The QUDT Ontologies, and derived XML Vocabularies, are being developed by TopQuadrant and NASA. Originally, they were developed for the NASA Exploration Initiatives Ontology Models (NExIOM) project, a Constellation Program initiative at the AMES Research Center (ARC). They now for the basis of the NASA QUDT Handbook to be published by NASA Headquarters.
The current release of the QUDT ontologies is version 1.1 and may be downloaded from the QUDT Catalog, which can also be accessed from LinkedModel.org.
Release 2 of QUDT will be published incrementally. Currently the content, in the form of the NASA QUDT Handbook, is being reviewed by NASA.
A presentation on QUDT can be found at scribd.com/ralphtq.
The goals of QUDT are to provide:
The QUDT Specification is more than a list of quantities, units, dimensions, data types, enumerations, and structures. In order to provide for interoperability and data exchange between information systems, the specification needs to be available in a machine processable form, with no ambiguities.
For these reasons, the QUDT approach to specifying quantities, units, dimensions, data types, enumerations, and other data structures is to use precise semantically grounded specifications in an ontology model with translation into machine-processable representations.
Ontologies provide the object-oriented strengths of encapsulation, inheritance, and polymorphism, strengths which are unavailable in other structured modeling approaches. The characteristics modeled in QUDT require a model-based approach because they are functionally dependent.
Modeling one without modeling its dependency on the other requires that the understanding of those dependencies be carried by the observer, which injects ambiguity into the modeling approach. These models (dimensions, coordinate systems, etc.), like everything else, are hierarchical, so using a language to model them which doesn't support inheritance imposes constraints on the models and their use which, again, results in ambiguity.
QUDT semantics are based on dimensional analysis expressed in the OWL Web Ontology Language (OWL). The dimensional approach relates each unit to a system of base units using numeric factors and a vector of exponents defined over a set of fundamental dimensions. In this way, the role of each base unit in the derived unit is precisely defined. A further relationship establishes the semantics of units and quantity kinds. By this means, QUDT supports reasoning over quantities as well as units.
All QUDT models may be translated into other representations for machine processing, or other programming language structures according to need.
An overview of the ontological structure of QUDT is provided below.
The diagram below, exported from TopBraid Composer, illustrates the main class structure of the QUDT ontology in OWL.
A Quantity is an observable property of an object, event or system that can be measured and quantified numerically. Quantities are differentiated by two attributes which together comprise the essential parameters needed to formalize the structure of quantities: kind and magnitude. The kind attribute of a quantity identifies the observable property quantified, e.g. length, force, frequency; the magnitude of the quantity expresses its relative size compared to other quantities of the same kind.
For example, the speed of light in a vacuum and the escape velocity of the Earth are both quantities of the kind speed but are of different magnitudes. The speed of light in a vacuum is greater than the escape velocity of the Earth. More generally, the speed of light in a vacuum is comparable to the escape velocity of the Earth. Thus, if two quantities are of the same kind, their magnitudes can be compared and ordered. However, the same is not true if the quantities are of different kinds. There is no intrinsic way to compare the magnitude of a quantity of mass with the magnitude of a quantity of length.
Quantities may arise from definition or convention, or they may be the result of one or a series of experiments and measurements. In the first case, the quantity is exact; in the second case, measurement uncertainty cannot be discounted so the expression of a quantity's magnitude must account for the parameters of uncertainty.
A Quantity Kind is any observable property that can be measured and quantified numerically. Familiar examples include physical properties such as length, mass, time, force, energy, power, electric charge, etc. Less familiar examples include currency, interest rate, price to earning ratio, and information capacity.
A Unit of Measure or Unit is a particular quantity of a given kind that has been chosen as a scale for measuring other quantities of the same kind. For example, the Meter is a quantity of length that has been empirically defined by the BIPM. Any quantity of length can be expressed as a number multiplied by the unit meter.
More formally, the value of a quantity Q with respect to a unit (U) is expressed as the scalar multiple of a real number (n) and U:
Q = nU
A quantity value expresses the magnitude and kind of a quantity and is given
by the product of a numerical value n
and a unit of measure U
. The number multiplying
the unit is referred to as the numerical value of the quantity expressed in that
unit. Refer to NIST SP 811 section 7 for more on quantity values.
The numerical value of a quantity is the numerical value without the unit of measure.
For example, the value of Planck's
constant in Joule-Seconds (J s) is approximately 6.62606896E-34
, whereas
the value in Erg-Seconds (erg s) is approximately 6.62606896E-27
.
The numerical value of a quantity n
is a mere scaling factor for the unit U
.
It is the product of the two, n X U
, that expresses the value (magnitude and quantity kind) of the unit.
In the same way that a unit has a symbol, a quantity also has a symbol.
For example a quantity of the (quantity) kind mass usually has the symbol m
.
Each quantity kind has a recommended symbol associated with it.
For example, t
for time, Q
for charge, v
for velocity, T
for temperature, P
for power and p
for pressure.
A quantity usually receives a symbol that consists of the symbol of its quantity kind and an optional subscript.
Symbols for quantities should be chosen according to the international recommendations from ISO/IEC~80000, the IUPAP red book and the IUPAC green book.
The OWL model for the classes qudt:QuantityKind, qudt:Quantity, qudt:QuantityValue, qudt:Unit is shown below.
The art and science of defining, standardizing, and organizing quantity kinds and units is ancient and modern. Today, scientific boards and standards bodies maintain rigorous definitions for quantity kinds and units. The definitions of quantity kinds and their relationships are derived from physical laws and mathematical transformations. Units are defined by experimental observations, by the application of physical laws, as ratios of fundamental physical constants, or by reference. One significant advance in the modern treatment of metrology has been the use of logic and mathematics to organize quantity kinds and units into systems and to analyze the relationships between them.
A system of quantity kinds is a set of one or more quantity kinds together with a set of zero or more algebraic equations that define relationships between quantity kinds in the set. In the physical sciences, the equations relating quantity kinds are typically physical laws and definitional relations, and constants of proportionality. Examples include Newton’s First Law of Motion, Coulomb’s Law, and the definition of velocity as the instantaneous change in position.
In almost all cases, the system identifies a subset of base quantity kinds. The base set is chosen so that all other quantity kinds of interest can be derived from the base quantity kinds and the algebraic equations.
A system of units is a set of units which are chosen as the reference scales for some set of quantity kinds together with the definitions of each unit. Units may be defined by experimental observation or by proportion to another unit not included in the system. If the unit system is explicitly associated with a quantity kind system, then the unit system must define at least one unit for each quantity kind.
Many systems of quantity kinds identify a special subset of the included quantity kinds called the base quantity kinds. Base quantity kinds are typically chosen so that no base quantity kind can be expressed as an algebraic relation of one or more other base quantity kinds using only the constituent equations included in the system. A quantity kind that can be expressed as an algebraic relation of one or more base quantity kind is called a derived quantity kind. Thus, in any quantity kind system, the base set and derived set are disjoint.
Similarly, unit systems may distinguish between base units and derived units. A base unit is a unit of measurement for a base quantity, and a derived unit is a unit of measurement for a derived quantity. Unit systems define at least one base unit for each base quantity and at least one derived unit for each derived quantity.
Quantity kind systems that define base and derived sets have certain mathematical properties that permit quantity kinds to be manipulated symbolically. The construction goes as follows: Assign a distinct dimension symbol to each base quantity kind. For each derived quantity kind, take the formula that expresses it in terms of the base quantity kinds and replace every occurrence of a base quantity with its symbol. This is the dimension symbol for the derived quantity kind. In this way, every quantity kind maps to a dimension symbol of the form:
dim Q = (B_{1})^{d1}(B_{2})^{d2}…(B_{n})^{dn}
Here {B_{1},…,B_{n}} are the dimension symbols for the base quantities and {d_{1},…,d_{n}} are rational numbers. Typically, the values of the d_{i} are between -3 and 3, however magnitudes as high as 7 are required to cover the range of quantity kinds currently defined. Using the multiplication identity for exponents A^{n}A^{m} = A^{n+m} one can show that the set of dimension symbols is homomorphic to an n-dimensional vector space over the rational numbers. Multiplication of quantity kinds corresponds to vector addition, division corresponds to vector subtraction, and inverting a quantity kind corresponds to computing the additive inverse of its dimension vector.
In some cases, distinct quantity kinds may have the same dimension symbol. This often occurs in cases where physical laws are discovered and formalized independently of each other, but reduce to the same base quantity kinds. A commonly quoted example is the dimensional equivalence of mechanical torque and energy. Both have the same dimensions (L^{2}M^{1}T^{-2}) but are defined very differently.
One consequence of the equivalence is that the same units of measure are applicable to both. A salient difference between the two in this example is that torque is a pseudo-vector while energy is a scalar. However, this distinction (value type) is not accounted for in the quantity kind system formalism.
The OWL model of Dimensions is illustrated below.
Dimensionless Quantities, or quantities of dimension 1, are those for which all the exponents of the factors corresponding to the base quantities in its quantity dimension are zero. Counts, ratios and plane angles are examples of dimensionless quantities.
Some unit systems identify units that are not defined within the system but are allowed to be used in combination with units that are defined within the system. Allowed units must be commensurable with some defined unit of the system, so that quantities expressed in the allowed unit may be converted to a defined unit. The SI System explicitly allows a number of non-SI units.
This section contains tables of several of the quantity kind and unit systems that are currently defined in the ontology. The table columns are:
Category – Either “Base᾿, “Derived᾿, or “TBD᾿
Quantity Kind – The name of the quantity kind
Quantity QName – The QName of the quantity kind
Dimension Symbol – The dimension symbol for the quantity kind. For derived quantity kinds, the symbol is a linear combination of the base quantity symbols, as described above.
Unit – The name of a unit in the unit system that is the defined unit for the quantity kind
Unit QName – The QName of the unit
Unit Symbol – A common symbol or abbreviation for the unit
SI Base and Derived Quantities and Units
Category |
Quantity Kind |
QName |
Dimension Symbol |
Unit |
QName |
Unit Symbol |
Base |
Dimensionless |
U |
Unity |
U |
||
Length |
L |
Meter |
m |
|||
Mass |
M |
Kilogram |
kg |
|||
Time |
T |
Second |
s |
|||
Electric Current |
I |
Ampere |
A |
|||
Temperature |
Θ |
Kelvin |
K |
|||
Amount of Substance |
N |
Mole |
mol |
|||
Luminous Intensity |
J |
Candela |
cd |
|||
Derived |
Absorbed Dose |
L^{2}T^{-2} |
Gray |
Gy |
||
Absorbed Dose Rate |
L^{2}T^{-3} |
Gray per second |
Gy/s |
|||
Activity |
T^{-1} |
Becquerel |
Bq |
|||
Amount of Substance Per Unit Volume |
L^{-3}N^{1} |
Mole per cubic meter |
mol/m^3 |
|||
Amount of Substance per Unit Mass |
M^{-3}N^{1} |
Mole per kilogram |
mol/kg |
|||
Angular Acceleration |
U^{1}T^{-2} |
Radian per second squared |
rad/s^2 |
|||
Angular Mass |
L^{2}M^{1} |
Kilogram Meter Squared |
kg-m^2 |
|||
Angular Momentum |
L^{2}M^{1}T^{-1} |
Joule Second |
J s |
|||
Angular Velocity |
U^{1}T^{-1} |
Radian per second |
rad/s |
|||
Area |
L^{2} |
Square meter |
m^2 |
|||
Area Angle |
U^{1}L^{2} |
Square meter steradian |
m^2-sr |
|||
Area Temperature |
L^{2}Θ^{1} |
Square meter kelvin |
m^2-K |
|||
Area Thermal Expansion |
L^{2}Θ^{-1} |
Square meter per kelvin |
m^2/K |
|||
Capacitance |
L^{-2}M^{-1}T^{4}I^{2} |
Farad |
F |
|||
Catalytic Activity |
T^{-1}N^{1} |
Katal |
kat |
|||
Coefficient of Heat Transfer |
M^{1}T^{-3}Θ^{-1} |
Watt per square meter kelvin |
W/(m^2-K) |
|||
Density |
L^{-3}M^{1} |
Kilogram per cubic meter |
kg/m^3 |
|||
Dose Equivalent |
L^{2}T^{-2} |
Sievert |
Sv |
|||
Dynamic Viscosity |
L^{-1}M^{1}T^{-1} |
Pascal second |
Pa-s |
|||
Electric Charge |
T^{1}I^{1} |
Coulomb |
C |
|||
Electric Charge Line Density |
L^{-1}T^{1}I^{1} |
Coulomb per meter |
C/m |
|||
Electric Charge Volume Density |
L^{-3}T^{1}I^{1} |
Coulomb per cubic meter |
C/m^3 |
|||
Electric Charge per Amount of Substance |
T^{1}I^{1}N^{-1} |
Coulomb per mole |
C/mol |
|||
Electric Current Density |
L^{-2}I^{1} |
Ampere per square meter |
A/m^2 |
|||
Electric Current per Angle |
U^{-1}I^{1} |
Ampere per radian |
A/rad |
|||
Electric Dipole Moment |
L^{1}T^{1}I^{1} |
Coulomb meter |
C-m |
|||
Electric Field Strength |
L^{1}M^{1}T^{-3}I^{-1} |
Volt per Meter |
V/m |
|||
Electric Flux Density |
L^{-2}T^{1}I^{1} |
Coulomb per Square Meter |
C/m^2 |
|||
Electrical Conductivity |
L^{-2}M^{-1}T^{3}I^{2} |
Siemens |
S |
|||
Electromotive Force |
L^{2}M^{1}T^{-3}I^{-1} |
Volt |
V |
|||
Energy Density |
L^{-1}M^{1}T^{-2} |
Joule per cubic meter |
J/m^3 |
|||
Energy and Work |
L^{2}M^{1}T^{-2} |
Joule |
J |
|||
Energy per Unit Area |
M^{1}T^{-2} |
Joule per square meter |
J/m^2 |
|||
Exposure |
M^{-1}T^{1}I^{1} |
Coulomb per kilogram |
C/kg |
|||
Force |
L^{1}M^{1}T^{-2} |
Newton |
N |
|||
Force per Electric Charge |
L^{1}M^{1}T^{-3}I^{-1} |
Newton per coulomb |
N/C |
|||
Force per Unit Length |
M^{1}T^{-2} |
Newton per meter |
N/m |
|||
Frequency |
T^{-1} |
Hertz |
Hz |
|||
Inverse second time |
s^-1 |
|||||
Gravitational Attraction |
L^{3}M^{-1}T^{-2} |
Cubic meter per kilogram second squared |
m^3/(kg-s^2) |
|||
Heat Capacity and Entropy |
L^{2}M^{1}T^{-2}Θ^{-1} |
Joule per kelvin |
J/K |
|||
Heat Flow Rate |
L^{2}M^{1}T^{-3} |
Watt |
W |
|||
Heat Flow Rate per Unit Area |
M^{1}T^{-3} |
Watt per square meter |
W/m^2 |
|||
Illuminance |
U^{1}L^{-2}J^{1} |
Lux |
lx |
|||
Inductance |
L^{2}M^{1}T^{-2}I^{-2} |
Henry |
H |
|||
Inverse Amount of Substance |
N^{-1} |
Per mole |
mol^(-1) |
|||
Inverse Permittivity |
L^{3}M^{1}T^{-4}I^{-2} |
Meter per farad |
m/F |
|||
Kinematic Viscosity |
L^{2}T^{-1} |
Square meter per second |
m^2/sec |
|||
Length Mass |
L^{1}M^{1} |
Meter kilogram |
m-kg |
|||
Length Temperature |
L^{1}Θ^{1} |
Meter kelvin |
m-K |
|||
Linear Acceleration |
L^{1}T^{-2} |
Meter per second squared |
m/s^2 |
|||
Linear Momentum |
L^{1}M^{1}T^{-1} |
Kilogram Meter Per Second |
kg-m/s |
|||
Linear Thermal Expansion |
L^{1}Θ^{-1} |
Meter per kelvin |
m/K |
|||
Linear Velocity |
L^{1}T^{-1} |
Meter per second |
m/s |
|||
Luminance |
L^{-2}J^{1} |
Candela per square meter |
cd/m^2 |
|||
Luminous Flux |
U^{1}J^{1} |
Lumen |
lm |
|||
Magnetic Dipole Moment |
L^{2}I^{1} |
Joule per Tesla |
J/T |
|||
Magnetic Field Strength |
L^{-1}I^{1} |
Ampere Turn per Meter |
At/m |
|||
Ampere per meter |
A/m |
|||||
Magnetic Flux |
L^{2}M^{1}T^{-2}I^{-1} |
Weber |
Wb |
|||
Magnetic Flux Density |
M^{1}T^{-2}I^{-1} |
Tesla |
T |
|||
Magnetomotive Force |
U^{1}I^{1} |
Ampere Turn |
At |
|||
Mass Temperature |
M^{1}Θ^{1} |
Kilogram kelvin |
kg-K |
|||
Mass per Time |
M^{1}T^{-1} |
Kilogram per second |
kg/s |
|||
Mass per Unit Area |
L^{-2}M^{1} |
Kilogram per square meter |
kg/m^2 |
|||
Mass per Unit Length |
L^{-1}M^{1} |
Kilogram per meter |
kg/m |
|||
Molar Energy |
L^{2}M^{1}T^{-2}N^{-1} |
Joule per mole |
J/mol |
|||
Molar Heat Capacity |
L^{2}M^{1}T^{-2}Θ^{-1}N^{-1} |
Joule per mole kelvin |
J/(mol-K) |
|||
Permeability |
L^{1}M^{1}T^{-2}I^{-2} |
Henry per meter |
H/m |
|||
Permittivity |
L^{-3}M^{-1}T^{4}I^{2} |
Farad per meter |
F/m |
|||
Plane Angle |
U^{1} |
Radian |
rad |
|||
Power |
L^{2}M^{1}T^{-3} |
Watt |
W |
|||
Power per Angle |
U^{-1}L^{2}M^{1}T^{-3} |
Watt per steradian |
W/sr |
|||
Power per Area Angle |
U^{-1}M^{1}T^{-3} |
Watt per square meter steradian |
W/(m^2-sr) |
|||
Power per Unit Area |
M^{1}T^{-3} |
Watt per square meter |
W/m^2 |
|||
Pressure or Stress |
L^{-1}M^{1}T^{-2} |
Pascal |
Pa |
|||
Resistance |
L^{2}M^{1}T^{-3}I^{-2} |
Ohm |
Ohm |
|||
Solid Angle |
U^{1} |
Steradian |
sr |
|||
Specific Energy |
L^{2}T^{-2} |
Joule per kilogram |
J/kg |
|||
Specific Heat Capacity |
L^{2}T^{-2}Θ^{-1} |
Joule per kilogram kelvin |
J/(kg-K) |
|||
Specific Heat Pressure |
L^{3}M^{-1}Θ^{-1} |
Joule per kilogram kelvin per pascal |
J/(km-K-Pa) |
|||
Specific Heat Volume |
L^{-1}T^{-2}Θ^{-1} |
Joule per kilogram kelvin per cubic meter |
J/(kg-K-m^3) |
|||
Temperature Amount of Substance |
Θ^{1}N^{1} |
Mole kelvin |
mol-K |
|||
Thermal Conductivity |
L^{1}M^{1}T^{-3}Θ^{-1} |
Watt per meter kelvin |
W/(m*K) |
|||
Thermal Diffusivity |
L^{2}T^{-1} |
Square meter per second |
m^2/sec |
|||
Thermal Insulance |
M^{-1}T^{3}Θ^{1} |
Square meter Kelvin per watt |
(K^2)m/W |
|||
Thermal Resistance |
L^{-2}M^{-1}T^{3}Θ^{1} |
Kelvin per watt |
K/W |
|||
Thermal Resistivity |
L^{-1}M^{-1}T^{3}Θ^{1} |
Meter Kelvin per watt |
K-m/W |
|||
Thrust to Mass Ratio |
L^{1}T^{-2} |
Newton per kilogram |
N/kg |
|||
Time Squared |
T^{2} |
Second time squared |
s^2 |
|||
Torque |
L^{2}M^{1}T^{-2} |
Newton meter |
N-m |
|||
Volume |
L^{3} |
Cubic Meter |
m^3 |
|||
Volume Thermal Expansion |
L^{3}Θ^{-1} |
Cubic meter per kelvin |
m^3/K |
|||
Volume per Unit Time |
L^{3}T^{-1} |
Cubic meter per second |
m^3/s |
|||
Volumetric heat capacity |
L^{-1}M^{1}T^{-2}Θ^{-1} |
Joule per cubic meter kelvin |
J/(m^3 K) |
CGS Base and Derived Quantity Kinds and Units
Category |
Quantity Kind |
QName |
Dimension Symbol |
Unit |
QName |
Unit Symbol |
Base |
Dimensionless |
U |
Unity |
U |
||
Length |
L |
Centimeter |
cm |
|||
Mass |
M |
Gram |
g |
|||
Time |
T |
Second |
s |
|||
Derived |
Angular Momentum |
L^{2}M^{1}T^{-1} |
Erg second |
erg s |
||
Area |
L^{2} |
Square centimeter |
cm^2 |
|||
Dynamic Viscosity |
L^{-1}M^{1}T^{-1} |
Poise |
P |
|||
Energy Density |
L^{-1}M^{1}T^{-2} |
Erg per cubic centimeter |
erg/cm^3 |
|||
Energy and Work |
L^{2}M^{1}T^{-2} |
Erg |
erg |
|||
Force |
L^{1}M^{1}T^{-2} |
Dyne |
dyn |
|||
Frequency |
T^{-1} |
Inverse second time |
s^-1 |
|||
Linear Acceleration |
L^{1}T^{-2} |
Centimeter per second squared |
cm/s^2 |
|||
Linear Velocity |
L^{1}T^{-1} |
Centimeter per second |
cm/s |
|||
Power |
L^{2}M^{1}T^{-3} |
Erg per second |
erg/s |
|||
Power per Unit Area |
M^{1}T^{-3} |
Erg per square centimeter second |
erg/(cm^2-s) |
|||
Pressure or Stress |
L^{-1}M^{1}T^{-2} |
Dyne per square centimeter |
dyn/cm^2 |
|||
Time Area |
L^{2}T^{1} |
Square centimeter second |
cm^2-s |
|||
Torque |
L^{2}M^{1}T^{-2} |
Dyne centimeter |
dyn-cm |
|||
Volume |
L^{3} |
Cubic Centimeter |
cm^3 |
There are two different approaches to defining electric and magnetic quantities using the base CGS mechanical quantities of length, mass and time. The Electromagnetic Unit (EMU) approach derives electric charge from Coulomb’s Law, while the Electrostatic Unit (ESU) approach derives electric charge from Ampere’s Law.
Coulomb’s Law states that the force exerted between two charged particles, q_{1} and q_{2}, is inversely proportional to the square of their distance, r.
F=k(q_{1}q_{2})/r^{2}
Retaining only the terms of the quantity kinds involved (force, electric charge, distance), this equation can be rearranged to express electric charge as length multiplied by the square root of force. The CGS Electromagnetic Unit is called the Abcoulomb. The table below contains the dimension symbols and corresponding units of other electricity and magnetism quantity kinds in terms of the base CGS quantity kinds and the definition of electric charge above.
CGS EMU Derived Units for Electricity and Magnetism
Quantity Kind |
QName |
Dimension Symbol |
Unit |
QName |
Unit Symbol |
Capacitance |
L^{-1}T^{2} |
Abfarad |
abF |
||
Electric Charge |
L^{0.5}M^{0.5} |
Abcoulomb |
abC |
||
Electric Current |
L^{0.5}M^{0.5}T^{-1} |
Abampere |
abA |
||
Electric Field Strength |
L^{0.5}M^{0.5}T^{-2} |
Abvolt per Centimeter |
abV/cm |
||
Electric Flux Density |
L^{-1.5}M^{0.5} |
Abcoulomb per square centimeter |
abC/cm^2 |
||
Electrical Conductivity |
L^{-1}T^{1} |
Absiemen |
aS |
||
Electromotive Force |
L^{1.5}M^{0.5}T^{-2} |
Abvolt |
abV |
||
Inductance |
L^{1} |
Abhenry |
abH |
||
Magnetic Field Strength |
L^{-0.5}M^{0.5}T^{-1} |
Abtesla |
abT |
||
Magnetic Flux |
L^{1.5}M^{0.5}T^{-1} |
Abvolt Second |
abV-s |
||
Magnetic Flux Density |
L^{-0.5}M^{0.5}T^{-1} |
Abtesla |
abT |
||
Magnetomotive Force |
L^{0.5}M^{0.5}T^{-1} |
Gilbert |
Gi |
||
Permeability |
U^{1} |
Relative permeability |
μ _{r} |
||
Permittivity |
L^{-2}T^{2} |
Abfarad per centimeter |
abF/cm |
||
Resistance |
L^{1}T^{-1} |
Abohm |
abOhm |
Ampere’s Law of Magnetic Induction states that the force per unit length exerted between two infinite parallel wires at a distince, d, and carrying electric currents I_{1} and I_{2} is proportional to their product divided by the distance between them. I.e.
dF/dl = k(I_{1}I_{2}/d)
Retaining only the terms of the quantity kinds involved (force, electric current, distance), this equation can be rearranged to express electric current as the square root of force. The CGS Electrostatic Unit of electric current is called the Statampere. The table below contains the dimension symbols and corresponding units of other electricity and magnetism quantity kinds in terms of the base CGS quantity kinds and the definition of electric current above.
CGS ESU Derived Units for Electricity and Magnetism
Quantity Kind |
QName |
Dimension Symbol |
Unit |
QName |
Unit Symbol |
Capacitance |
L^{1} |
Statfarad |
statF |
||
Electric Charge |
L^{1.5}M^{0.5}T^{-1} |
Statcoulomb |
statC |
||
Electric Current |
L^{1.5}M^{0.5}T^{-2} |
Statampere |
statA |
||
Electric Field Strength |
L^{-0.5}M^{0.5}T^{-1} |
Statvolt per centimeter |
statV/cm |
||
Electric Flux Density |
L^{-0.5}M^{0.5}T^{-1} |
Statcoulomb per square centimeter |
statC/cm^2 |
||
Electromotive Force |
L^{0.5}M^{0.5}T^{-1} |
Statvolt |
statV |
||
Inductance |
L^{-1}T^{2} |
Stathenry |
statH |
||
Magnetic Field Strength |
L^{0.5}M^{0.5}T^{-2} |
Oersted |
Oe |
||
Magnetic Flux |
L^{0.5}M^{0.5} |
Maxwell |
Mx |
||
Magnetic Flux Density |
L^{-1.5}M^{0.5} |
Gauss |
G |
||
Magnetomotive Force |
L^{1.5}M^{0.5}T^{-2} |
Oersted centimeter |
Oe-cm |
||
Permeability |
L^{-2}T^{2} |
Stathenry per centimeter |
statH/cm |
||
Permittivity |
U^{1} |
Relative permittivity |
ε _{r} |
||
Resistance |
L^{-1}T^{1} |
Statohm |
statOhm |
[TBR]
Last Updated August 24, 2013
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