# How was the value of the permittivity of free space determined?

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• Steven_Scott
In summary, the permittivity of free space, ε0, was first experimentally determined through a setup that measured electrostatic forces. However, with the current definition of the meter, it is directly defined through the speed of light and the permeability of free space. In the future, with the expected change in SI units, the permittivity of free space will become an experimentally measured quantity again, related to the fine structure constant. This may involve the use of a vacuum capacitor in a laboratory setting.
Steven_Scott
The permittivity of free space, ε0, is usually given without any derivation or historical context as to how it was experimentally determined.

Could you explain to me how the value of ε0 was first determined experimentally or provide a resource that gives such a derivation?

Thanks!

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Did you try Google / Wikipedia?

Worth noting: It was only measured historically when the definition of the meter was different than it is today. Today, it is directly defined through the definition of ##c## and ##\mu_0##.

See https://en.wikipedia.org/wiki/Vacuum_permittivity

However, if you want to do it the ”old way” you can create a setup where you can determine electrostatic forces.

Orodruin said:
Worth noting: It was only measured historically when the definition of the meter was different than it is today. Today, it is directly defined through the definition of ##c## and ##\mu_0##.

See https://en.wikipedia.org/wiki/Vacuum_permittivity

However, if you want to do it the ”old way” you can create a setup where you can determine electrostatic forces.
Interestingly, if the SI units are changed at the next meeting as expected then the permittivity of free space will again be an experimentally measured quantity. It will be related to the fine structure constant.

Dale said:
Interestingly, if the SI units are changed at the next meeting as expected then the permittivity of free space will again be an experimentally measured quantity. It will be related to the fine structure constant.
Yes, the underlying reason being that ##\mu_0## no longer will set the definition of the Ampere, but the Ampere will instead be defined as a number of elementary charges per second.

Orodruin said:
Yes, the underlying reason being that $\mu_0$ no longer will set the definition of the Ampere,

So π (or at least 4π x 107) becomes a measured quantity?

So π (or at least 4π x 107) becomes a measured quantity?
The definition will change to ##\mu_0=\frac{2h\alpha}{ce^2}##. All of those will be exact except for the fine structure constant.

I've a vague recollection of a College or Uni lab with a 'vacuum capacitor', plate edge effects mitigated by guard rings and other arcane topology.
Sadly, it was more an exercise in error bars than a definitive determination...

## 1. What is the permittivity of free space?

The permittivity of free space, denoted by the symbol ε0, is a physical constant that represents the ability of a vacuum to permit the flow of electric field lines. It has a value of approximately 8.854 x 10^-12 farads per meter.

## 2. How was the value of the permittivity of free space determined?

The value of ε0 was first determined by the French physicist Charles-Augustin de Coulomb in the late 18th century through his experiments with electric charges and the resulting forces between them. Later, in the 19th century, James Clerk Maxwell used Coulomb's findings to derive the value of ε0 using his famous equations of electromagnetism.

## 3. Why is the permittivity of free space an important constant?

The permittivity of free space is an important constant in physics because it is used in various equations to calculate the strength of electric fields, and is also a key component in the calculation of capacitance and electromagnetic radiation. It serves as a fundamental constant in many areas of physics and engineering.

## 4. Is the value of the permittivity of free space exact?

No, the value of the permittivity of free space is not exact. It is an experimental value that has been measured and refined over time. The current accepted value is based on the International System of Units (SI) and is considered to be accurate up to 11 decimal places.

## 5. Has the value of the permittivity of free space changed over time?

Yes, the value of the permittivity of free space has changed over time as our understanding and measurement techniques have improved. For example, early measurements by Coulomb and Maxwell resulted in values that were slightly different from the current accepted value. However, the changes have been minor and the current value is considered to be highly accurate.

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