# Permeability and Permittivity of Free space

## Main Question or Discussion Point

Does anyone know of a physical explanation of $\epsilon_{0}$ and $\mu_{0}$?

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Andrew Mason
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metrictensor said:
Does anyone know of a physical explanation of $\epsilon_{0}$ and $\mu_{0}$?
I would say that:

a) $\epsilon_0$ is a measure of the ratio between electric charge and the electric field of the charge at a unit distance or the ratio of enclosed charge to flux at a unit distance (ie. through a sphere of radius 1 and area 4\pi)

$$\epsilon_0 = \frac{Q}{4\pi E}$$ from the Coulomb force law.
$$\epsilon_0 = \frac{Q}{\oint E\cdot dA} = \frac{Q}{4\pi E}$$ from Gauss' law

b) $\mu_0$ is a measure of the ratio between magnetic field and the enclosed current:

$$\mu_0 = \frac{\oint B\cdot ds}{I}$$ from Ampere's law

For a conducting wire $\mu_0$ is the ratio of the magnetic field - at unit distance - to the current in the wire:

$$\mu_0 = \frac{2\pi B}{I}$$

AM

Hmm, also consider this interpretation. Mechanical waves (wave on a string) have a speed equal to sqrt(Tension/Inertia) where the tension and inertial terms reflect the tension and inertial properties of the medium the wave is traveling in.

EM waves have a speed equal to sqrt(1/e*m). Think of how e and m correspond with eachother, specifically in Gauss's and Ampere's laws. 1/e corresponds to m, in other words.

So (1/em) = (1/e)/m = tension/ inertia.

Thus, 1/e corresponds to the tension of the medium (the higher the tension, the faster the string responds to a pluck. Maxwell himself talked about electric field lines being "under tension", stronger field = more tension).

Then m corresponds to inertia. This makes sense if you thing about an inductor, where the magnetic field opposes the change in current.

These analogies are nice, and it would be nice if you could create a grand unified theory from them. Thanks in advance ;)