# Permittivity and Permeability of Free Space

1. May 27, 2006

### Hetware

Permittivity of a vacuum is a number arrived at beginning with a value for the speed of light in the vacuum and the permeability of the vacuum. NIST uses the term "electric constant" for what is commonly known as the permittivity of free space:

Here's their official value:

http://physics.nist.gov/cgi-bin/cuu/Value?eqep0

http://physics.nist.gov/cuu/Constant.../gif/eqep0.gif [Broken]

The permeability of a vacuum is called by NIST "the magnetic constant":

http://physics.nist.gov/cgi-bin/cuu/Value?eqmu0

and has a value of 4pi x 10^-7 N A^-2, which is clearly not an experimentally established value. The speed of light in a vacuum, on the other hand, is experimentally determined (at least originally). This constant is called "the speed of light in vacuum by NIST":

http://physics.nist.gov/cgi-bin/cuu/Value?c

As I understand the concept of permittivity, it represents something similar to a modulus of elasticity. It is a measure of how polarized a medium becomes when subjected to an electric field. Though most discussions I've encountered on the topic tend to give permittivity and permeability of free space very little discussion, I have always been inclined to believe these concepts are of essential relevance in correctly understanding Nature at a fundamental level.

Does anybody else agree or disagree with that suggestion? What do these concepts mean to you?

I am aware that the equations of EM can be written in units where these constants vanish. I guess if time were measured in meters, and permeability were set to 1, these constants could be dropped from the expressions. Nonetheless, there seem to be concepts which underpin Maxwell's equations that are implicitly, if not explicitly assumed. Does free space become polarized in the presence of an electric field? Put differently, one might ask if an electric field is the polarization of free space.

Last edited by a moderator: May 2, 2017
2. May 27, 2006

### jbusc

The second is _defined_ as a certain number of oscillations of a specific atomic element (cesium? I forget)

Then the meter is defined as the distance light travels in a vaccum in a specific amount of time.

Therefore the speed of light is _not_ an experimentally derived value, it is an exact defined constant.

We know that c^2 = u0e0 (permiability times permittivity)

Again we _define_ u0 to be exactly 4*pi*10^-7

In order to have everything consistant, e0 must equal c^2/u0. Therefore e0 is also _defined_ exactly, however it is not a very "clean" definition as is u0. But it is defined, meaning not experimentally derived and so you can calculate using a computer to however many decimal places you want.

3. May 27, 2006

### Hetware

That is the reason I added the parenthetic 'at least originally'. What I am trying to establish is which aspects of the equations of EM are "arbitrarily" chosen, and which are determined experimentally. If I'm not mistaken, the speed of light is a factor which must be determined experimentally - directly, or indirectly. I am aware that time can be measured in meters. A meter of time is simply the time it takes light to traverse a meter in free space. Or, going by what NIST has done, one begins with a unit of time, and then establishes the magnitude of a meter by the reverse method. In either case, the speed of light serves as a scale factor between space-like displacement and time-like displacement.

I also note that even the use of a particular number of periods of a specific band of cesium emission is in the end, experimentally established.

The other value which appears to be experimentally dictated is the unit of electric charge.

How is the period of a particular band of cesium emission determined?

We also have Coulomb's law F=k q1 q2/r^2, where k = 1/(4pi e0). I believe that is merely an historical artifact, and charge could be expressed in units equal to C/e0^(1/2) thus rendering k=1/4pi. It therefore appears that the experimentally established relationship between spacial extension, and duration (that is to say, the speed of light) is the single value dictated by Nature.

This is my question: is it meaningful to talk about the permittivity of free space? That is, can free space be polarized? I say the answer is yes.

4. May 31, 2006

### erickalle

Instead of dealing with: C/e0^1/2 i’d rather deal with:
(A=) C^2/e0 and (B=) C^2*u0, this way A is energy x length and B is mass x length, so that we have a feel of what those concepts are in mechanical units. (C=Coulomb). We can give A and B the smallest possible quanta by substituting C for the electronic charge.
Both (A*B)^1/2 and (A/B)^1/2 are then useful concepts.
Perhaps in the future it will be possible to make one more additional substitution which will result in A and B to be pure units of length and time, but this is controversial and for good reasons will not be shown here.

regards,
eric

5. May 31, 2006

### pervect

Staff Emeritus
The cleanest way to describe the origin of permittivity, IMO, is via Coulomb's force law.

The force between two charges q1 and q2 is just

F = k q1 q2 / d^2

where k is some constant, called columb's constant.

k is just 1/$4 \pi \epsilon_0$

So the value of k just sets "how large" the force is between two charges. And the value of $\epsilon_0$ sets the value of k.

As far as fundamental physical significance goes, there is very little by my interpretation of the phrase. The fact that the speed of light is a constant makes it a fundamental physical quantity. Our particular choice of the meter, and the second, were purely arbitrary. There is no "physical" significance to the meter, or the second, they are purely human inventions. There isn't anything to be gained by studying the "value" of the speed of lights in meters and seconds, because meters and seconds are just human inventions.

6. May 31, 2006

### rbj

you might want to look up

http://en.wikipedia.org/wiki/Planck_units .

in fact, just as the speed of light is a value arrived at solely by our anthropometric choice of units (which are now defined to be 299792458 m/s), as well as the permeablity of free space $\mu_0$ so is the permittivity of free space $\epsilon_0$. they can all be defined to be 1. the only restriction in degree of freedome is that $c^2 \mu_0 \epsilon_0 = 1$ in any consistent set of units.

the only physical quantities that are fundamentally salient are those that are dimensionless. perhaps the best known is the fine-structure constant:

$$\alpha = \frac{e^2}{4 \pi \epsilon_0 \hbar c} = \frac{1}{137.03599911}$$ .

that is a quantity that is somehow sewn into the fabic of free space (i really think it is a consequence of the amount of charge, measured in natural units of charge, that nature has bestowed upon the electron, proton, positron, or the quarks that make such particles, but that is my personal pet opinion). $\mu_0$ and $\epsilon_0$ are not fundamental but are simply quantities that result from our choice of units.

7. Jun 1, 2006

### erickalle

If we include the permittivity of free space in a new expression for charge such as in: C/e0^1/2 then it follows that we are now dealing with only 1 unit (which it should be in my view) instead of 2. In the past e0 was thought a property of space. Charge was a property of a particle. Now we will have to make a choice: is the new unit attributable to space or particle? If you then state that free space can be polarized, then it follows you attribute the new unit to space. But since 1905 space is a bit out of fashion. So I’m sitting on the fence here.

8. Jun 1, 2006

### Meir Achuz

epsilon zero is a superfluous constant invented by an engineer named Georgi about 100 years ago. He and his followers were persuasive advocates at international standards conferences, and eventually pushed Georgi units through about 50 years ago by a close vote, becoming SI. Sears was an early advocate, and since his elementary text was the standard for about 20 years, the SI took over, somewhat like Gresham's law (Bad money drives out good.). Free space can be polarized, but that has nothing to do with epsilon0. In QED, virtual electron-positron pairs get induced in the vacuum, acting like a frequency dependent permittivity.
At a photon energy of 90 GeV, alpha is up to 1/128 from 1/137.
In terms of distance, this means that alpha is 1/128 when two electrons are within 0.2 fm of each other.

9. Mar 19, 2010

### E.T.

not to be a stickler, but u0e0 = c^-2, thus e0 = 1/(u0c^2)..

10. Mar 20, 2010

### Bob S

Both ε0 and μ0 appear in the Maxwell curl equations, so there are two free parameters, their product and their ratio. The two curl equations determine the propagation velocity of an electromagnetic wave in vacuum (c = 1/sqrt(μ0ε0)), and the ratio is related to the magnitude of E over H (sqrt(μ00) = 377 ohms). As pointed out earlier, we are stuck with a lot of anthropogenic baggage. The unit of length could have been the foot or cubit, but is now based on the meter (originally based on distance from Equator to the North Pole). Volta (or his piles) gave us the volts. Ampere, Faraday, and others gave us amps. Permittivity is related to the energy stored in a capacitor to the Coulomb (=1 amp-second) and the volt. Permeability is related to the energy stored in a coil to the current. The second at one time was related to the escapement release time ("tick") of a 1-meter pendulum. It would have been nice to base ε0 and μ0 on universal (and unitless) parameters like α and π, but because they are both unitless, it is not possible. We (physicists) could have arbitrarily set ε0 and μ0 to 1, but then only physicists would measure time, length, speed of light, volts, amps impedance of free space, etc. in these units. My first E & M course was taught in Gaussian units, but then finding a resistor measured in esu volts per abamp was difficult. It was easier to use mks units.

Bob S