Speed of light, permeability and permitivity of free space

[bobsmith76]

See attachment for my text's explanation's on the permittivity and permeability of free space, if you want but it's not necessary. Anyway, after reading those explanations of the p & p of free space I'm having a very difficult time understanding why taking the inverse square root of the product of those equals the speed of light. Why? I guess it's one of those impossible brute facts that has no explanation such as why an electron absorbs a photon when it ascends to a higher energy level. In any case, I find that very bizarre. The permeability of free space is related to the current, that is the number of electrons moving and the permittivity is related to Coloumb's constant plus the surface of a sphere. I don't see why those entities when multiplied then square rooted then inversed should equal the speed of light.

 

[Janus]

See attachment for my text's explanation's on the permittivity and permeability of free space, if you want but it's not necessary. Anyway, after reading those explanations of the p & p of free space I'm having a very difficult time understanding why taking the inverse square root of the product of those equals the speed of light. Why? I guess it's one of those impossible brute facts that has no explanation such as why an electron absorbs a photon when it ascends to a higher energy level. In any case, I find that very bizarre. The permeability of free space is related to the current, that is the number of electrons moving

No, the permeability is the constant that relates (in the example) the current to the strength of the magnetic field. In essence, it is the constant that determines the strength of a the field at any given distance from a magnetic pole.

and the permittivity is related to Coloumb's constant plus the surface of a sphere.

Again, Essentially, permittivity relates strength of Electrostatic field to charge.

Permeability and Permittivity are for magnetic and electric fields as the gravitational constant is to gravity.

I don't see why those entities when multiplied then square rooted then inversed should equal the speed of light.

A changing electric field produces a changing magnetic field and vice-versa. Light is basically oscillating electric and magnetic fields supported by this interaction between them. Since the permittivity and permeability of space determine how these fields interact, it also determines the propagation speed of the EM radiation. For a more detailed understanding, you would have to study the Maxwell equations.

 

[Bob S]

There are four constants that are closely related; the speed of light c, the permeability of free space μ_o, the permittivity of free space ε_o, and the impedance of free space Z_o. Specifically,
$$Z_o= \left( \frac{\mu_o}{\epsilon_o} \right)^{1/2} ≈377 \space ohms$$
and
$$c= \left( \frac{1}{\mu_o \epsilon_o} \right)^{1/2}≈ 3 x 10^8 \space m/s$$
Two are independent constants (μ_o and c), and two are dependent.