Maxwells little silver hammer

When Maxwell formulated his equations the speed of light could be calculated directly from the equation:

$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

Where ${\mu }_0$ is the magnetic permeability of free space.
${\epsilon }_0$

 is the electrical permittivity of free space. 

“Reality is that which, when you stop believing in it, doesn't go away.”

― Philip K. Dick, I Hope I Shall Arrive Soon

And if you believe that then believe this 

dreams are a subset of reality

now suck on this one because they come three for a penny

dreams are products of sleep

if you have one and think it correlates

with reality go ahead and do the demo

if not define death as the process that processes

in the moments of momentum between the end of the gamma waves

and the end of the end of the decarbonization of the unit

In other words as soon as you stop thinking about a thing the salt is made available for other redox Rhode scholarly reciprocation lined up waiting to oxidize the wise into the wizened with wily witness

working well wide awake where WMWmWmWM munches

Water wet wild willing Waui in Maui

The ampere-defined vacuum permeability[edit]

Two thin, straight, stationary, parallel wires, a distance r apart in free space, each carrying a current I, will exert a force on each other. Ampère's force law states that the magnetic force F_m per length L is given by^[6]

$${\displaystyle {\frac {|{\boldsymbol {F}}_{m}|}{L}}={\mu _{0} \over 2\pi }{|{\boldsymbol {I}}|^{2} \over |{\boldsymbol {r}}|}.}$$

From 1948 until 2019 the ampere was defined as "that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2×10⁻⁷ newton per meter of length". This is equivalent to a definition of ${\displaystyle \mu _{0}}$ of exactly 4π×10⁻⁷ H/m.^[a], since

$${\displaystyle {\frac {{\boldsymbol {F}}_{m}}{L}}={\mu _{0} \over 2\pi }\mathrm {(1\,A)^{2} \over {1\,m}} }$$

$${\displaystyle {2\times 10^{-7}\mathrm {N \over m} }={\mu _{0} \over 2\pi }\mathrm {(1\,A)^{2} \over {1\,m}} }$$

$${\displaystyle \mu _{0}=4\pi \times 10^{-7}{\text{ H/m}}}$$

The current in this definition needed to be measured with a known weight and known separation of the wires, defined in terms of the international standards of mass, length and time in order to produce a standard for the ampere (and this is what the Kibble balance was designed for). In the 2019 redefinition of the SI base units, the ampere is defined exactly in terms of the elementary charge and the second, and the value of  is determined experimentally; 4π × 1.00000000055(15)×10⁻⁷ H⋅m⁻¹ is a recently measured value in the new system (and the Kibble balance has become an instrument for measuring weight from a known current, rather than measuring current from a known weight).

Value[edit]

The value of ε₀ is defined by the formula^[3]

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

where c is the defined value for the speed of light in classical vacuum in SI units,^[4]: 127 and μ₀ is the parameter that international Standards Organizations call the "magnetic constant" (commonly called vacuum permeability or the permeability of free space). Since μ₀ has an approximate value 4π × 10⁻⁷ H/m,^[5] and c has the defined value 299792458 m⋅s⁻¹, it follows that ε₀ can be expressed numerically as

${\displaystyle {\begin{aligned}\varepsilon _{0}&\approx {\frac {1}{\left(4\pi \times 10^{-7}\,{\textrm {N/A}}^{2}\right)\left(299792458\,{\textrm {m/s}}\right)^{2}}}\\[2pt]&={\frac {625000}{22468879468420441\pi }}\,{\textrm {F/m}}\\[2pt]&\approx 8.85418781762039\times 10^{-12}\,{\textrm {F}}{\cdot }{\textrm {m}}^{-1}\end{aligned}}}$

(or A²⋅s⁴⋅kg⁻¹⋅m⁻³ in SI base units, or C²⋅N⁻¹⋅m⁻² or C⋅V⁻¹⋅m⁻¹ using other SI coherent units).^[6][7]

The historical origins of the electric constant ε₀, and its value, are explained in more detail below.

The quessie quoth the raven quines thusly:

The speed of Nothing Mu to you between

the speed of the which is the wont to know

3.14159265359-2.992798491=0.13474402056

when three is one one of three is close to pi

1/5 Pi 0.06366197723

0.07957747154 1/4 Pi

1/3 Pi 0.10610329539

0.15915494309  1/2 Pi 

Redefinition of the SI units[edit]

Main article: 2019 redefinition of the SI base units

The ampere was redefined by defining the elementary charge as an exact number of coulombs as from 20 May 2019,^[4] with the effect that the vacuum electric permittivity no longer has an exactly determined value in SI units. The value of the electron charge became a numerically defined quantity, not measured, making μ₀ a measured quantity. Consequently, ε₀ is not exact. As before, it is defined by the equation ε₀ = 1/(μ₀c²), and is thus determined by the value of μ₀, the magnetic vacuum permeability which in turn is determined by the experimentally determined dimensionless fine-structure constant α:

${\displaystyle \varepsilon _{0}={\frac {1}{\mu _{0}c^{2}}}={\frac {e^{2}}{2\alpha hc}}\ ,}$

with e being the elementary charge, h being the Planck constant, and c being the speed of light in vacuum, each with exactly defined values. The relative uncertainty in the value of ε₀ is therefore the same as that for the dimensionless fine-structure constant, namely 1.5×10⁻¹⁰.^[8]

Terminology[edit]

Historically, the parameter ε₀ has been known by many different names. The terms "vacuum permittivity" or its variants, such as "permittivity in/of vacuum",^[9][10] "permittivity of empty space",^[11] or "permittivity of free space"^[12] are widespread. Standards Organizations worldwide now use "electric constant" as a uniform term for this quantity,^[6] and official standards documents have adopted the term (although they continue to list the older terms as synonyms).^[13][14]

Another historical synonym was "dielectric constant of vacuum", as "dielectric constant" was sometimes used in the past for the absolute permittivity.^[15][16] However, in modern usage "dielectric constant" typically refers exclusively to a relative permittivity ε/ε₀ and even this usage is considered "obsolete" by some standards bodies in favor of relative static permittivity.^[14][17] Hence, the term "dielectric constant of vacuum" for the electric constant ε₀ is considered obsolete by most modern authors, although occasional examples of continuing usage can be found.

As for notation, the constant can be denoted by either ${\displaystyle \varepsilon _{0}\,}$ or ${\displaystyle \epsilon _{0}\,}$, using either of the common glyphs for the letter epsilon.

Vacuum permittivity

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This article is about the electric constant. For the analogous magnetic constant, see Vacuum permeability. For the ordinal number ε₀, see Epsilon numbers (mathematics).

Value of ε0	Unit
8.8541878128(13)×10−12	F⋅m−1
55.26349406	e2⋅GeV−1⋅fm−1

Vacuum permittivity, commonly denoted ε₀ (pronounced as "epsilon nought" or "epsilon zero") is the value of the absolute dielectric permittivity of classical vacuum. Alternatively may 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:

ε₀ = 8.8541878128(13)×10⁻¹² F⋅m⁻¹ (farads per meter), with a relative uncertainty of 1.5×10⁻¹⁰.^[1]

Its dimensions in SI base units are ${\textstyle {\rm {s^{4}\cdot A^{2}\cdot kg^{-1}\cdot m^{-3}}}}$. It is the capability of an electric field to permeate a vacuum. This constant relates the units for electric charge to mechanical quantities such as length and force.^[2] For example, the force between two separated electric charges with spherical symmetry (in the vacuum of classical electromagnetism) is given by Coulomb's law:

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

Here, q₁ and q₂ are the charges, r is the distance between their centres, and the value of the constant fraction ${\displaystyle 1/4\pi \varepsilon _{0}}$ (known as the Coulomb constant, ${\displaystyle k_{e}}$) 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.

Theoretical physical Constant values that are changing from measurement to measurement...

Definition of CGS units in mechanics[edit]

In mechanics, the quantities in the CGS and SI systems are defined identically. The two systems differ only in the scale of the three base units (centimetre versus metre and gram versus kilogram, respectively), with the third unit (second) being the same in both systems.

There is a direct correspondence between the base units of mechanics in CGS and SI. Since the formulae expressing the laws of mechanics are the same in both systems and since both systems are coherent, the definitions of all coherent derived units in terms of the base units are the same in both systems, and there is an unambiguous correspondence of derived units:

• ${\displaystyle v={\frac {dx}{dt}}}$  (definition of velocity)
• ${\displaystyle F=m{\frac {d^{2}x}{dt^{2}}}}$  (Newton's second law of motion)
• ${\displaystyle E=\int {\vec {F}}\cdot \mathrm {d\,} {\vec {x}}}$  (energy defined in terms of work)
• ${\displaystyle p={\frac {F}{L^{2}}}}$  (pressure defined as force per unit area)
• ${\displaystyle \eta =\tau /{\frac {dv}{dx}}}$  (dynamic viscosity defined as shear stress per unit velocity gradient).

Thus, for example, the CGS unit of pressure, barye, is related to the CGS base units of length, mass, and time in the same way as the SI unit of pressure, pascal, is related to the SI base units of length, mass, and time:

1 unit of pressure = 1 unit of force/(1 unit of length)² = 1 unit of mass/(1 unit of length⋅(1 unit of time)²)

1 Ba = 1 g/(cm⋅s²)

1 Pa = 1 kg/(m⋅s²).

Expressing a CGS derived unit in terms of the SI base units, or vice versa, requires combining the scale factors that relate the two systems:

1 Ba = 1 g/(cm⋅s²) = 10⁻³ kg / (10⁻² m⋅s²) = 10⁻¹ kg/(m⋅s²) = 10⁻¹ Pa.

Definitions and conversion factors of CGS units in mechanics[edit]

Quantity	Quantity symbol	CGS unit name	Unit symbol	Unit definition	In coherent SI units
length, position	L, x	centimetre	cm	1/100 of metre	10−2 m
mass	m	gram	g	1/1000 of kilogram	10−3 kg
time	t	second	s	1 second	1 s
velocity	v	centimetre per second	cm/s	cm/s	10−2 m/s
acceleration	a	gal	Gal	cm/s2	10−2 m/s2
force	F	dyne	dyn	g⋅cm/s2	10−5 N
energy	E	erg	erg	g⋅cm2/s2	10−7 J
power	P	erg per second	erg/s	g⋅cm2/s3	10−7 W
pressure	p	barye	Ba	g/(cm⋅s2)	10−1 Pa
dynamic viscosity	μ	poise	P	g/(cm⋅s)	10−1 Pa⋅s
kinematic viscosity	ν	stokes	St	cm2/s	10−4 m2/s
wavenumber	k	kayser (K)	cm−1[10]	cm−1	100 m−1