What's the relationship b/w the permittivity of space and the speed of light?

Question

I've heard that the two constant are dependent, in the sense that if one were different the other would be to, but don't follow...

Answer 1

c^2 ϵ_0 μ_0 = 1

where c = speed of light in vacuum, ϵ_0 = electric constant (vacuum permittivity), μ_0 = magnetic constant (vacuum permeability)

So, yes, the values would have to change.

However, note that the speed of light in a vacuum _defines_ the meter, so that even if it were different, it would still have the value 299792458 m/s (the size of the meter would change). Similarly, the magnetic constant is exactly 4π×10^-7 N/A^2, so that even if it were different, it would still have this value (and the size of the ampere would change). So, only the electric constant could actually undergo a _numerical_ change in value.

Answer 2

The speed of light is related to the permittivity of free space in the following way:

1/c^2 = permittivity x permeability,

where c is the speed of light.

Answer 3

Permittivity, Magnetic Permeability, and speed of light are related.

The relation comes from solution of Maxwell's equations -- waves propogate at the speed c = 1/sqrt(mu_0 * epsilon_0)

where mu_0 is magnetic permiability, and epsilon_0 is the permittivity of free space.

If you're not in a vacuum -- like air, or glass -- the vacuum terms of mu_0 and epsilon_0 get replaced with values that depend on the material.  

It happens that most transparent materials are non-magnetic, and as a result mu = mu_0 for these materials.  The upshot is that the speed of light in a transparent material pretty much just depends on one over the square root of the dieelectric constant.

Answer 4

Wikipedia comments'...Around 1862, while lecturing at King's College, Maxwell calculated that the speed of propagation of an electromagnetic field is approximately that of the speed of light. He considered this to be more than just a coincidence, and commented "We can scarcely avoid the conclusion that light consists in the transverse undulations of the same medium which is the cause of electric and magnetic phenomena."

Working on the problem further, Maxwell showed that the equations predict the existence of waves of oscillating electric and magnetic fields that travel through empty space at a speed that could be predicted from simple electrical experiments; using the data available at the time, Maxwell obtained a velocity of 310,740,000 m/s. In his 1864 paper A Dynamical Theory of the Electromagnetic Field, Maxwell wrote, The agreement of the results seems to show that light and magnetism are affections of the same substance, and that light is an electromagnetic disturbance propagated through the field according to electromagnetic laws.

His famous equations, in their modern form of four partial differential equations, first appeared in fully developed form in his textbook A Treatise on Electricity and Magnetism in 1873. Most of this work was done by Maxwell at Glenlair during the period between holding his London post and his taking up the Cavendish chair. Maxwell was proven correct, and his quantitative connection between light and electromagnetism is considered one of the great triumphs of 19th century physics.'

Thus, to answer your question - When Maxwell's equations of electromagnetism are written down for free space of magnetic permeability  ÃƒÂŽÃ‚¼ and electrostatic permittivity ε0. it can be shown that the vacuum speed of light 'c' is: -

c = 1

....___

...√με0

try: -

http://en.wikipedia.org/wiki/Maxwell%27s...

for further information.