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

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1. Aug 29, 2018

### 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!

Last edited: Aug 29, 2018
2. Aug 29, 2018

### sophiecentaur

Did you try Google / Wikipedia?

3. Aug 29, 2018

### Orodruin

Staff Emeritus
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.

4. Aug 29, 2018

### Staff: Mentor

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.

5. Aug 29, 2018

### Orodruin

Staff Emeritus
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.

6. Aug 29, 2018

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

7. Aug 29, 2018

### Staff: Mentor

The definition will change to $\mu_0=\frac{2h\alpha}{ce^2}$. All of those will be exact except for the fine structure constant.

8. Sep 2, 2018

### Nik_2213

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...