations. Specifically, a four-vector is an element of a four-dimensional vector space considered as a ...
.


Calculation of current densities in matter


Free currents

Charge carriers which are free to move constitute a free current density, which are given by expressions such as those in this section. Electric current is a coarse, average quantity that tells what is happening in an entire wire. At position r at time ''t'', the ''distribution'' of
charge Charge or charged may refer to: Arts, entertainment, and media Films * '' Charge, Zero Emissions/Maximum Speed'', a 2011 documentary Music * ''Charge'' (David Ford album) * ''Charge'' (Machel Montano album) * ''Charge!!'', an album by The Aqu ...
flowing is described by the current density: :\mathbf(\mathbf, t) = \rho(\mathbf,t) \; \mathbf_\text (\mathbf,t) \, where j(r, ''t'') is the current density vector, vd(r, ''t'') is the particles' average
drift velocity In physics, a drift velocity is the average velocity attained by charged particles, such as electrons, in a material due to an electric field. In general, an electron in a conductor will propagate randomly at the Fermi velocity, resulting in an a ...
(SI unit: ms−1), and :\rho(\mathbf, t) = q \, n(\mathbf,t) is the
charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system i ...
(SI unit: coulombs per
cubic metre The cubic metre (in Commonwealth English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the unit of volume in the International System of Units (SI). Its symbol is m ...
), in which ''n''(r, ''t'') is the number of particles per unit volume ("number density") (SI unit: m−3), ''q'' is the charge of the individual particles with density ''n'' (SI unit:
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). A common approximation to the current density assumes the current simply is proportional to the electric field, as expressed by: :\mathbf = \sigma \mathbf \, where E is the
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 ...
and ''σ'' is the
electrical 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 ...
. Conductivity ''σ'' is the
reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another pol ...
(
inverse Inverse or invert may refer to: Science and mathematics * Inverse (logic), a type of conditional sentence which is an immediate inference made from another conditional sentence * Additive inverse (negation), the inverse of a number that, when a ...
) of electrical
resistivity 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 ...
and has the SI units of
siemens Siemens AG ( ) is a German multinational conglomerate corporation and the largest industrial manufacturing company in Europe headquartered in Munich with branch offices abroad. The principal divisions of the corporation are ''Industry'', ''E ...
per
metre 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 pre ...
(S⋅m−1), and E has the SI units of newtons per
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 ...
(N⋅C−1) or, equivalently,
volt The volt (symbol: V) is the unit of electric potential, electric potential difference (voltage), and electromotive force in the International System of Units (SI). It is named after the Italian physicist Alessandro Volta (1745–1827). Defin ...
s per
metre 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 pre ...
(V⋅m−1). A more fundamental approach to calculation of current density is based upon: :\mathbf (\mathbf, t) = \int_^t \left \int_ \sigma(\mathbf-\mathbf', t-t') \; \mathbf(\mathbf', t') \; \text^3 \mathbf' \, \right\textt' \, indicating the lag in response by the time dependence of ''σ'', and the non-local nature of response to the field by the spatial dependence of ''σ'', both calculated in principle from an underlying microscopic analysis, for example, in the case of small enough fields, the linear response function for the conductive behaviour in the material. See, for example, Giuliani & Vignale (2005) or Rammer (2007). The integral extends over the entire past history up to the present time. The above conductivity and its associated current density reflect the fundamental mechanisms underlying charge transport in the medium, both in time and over distance. A
Fourier transform A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed ...
in space and time then results in: :\mathbf (\mathbf, \omega) = \sigma(\mathbf, \omega) \; \mathbf(\mathbf, \omega) \, where ''σ''(k, ''ω'') is now a complex function. In many materials, for example, in crystalline materials, the conductivity is a
tensor In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects related to a vector space. Tensors may map between different objects such as vectors, scalars, and even other tensor ...
, and the current is not necessarily in the same direction as the applied field. Aside from the material properties themselves, the application of magnetic fields can alter conductive behaviour.


Polarization and magnetization currents

Currents arise in materials when there is a non-uniform distribution of 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 ma ...
materials, there is a current density corresponding to the net movement 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). ...
s per unit volume, i.e. the polarization P: :\mathbf_\mathrm=\frac Similarly with
magnetic materials A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, ...
, circulations of the
magnetic dipole moment In electromagnetism, the magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include loops of electric current (such as electromagnet ...
s per unit volume, i.e. the
magnetization In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or D ...
M, lead to magnetization currents: :\mathbf_\mathrm=\nabla\times\mathbf Together, these terms add up to form the
bound current In classical electromagnetism, magnetization is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. Movement within this field is described by direction and is either Axial or Dia ...
density in the material (resultant current due to movements of electric and magnetic dipole moments per unit volume): :\mathbf_\mathrm=\mathbf_\mathrm+\mathbf_\mathrm


Total current in materials

The total current is simply the sum of the free and bound currents: :\mathbf = \mathbf_\mathrm+\mathbf_\mathrm


Displacement current

There is also a
displacement current In electromagnetism, displacement current density is the quantity appearing in Maxwell's equations that is defined in terms of the rate of change of , the electric displacement field. Displacement current density has the same units as electric ...
corresponding to the time-varying
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: :\mathbf_\mathrm=\frac which is an important term in Ampere's circuital law, one of Maxwell's equations, since absence of this term would not predict
electromagnetic waves In physics, electromagnetic radiation (EMR) consists of waves of the electromagnetic (EM) field, which propagate through space and carry momentum and electromagnetic radiant energy. It includes radio waves, microwaves, infrared, (visible) ...
to propagate, or the time evolution of
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 ...
s in general.


Continuity equation

Since charge is conserved, current density must satisfy 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. ...
. Here is a derivation from first principles. The net flow out of some volume ''V'' (which can have an arbitrary shape but fixed for the calculation) must equal the net change in charge held inside the volume: :\int_S = -\frac \int_V = - \int_V where ''ρ'' is the
charge density In electromagnetism, charge density is the amount of electric charge per unit length, surface area, or volume. Volume charge density (symbolized by the Greek letter ρ) is the quantity of charge per unit volume, measured in the SI system i ...
, and dA is a surface element of the surface ''S'' enclosing the volume ''V''. The surface integral on the left expresses the current ''outflow'' from the volume, and the negatively signed
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 ...
on the right expresses the ''decrease'' in the total charge inside the volume. From 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 ...
: :\int_S = \int_V Hence: :\int_V\ = - \int_V This relation is valid for any volume, independent of size or location, which implies that: :\nabla \cdot \mathbf = - \frac and this relation is called 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. ...
.


In practice

In
electrical wiring Electrical wiring is an electrical installation of cabling and associated devices such as switches, distribution boards, sockets, and light fittings in a structure. Wiring is subject to safety standards for design and installation. Allowable ...
, the maximum current density (for a given temperature rating) can vary from 4 A⋅mm−2 for a wire with no air circulation around it, to over 6 A⋅mm−2 for a wire in free air. Regulations for
building wiring Electrical wiring is an electrical installation of cabling and associated devices such as switches, distribution boards, sockets, and light fittings in a structure. Wiring is subject to safety standards for design and installation. Allowable ...
list the maximum allowed current of each size of cable in differing conditions. For compact designs, such as windings of SMPS transformers, the value might be as low as 2 A⋅mm−2. If the wire is carrying high-frequency
alternating current Alternating current (AC) is an electric current which periodically reverses direction and changes its magnitude continuously with time in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in whic ...
s, the
skin effect Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the co ...
may affect the distribution of the current across the section by concentrating the current on the surface of the conductor. In
transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple circuits. A varying current in any coil of the transformer produces a varying magnetic flux in the transformer' ...
s designed for high frequencies, loss is reduced if
Litz wire Litz wire is a particular type of multistrand wire or cable used in electronics to carry alternating current (AC) at radio frequencies. The wire is designed to reduce the skin effect and proximity effect losses in conductors used at frequencie ...
is used for the windings. This is made of multiple isolated wires in parallel with a diameter twice the
skin depth Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor such that the current density is largest near the surface of the conductor and decreases exponentially with greater depths in the co ...
. The isolated strands are twisted together to increase the total skin area and to reduce the resistance due to skin effects. For the top and bottom layers of
printed circuit boards A printed circuit board (PCB; also printed wiring board or PWB) is a medium used in electrical and electronic engineering to connect electronic components to one another in a controlled manner. It takes the form of a laminated sandwich struc ...
, the maximum current density can be as high as 35 A⋅mm−2 with a copper thickness of 35 μm. Inner layers cannot dissipate as much heat as outer layers; designers of circuit boards avoid putting high-current traces on inner layers. In the
semiconductors A semiconductor is a material which has an electrical conductivity value falling between that of a conductor, such as copper, and an insulator, such as glass. Its resistivity falls as its temperature rises; metals behave in the opposite way. ...
field, the maximum current densities for different elements are given by the manufacturer. Exceeding those limits raises the following problems: * The
Joule effect Joule effect and Joule's law are any of several different physical effects discovered or characterized by English physicist James Prescott Joule. These physical effects are not the same, but all are frequently or occasionally referred to in the lit ...
which increases the temperature of the component. * The electromigration effect which will erode the interconnection and eventually cause an open circuit. * The slow diffusion effect which, if exposed to high temperatures continuously, will move metallic ions and
dopants A dopant, also called a doping agent, is a trace of impurity element that is introduced into a chemical material to alter its original electrical or optical properties. The amount of dopant necessary to cause changes is typically very low. Whe ...
away from where they should be. This effect is also synonym to ageing. The following table gives an idea of the maximum current density for various materials. Even if manufacturers add some margin to their numbers, it is recommended to, at least, double the calculated section to improve the reliability, especially for high-quality electronics. One can also notice the importance of keeping electronic devices cool to avoid exposing them to
electromigration Electromigration is the transport of material caused by the gradual movement of the ions in a conductor due to the momentum transfer between conducting electrons and diffusing metal atoms. The effect is important in applications where high dir ...
and slow
diffusion Diffusion is the net movement of anything (for example, atoms, ions, molecules, energy) generally from a region of higher concentration to a region of lower concentration. Diffusion is driven by a gradient in Gibbs free energy or chemical ...
. In
biological organism In biology, an organism () is any living system that functions as an individual entity. All organisms are composed of cells (cell theory). Organisms are classified by taxonomy into groups such as multicellular animals, plants, and fungi ...
s,
ion channel Ion channels are pore-forming membrane proteins that allow ions to pass through the channel pore. Their functions include establishing a resting membrane potential, shaping action potentials and other electrical signals by gating the flow of ...
s regulate the flow of ions (for example,
sodium Sodium is a chemical element with the symbol Na (from Latin ''natrium'') and atomic number 11. It is a soft, silvery-white, highly reactive metal. Sodium is an alkali metal, being in group 1 of the periodic table. Its only stable ...
,
calcium Calcium is a chemical element with the symbol Ca and atomic number 20. As an alkaline earth metal, calcium is a reactive metal that forms a dark oxide-nitride layer when exposed to air. Its physical and chemical properties are most similar ...
,
potassium Potassium is the chemical element with the symbol K (from Neo-Latin '' kalium'') and atomic number19. Potassium is a silvery-white metal that is soft enough to be cut with a knife with little force. Potassium metal reacts rapidly with atmos ...
) across the
membrane A membrane is a selective barrier; it allows some things to pass through but stops others. Such things may be molecules, ions, or other small particles. Membranes can be generally classified into synthetic membranes and biological membranes. ...
in all
cells Cell most often refers to: * Cell (biology), the functional basic unit of life Cell may also refer to: Locations * Monastic cell, a small room, hut, or cave in which a religious recluse lives, alternatively the small precursor of a monastery w ...
. The membrane of a cell is assumed to act like a capacitor. Current densities are usually expressed in pA⋅pF−1 (
pico Pico may refer to: Places The Moon * Mons Pico, a lunar mountain in the northern part of the Mare Imbrium basin Portugal * Pico, a civil parish in the municipality of Vila Verde * Pico da Pedra, a civil parish in the municipality of Ribe ...
ampere The ampere (, ; symbol: A), often shortened to amp,SI supports only the use of symbols and deprecates the use of abbreviations for units. is the unit of electric current in the International System of Units (SI). One ampere is equal to elect ...
s per
pico Pico may refer to: Places The Moon * Mons Pico, a lunar mountain in the northern part of the Mare Imbrium basin Portugal * Pico, a civil parish in the municipality of Vila Verde * Pico da Pedra, a civil parish in the municipality of Ribe ...
farad The farad (symbol: F) is the unit of electrical capacitance, the ability of a body to store an electrical charge, in the International System of Units (SI). It is named after the English physicist Michael Faraday (1791–1867). In SI base unit ...
) (i.e., current divided by
capacitance Capacitance is the capability of a material object or device to store electric charge. It is measured by the change in charge in response to a difference in electric potential, expressed as the ratio of those quantities. Commonly recognized are ...
). Techniques exist to empirically measure capacitance and surface area of cells, which enables calculation of current densities for different cells. This enables researchers to compare ionic currents in cells of different sizes. In gas discharge lamps, such as flashlamps, current density plays an important role in the output
spectrum A spectrum (plural ''spectra'' or ''spectrums'') is a condition that is not limited to a specific set of values but can vary, without gaps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors ...
produced. Low current densities produce
spectral line A spectral line is a dark or bright line in an otherwise uniform and continuous spectrum, resulting from emission or absorption of light in a narrow frequency range, compared with the nearby frequencies. Spectral lines are often used to ident ...
emission spectrum, emission and tend to favour longer wavelengths. High current densities produce continuum emission and tend to favour shorter wavelengths. Low current densities for flash lamps are generally around 10 A⋅mm−2. High current densities can be more than 40 A⋅mm−2.


See also

*Hall effect *Quantum Hall effect *Superconductivity *Electron mobility *Drift velocity *Effective mass (solid-state physics), Effective mass *Electrical resistance *Sheet resistance *Speed of electricity *Electrical conduction *Green–Kubo relations *Green's function (many-body theory)


References

{{Authority control Electromagnetism Density