Statcoulomb
Encyclopedia
The statcoulomb or franklin (Fr) or electrostatic unit of charge (esu) is the physical unit
for electrical charge used in the centimetre-gram-second system of units
(cgs) and Gaussian units
. It is a derived unit given by
The SI
system of units uses the coulomb (C) instead. The conversion between C and statC is different in different contexts. The most common contexts are:
The symbol "↔" is used instead of "=" because the two sides are not necessarily interchangeable, as discussed below. The number is 10 times the value of the speed of light
expressed in meters/second, and the conversions are exact except where indicated.
The coulomb is an extremely large charge rarely encountered in electrostatics, while the statcoulomb is closer to everyday charges.
. This repulsion is governed by Coulomb's law
, which in the Gaussian-cgs system
states:
where F is the force, q1 and q2 are the two charges, and r is the distance between the charges. Performing dimensional analysis
on Coulomb's law, the dimension of electrical charge in cgs must be [mass]1/2 [length]3/2 [time]−1. (This statement is not true in SI
units; see below.) We can be more specific in light of the definition above: Plugging in F=1 dyne, q1=q2=1 statC, and r = 1 cm, we get:
as expected.
in cgs-Gaussian unit system
and SI
are respectively:
(cgs-Gaussian)
(SI)
Since ε0, the vacuum permittivity, is not dimensionless, the coulomb (the SI unit of charge) is not dimensionally equivalent to [mass]1/2 [length]3/2 [time]−1, unlike the statcoulomb. In fact, it is impossible to express the Coulomb in terms of mass, length, and time alone.
Consequently, a conversion equation like "1 C = X statC" can be misleading: the units on the two sides are not consistent. One cannot freely switch between Coulombs and statcoulombs within a formula or equation, as one would freely switch between centimeters and meters. One can, however, find a correspondence between Coulombs and statcoulombs in different contexts. As described below, "1 C corresponds to " when describing the charge of objects. In other words, if a physical object has a charge of 1 C, it also has a charge of . Likewise, "1 C corresponds to statcoulombs" when describing an electric displacement field flux.
. From this definition, it is straightforward to find an equivalent charge in SI
coulombs
. Using the SI
equation
(SI),
and plugging in F=1 dyne = 10-5 N, and r=1 cm=10-2 m, and then solving for q=q1=q2, the result is q=(1/2997924580)C ≈ . Therefore an object with a charge of 1 statC has a charge of .
This can also be expressed by the following conversion, which is fully dimensionally consistent, and often useful for switching between SI and cgs formulae:
:
(cgs)
(SI)
where
Therefore the conversion factor for flux is 4π different than the conversion factor for charge:
(as unit of ΦD).
The dimensionally-consistent version is:
(as unit of ΦD).
Units of measurement
A unit of measurement is a definite magnitude of a physical quantity, defined and adopted by convention and/or by law, that is used as a standard for measurement of the same physical quantity. Any other value of the physical quantity can be expressed as a simple multiple of the unit of...
for electrical charge used in the centimetre-gram-second system of units
Centimetre gram second system of units
The centimetre–gram–second system is a metric system of physical units based on centimetre as the unit of length, gram as a unit of mass, and second as a unit of time...
(cgs) and Gaussian units
Gaussian units
Gaussian units comprise a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units...
. It is a derived unit given by
- 1 statC = 1 g1/2 cm3/2 s−1 = 1 erg1/2 cm1/2.
The SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
system of units uses the coulomb (C) instead. The conversion between C and statC is different in different contexts. The most common contexts are:
- 1 C ↔ statC ≈ (for electric chargeElectric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
) - 1 statC ↔ ≈ (for electric chargeElectric chargeElectric charge is a physical property of matter that causes it to experience a force when near other electrically charged matter. Electric charge comes in two types, called positive and negative. Two positively charged substances, or objects, experience a mutual repulsive force, as do two...
).
- 1 C ↔ 4π× statC ≈ (for electric flux ΦD)
- 1 statC ↔ ≈ (for electric flux ΦD).
- 1 C/m2 ↔ 4π××10-4 statC/cm2 ≈ (for electric displacement field D)
- 1 statC/cm2 ↔ ≈ (for electric displacement field D).
The symbol "↔" is used instead of "=" because the two sides are not necessarily interchangeable, as discussed below. The number is 10 times the value of the speed of light
Speed of light
The speed of light in vacuum, usually denoted by c, is a physical constant important in many areas of physics. Its value is 299,792,458 metres per second, a figure that is exact since the length of the metre is defined from this constant and the international standard for time...
expressed in meters/second, and the conversions are exact except where indicated.
The coulomb is an extremely large charge rarely encountered in electrostatics, while the statcoulomb is closer to everyday charges.
Definition and relation to cgs base units
The statcoulomb is defined as follows: if two stationary objects each carry a charge of 1 statC and are 1 cm apart, they will electrically repel each other with a force of 1 dyneDyne
In physics, the dyne is a unit of force specified in the centimetre-gram-second system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µN...
. This repulsion is governed by Coulomb's law
Coulomb's law
Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...
, which in the Gaussian-cgs system
Gaussian units
Gaussian units comprise a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units...
states:
where F is the force, q1 and q2 are the two charges, and r is the distance between the charges. Performing dimensional analysis
Dimensional analysis
In physics and all science, dimensional analysis is a tool to find or check relations among physical quantities by using their dimensions. The dimension of a physical quantity is the combination of the basic physical dimensions which describe it; for example, speed has the dimension length per...
on Coulomb's law, the dimension of electrical charge in cgs must be [mass]1/2 [length]3/2 [time]−1. (This statement is not true in SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
units; see below.) We can be more specific in light of the definition above: Plugging in F=1 dyne, q1=q2=1 statC, and r = 1 cm, we get:
- 1 statC = g1/2 cm3/2 s−1
as expected.
General incompatibility
Coulomb's lawCoulomb's law
Coulomb's law or Coulomb's inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. It was first published in 1785 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism...
in cgs-Gaussian unit system
Gaussian units
Gaussian units comprise a metric system of physical units. This system is the most common of the several electromagnetic unit systems based on cgs units. It is also called the Gaussian unit system, Gaussian-cgs units, or often just cgs units...
and SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
are respectively:
(cgs-Gaussian) (SI)Since ε0, the vacuum permittivity, is not dimensionless, the coulomb (the SI unit of charge) is not dimensionally equivalent to [mass]1/2 [length]3/2 [time]−1, unlike the statcoulomb. In fact, it is impossible to express the Coulomb in terms of mass, length, and time alone.
Consequently, a conversion equation like "1 C = X statC" can be misleading: the units on the two sides are not consistent. One cannot freely switch between Coulombs and statcoulombs within a formula or equation, as one would freely switch between centimeters and meters. One can, however, find a correspondence between Coulombs and statcoulombs in different contexts. As described below, "1 C corresponds to " when describing the charge of objects. In other words, if a physical object has a charge of 1 C, it also has a charge of . Likewise, "1 C corresponds to statcoulombs" when describing an electric displacement field flux.
As a unit of charge
The statcoulomb is defined as follows: If two stationary objects each carry a charge of 1 statC and are 1 cm apart, they will electrically repel each other with a force of 1 dyneDyne
In physics, the dyne is a unit of force specified in the centimetre-gram-second system of units, a predecessor of the modern SI. One dyne is equal to exactly 10 µN...
. From this definition, it is straightforward to find an equivalent charge in SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
coulombs
Coulombs
Coulomb or Coulombs may refer to:* Charles-Augustin de Coulomb , French physicist, also:** Coulomb, a unit of electric charge** Coulomb's law, in electrostatics** Coulomb blockade, an increased resistance of certain electronic devices...
. Using the SI
Si
Si, si, or SI may refer to :- Measurement, mathematics and science :* International System of Units , the modern international standard version of the metric system...
equation
(SI),and plugging in F=1 dyne = 10-5 N, and r=1 cm=10-2 m, and then solving for q=q1=q2, the result is q=(1/2997924580)C ≈ . Therefore an object with a charge of 1 statC has a charge of .
This can also be expressed by the following conversion, which is fully dimensionally consistent, and often useful for switching between SI and cgs formulae:
As a unit of electric displacement field or flux
An electric flux (specifically, a flux of the electric displacement field D) has units of charge: statC in cgs and coulombs in SI. The conversion factor can be derived from Gauss's lawGauss's law
In physics, Gauss's law, also known as Gauss's flux theorem, is a law relating the distribution of electric charge to the resulting electric field. Gauss's law states that:...
:
(cgs) (SI)where
Therefore the conversion factor for flux is 4π different than the conversion factor for charge:
(as unit of ΦD).The dimensionally-consistent version is:
(as unit of ΦD).