# When was Coulomb's constant made/established?

Charles-Augustin de Coulomb lived from 14 June 1736 – 23 August 1806. Coulomb's constant is

$$k_{\text e}=\alpha\frac{\hbar c}{e^2},$$

a form of Planck's constant is included, but Max Planck lived 23 April 1858 – 4 October 1947.

• Isn't this just a case of a constant being first empirically determined through measurements, and then explained as physical theory develops? – Anders Sandberg Apr 12 at 4:00

## 2 Answers

The Coulomb constant appears in a wide variety of relationships. Some of those can be used as definitions of the constant, while others only serve to delineate its relationships to other concepts. The fact that it appears in a given relationship does not man that that relationship is its definition. (What is the definition? Well, there is no unique definition, and the choice depends on the details of how you want to structure things.

The relationship you've quoted, $$k_e = \alpha \frac{\hbar c}{e^2},$$ does not serve as a definition of $$k_e$$. At best, it serves as a definition of the fine structure constant, $$\alpha$$, which can be thought of in two distinct ways:

• It gives the strength of the electromagnetic interaction in 'natural units' - that is, in the units that are natural once you have established both quantum mechanics and special relativity, so you can set both $$\hbar$$ and $$c$$ to unity.
• It gives (the inverse of) the speed of light in 'atomic' units, which are also quantum mechanical, and in which you set both $$\hbar$$ and the electron-electron interaction constant to unity.

In either case, $$\alpha$$ is an intrinsically quantum-mechanical object, and (unless you're fully committed to an outlook fully encased within quantum field theory) it cannot really be used to define the Coulomb constant.

From the observations that you made, it is clear that someone made the theory about the Coulomb constant involving the Planck's constant after Coulomb died himself. Probably Planck or someone else.

• Why the downvote? It answers the query very well. The OP just wanted a date. – KV18 Apr 12 at 8:57