# Electric field constant

Physical constant
Surname Electric field constant
Formula symbol ${\ displaystyle \ varepsilon _ {0} \,}$
Size type Permittivity
value
SI 8th.854 187 8128 (13)e-12 ${\ displaystyle \ textstyle {\ frac {\ mathrm {A \, s}} {\ mathrm {V \, m}}}}$
Uncertainty  (rel.) 1.5e-10
Planck units (4π) −1 , i.e. 7.957 747 15 ...e-2
Relation to other constants
${\ displaystyle \ varepsilon _ {0} = 1 / (\ mu _ {0} \, c ^ {2})}$
${\ displaystyle \ mu _ {0}}$: Magnetic field constant : speed of light
${\ displaystyle c}$
Sources and Notes
Source SI value: CODATA 2018 ( direct link )

The electric field constant , also the permittivity of the vacuum , electric constant , dielectric constant of the vacuum or influence constant , is a physical constant that plays a role in the description of electric fields . It indicates the ratio of the electric flux density to the electric field strength in a vacuum . The reciprocal of the electric field constant appears as a proportionality factor in Coulomb's law . ${\ displaystyle \ varepsilon _ {0}}$

## terminology

According to the German version of the International System of Units, the constant is known as the electric field constant . The permittivity of the vacuum has the same value and is mentioned as an explanation. ${\ displaystyle \ varepsilon _ {0}}$

## Relationships with other field constants

The permittivity of a material, the permittivity of the vacuum and the relative permittivity are related according to the relationship . ${\ displaystyle \ varepsilon}$${\ displaystyle \ varepsilon _ {0}}$${\ displaystyle \ varepsilon _ {\ text {r}}}$${\ displaystyle \ varepsilon = \ varepsilon _ {0} \ cdot \ varepsilon _ {\ text {r}}}$

## Numerical value and unit

In the International System of Units (SI), the Maxwell equations result in a simple relationship between the electric field constant, the magnetic field constant and the speed of light : ${\ displaystyle \ mu _ {0}}$ ${\ displaystyle c}$

${\ displaystyle \ varepsilon _ {0} \ mu _ {0} c ^ {2} = 1}$.

${\ displaystyle \ varepsilon _ {0}}$can be determined from the fine structure constant, which is subject to measurement uncertainty, and the precisely defined natural constants of the speed of light (c) , elementary charge (e) and Planck's constant (h) : ${\ displaystyle \ alpha}$

${\ displaystyle \ varepsilon _ {0} = {\ frac {e ^ {2}} {2 \ cdot h \ cdot c \ cdot \ alpha}}}$

The unit of can be expressed in different ways by the derived SI units volt  (V), coulomb  (C) and farad  (F): ${\ displaystyle \ varepsilon _ {0}}$

${\ displaystyle {\ frac {\ mathrm {A} \, \ mathrm {s}} {\ mathrm {V} \, \ mathrm {m}}} = {\ frac {\ mathrm {C}} {\ mathrm { V} \, \ mathrm {m}}} = {\ frac {\ mathrm {F}} {\ mathrm {m}}} = {\ frac {\ mathrm {A} ^ {2} \, \ mathrm {s } ^ {4}} {\ mathrm {kg} \, \ mathrm {m} ^ {3}}} = {\ frac {\ mathrm {C} ^ {2}} {\ mathrm {N} \, \ mathrm {m} ^ {2}}}}$

## history

After the magnetic field constant and the speed of light were set to an exact value in 1948, the value of the electric field constant was also precisely set by 2019. This value was:

{\ displaystyle {\ begin {aligned} \ varepsilon _ {0} & = {\ frac {1} {\ mu _ {0} \ c ^ {2}}} = {\ frac {1} {4 \, \ pi \ cdot 10 ^ {- 7} {\ frac {\ mathrm {N}} {\ mathrm {A} ^ {2}}} \ cdot \ left (299 \, 792 \, 458 \; {\ frac {\ text {m}} {s}} \ right) ^ {2}}} \\ & = 8 {,} 854 \ 187 \ 817 \ ldots \ cdot 10 ^ {- 12} {\ frac {\ mathrm {As} } {\ mathrm {Vm}}} \ end {aligned}}}

As a result of the revision of the International System of Units resolved at the 26th General Conference on Weights and Measures , the definition of the ampere has been based on the elementary charge and the definition of the second since May 20, 2019 . The magnetic field constant and thus also the electrical field constant have since been measured variables with measurement uncertainty . ${\ displaystyle e}$${\ displaystyle \ mu _ {0}}$${\ displaystyle \ varepsilon _ {0}}$

## Individual evidence

1. ^ The International System of Units (translation of the SI brochure, 8th edition) . In: PTB Mitteilungen . tape 117 , no. 2 , 2007, p. 147 ( ptb.de [PDF; 4.7 MB ]).