The Development of Coulomb's Law

[BelaLuna]

Hello, I am new here. I have a question that I cannot seem to find an answer to and is beginning to bother me in the worst way.
I was researching to find out how Coulomb developed the formula that is used today (since I do not have the programme, I shall not even attempt to write it) and found that not one source could give me a straight-forward answer. It simply said that he thought the relationship was caused by two different fluids and that the unit coulomb and Coulomb's Law is named after him. This is leading me to believe that someone else had continued upon the theory, fully explained the relationship, and developed the formula. And if this is so, who? Who developed it?
This may seem silly, but it is frustrating after reading at least eleven different articles of the subject and not being able to find an answer to a relatively simple question. Does anyone have an idea as to who this person may be? Or am I gravely mistaken in thinking that there is another person?

(if this is a double post, i offer my sincerest of apologies, but my internet is acting rather strange tonight and am not sure if this came through)

 

[Allday]

torsion balance

From what i know Coloumb just noted the simple fact that the magnitude of the force one charged object exerts on another (like conducting spheres) is proportional to the amount of charge on both objects and inversly proportional to the distance between them squared.

http://en.wikipedia.org/wiki/Image:Bcoulomb.png

above is a link to a drawing of the torsion balance he used to make his measurements.

 

[BelaLuna]

Did some more research and had that question answered, but I still cannot find how Coulomb found the constant "k." It is a queer number and must have been found somehow, but I can't find how he did it. The torsian balance was used, of this I am sure, but how?

 

[ranger]

The electrostatic can be found by:

$$k_c = \frac{1} {4 \pi \epsilon_0}$$

where $\epsilon_0$ is the permittivity of free space and is found by:

$$\epsilon_0 = \frac {1} {c^2 \mu_0}$$

 

[Claude Bile]

Did some more research and had that question answered, but I still cannot find how Coulomb found the constant "k." It is a queer number and must have been found somehow, but I can't find how he did it. The torsian balance was used, of this I am sure, but how?

He simply measured the force for a known pair of charges and a known separation.

To Ranger: I'm not sure Couloumb had the luxury of using those equations, since Couloumbs work preceded that of Gauss and Maxwell!

Claude.