How are Electrical Permittivity and Magnetic Permeability Measured?

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Discussion Overview

The discussion revolves around the measurement of electrical permittivity and magnetic permeability, exploring how these values are defined and derived from experimental data and theoretical frameworks. It includes aspects of theoretical understanding, measurement techniques, and practical applications in physics.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Experimental/applied

Main Points Raised

  • Some participants note that the speed of light in vacuum is dependent on electrical permittivity and magnetic permeability, as shown by Maxwell's equations.
  • Others argue that electrical permittivity and magnetic permeability are defined based on Maxwell's equations rather than directly measured, with the speed of light being a fixed value.
  • One participant clarifies that knowing the speed of light and magnetic permeability allows for the calculation of electrical permittivity.
  • Another participant mentions alternative methods for measuring permittivity, such as measuring capacitance in capacitors or using cavity perturbation methods, suggesting that direct measurement of the speed of light is not commonly used.
  • A later reply discusses measuring the impedance of coaxial cables to estimate permittivity and permeability, providing a specific calculation method involving the impedance of free space.

Areas of Agreement / Disagreement

Participants express differing views on whether electrical permittivity and magnetic permeability are measured directly or defined through theoretical constructs. There is no consensus on a singular method for measurement, as various techniques and definitions are proposed.

Contextual Notes

Some limitations include the dependence on definitions of units, the context of measurements, and the potential for different measurement techniques to yield varying results. The discussion does not resolve these complexities.

Zman
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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?
 
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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.
 
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?
 
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)
 
Zman said:
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.
 
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
 
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