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

• I
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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sophiecentaur
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Did you try Google / Wikipedia?

Orodruin
Staff Emeritus
Homework Helper
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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.

Dale
Mentor
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.

Orodruin
Staff Emeritus
Homework Helper
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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.

Staff Emeritus
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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?

Dale
Mentor
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...