How are Electrical Permittivity and Magnetic Permeability Measured?

[Zman]

Maxwell showed us that the speed of light in vacuum is dependent on two values.
The two values are the electrical permittivity and the magnetic permeability.

But how are these two values measured?

 

[mgb_phys]

They aren't - it's the other way around, you define them from Maxwell's equations.
You can define electrical permittivity in terms of the speed of light and and the magnetic permeability. The magnetic permeability is fixed by the definition of the Amp and the speed of light is fixed by the definition of the metre.

 

[Zman]

Thanks for that. But I am still unclear.

The equation relating c, permittivity of free space (e) and permeability of free space(u)
c = 1/SQRT(e u)

Are you saying that knowing c from experiment, and u from something else, then the value of e is found?

 

[mgb_phys]

Yes
\mu is fixed at 4 \pi 10 ^{-7} from the definition of the Amp (the 10^-7 is because it was originally in cm and g rather than kg and m)
The speed of light is fixed, the metre is now defined in terms of the speed of light (so if a new measurement is made of c we change the length of the metre)

 

[f95toli]

Are you saying that knowing c from experiment, and u from something else, then the value of e is found?

But it is of course also possible to just measure the capacitance of a capacitor of known calculable) geometry (or, if you need accurate results, to use a cavity perturbation method).
I've never heard of anyone actually measuring the relative permittivity in a material by directly measuring the speed of light.

Dielectric spectroscopy is HUGE field and there are many different ways to measure permittivity.

 

[Bob S]

By measuring the impedance of an air-dielectric coax cable of known geometry (e.g., Andrew HJ7-50A heliax) or other transmission line geometry, the impedance of free space (Z₀ = 377 ohms) can be estimated.
Then solve

sqrt(u₀/e₀) = Z₀ = 376.730 ohms.

Then knowing the speed of light 1/sqrt(u₀ e₀) = c = 2.9979 x 10⁸ meters per sec

e₀ and u₀ can be calculated separately.

u₀ = Z₀/c = 4 pi x 10^-7 Henrys per rmeter

e₀ = 1/(Z₀c) = 8.85 x 10^-12 Farads per meter