Vacuum permittivity

Vacuum permittivity, commonly denoted ε0 (pronounced "epsilon nought" or "epsilon zero"), is the value of the absolute dielectric permittivity of classical vacuum. It may also be referred to as the permittivity of free space, the electric constant, or the distributed capacitance of the vacuum. It is an ideal (baseline) physical constant. Its CODATA value is:

It is a measure of how dense of an electric field is "permitted" to form in response to electric charges and relates the units for electric charge to mechanical quantities such as length and force. For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law:

F

C

=

1

4

π

ε

0

q

1

q

2

r

2

{\displaystyle F_{\text{C}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{1}q_{2}}{r^{2}}}}

Here, q1 and q2 are the charges, r is the distance between their centres, and the value of the constant fraction 1/(4πε0) is approximately 9×109 N⋅m2⋅C−2. Likewise, ε0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources. In electrical engineering, ε0 itself is used as a unit to quantify the permittivity of various dielectric materials.

Value

The value of ε0 obeys the formula

ε

0

=

1

μ

0

c

2

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

where c is the defined value for the speed of light in classical vacuum in SI units, and μ0 is the parameter that international standards organizations refer to as the magnetic constant (also called vacuum permeability or the permeability of free space). Since μ0 has an approximate value of 4π × 10−7 H/m (by the former definition of the ampere), and c has the defined value 299792458 m/s, it follows that ε0 can be expressed numerically as

ε

0

≈

1

(

4

π

×

10

−

7

N

/

A

2

)

(

299

792

458

m

/

s

)

2

≈

8.854

187

8176

×

10

−

12

F

/

m

.

{\displaystyle \varepsilon _{0}\approx {\frac {1}{\left(4\pi \times {10}^{-7}\,\mathrm {N/A^{2}} \right){\left(299\,792\,458\,\mathrm {m/s} \right)}^{2}}}\approx {8.854\,187\,8176}\times {10}^{-12}\,\mathrm {F/m} .}

The relative deviation of the recommended measured value (1.3×10−10 or 0.13 parts per billion) from the former defined value is within its uncertainty (1.6×10−10, in relative terms, or 0.16 parts per billion).