# Naked Science Forum

## Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: Bogie_smiles on 29/08/2017 20:31:42

Title: Speed of light, permittivity and permeability: Are they constants?
Post by: Bogie_smiles on 29/08/2017 20:31:42
I have a question about the three constants associated with electric and magnetic fields and their propagation, as mentioned in this link from Hyperphysics:
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html#c3 (http://hyperphysics.phy-astr.gsu.edu/hbase/electric/elefie.html#c3)
Looking at the link, the three constants are, 1) the speed of light in a vacuum which is given and invariant, 2) the electric permittivity of free space, and the magnetic permeability of free space are the other two. Are they also always constants, or can permittivity and permeability vary relative to each other, as long as 1 divided by the square root of their product equals the speed of light?

Stated differently, is it their combined relationship relative to invariant speed of light that must remain constant, or do both values always individually remain constant in the context of the Hyperphysics link above?
Title: Re: Speed of light, permittivity and permeability: Are they constants?
Post by: Bored chemist on 29/08/2017 21:19:22
One of them (and you can  take your pick which one) is defined by the other definitions we use for units for measuring electricity.
The definition of the Amp
"The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed one metre apart in vacuum, would produce between these conductors a force
equal to 2 E−7 newtons per metre of length"
fixes the magnetic permeability of the vacuum as exactly  4π E−7 H/m

Title: Re: Speed of light, permittivity and permeability: Are they constants?
Post by: Bogie_smiles on 29/08/2017 22:21:53
http://philschatz.com/physics-book/contents/m42386.html (http://philschatz.com/physics-book/contents/m42386.html)

So am I correct to say that when the medium is a vacuum, all three are constants? However, if the medium is the air at sea level on a nice day, then the speed of light will be slower than c from point a to point b. Then the values for permittivity and permeability would be variable relative to the change in the local speed of light through air, correct? If so, then is the local speed of light equal to the inverse of the square root of the product of permittivity and permeability, i.e., one divided by the square root of the product of permittivity and permeability?
Title: Re: Speed of light, permittivity and permeability: Are they constants?
Post by: evan_au on 30/08/2017 02:28:34
Yes, that is right, for measurements done in your lab, in your frame of reference.

The speed of light in air is not much lower than in a vacuum. It's enough that high-energy cosmic rays can be detected by the Cerenkov radiation they emit. See: https://en.wikipedia.org/wiki/Pierre_Auger_Observatory#Physical_background

In glass, light travels about 2/3 the speed of a vacuum (or air), which is why camera lenses and spectacles work so well to bend the light. The amount light is slowed is determined by the refractive index (https://en.wikipedia.org/wiki/Refractive_index) of the material.

However, when you are observing the behavior of light in a laboratory in a deeper gravitational well than yourself, or traveling at high speed relative to yourself, relativistic effects come into play, and these three "constants" need to be adjusted to account for the behavior in the "other" laboratory.
Title: Re: Speed of light, permittivity and permeability: Are they constants?
Post by: Bogie_smiles on 30/08/2017 18:40:26
Thank you. [/font]

https://www.thenakedscientists.com/forum/gallery/43933_30_08_17_6_35_31.gif (https://www.thenakedscientists.com/forum/gallery/43933_30_08_17_6_35_31.gif)[/font]
(https://www.thenakedscientists.com/forum/gallery/43933_30_08_17_6_35_31.gif)
(gif of speed of speed of light equation relative to permittivity and permeability).[/font]

Title: Re: Speed of light, permittivity and permeability: Are they constants?
Post by: yor_on on 08/09/2017 18:44:22
I will beg to differ there. c is not a variable, even though it present you with different 'speeds' passing through different materials etc. That one should be covered by the way atoms/electrons excite and release, giving us delays. On the other hand it's also a question of semantics. For example, 'stopping light' doesn't 'stop' anything except the reaction to a excitation as far as I know.