# Electrical permittivity

1. Apr 1, 2009

### 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?

2. Apr 1, 2009

### 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.

3. Apr 1, 2009

### 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?

4. Apr 1, 2009

### 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)

5. Apr 1, 2009

### f95toli

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.

6. Apr 1, 2009

### 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

Last edited: Apr 1, 2009