How to measure quantity of electricity without Coulomb law?

[Naoki Shibuya]

Or how did Coulomb measure quantity of electricity while doing his experiments that leads him to claim his famous Coulomb's law.

$$F=k\frac{q_1 q_2}{r^2}$$

You can measure F and r for sure. But how about q1 and q2 ?

 

[dE_logics]

He assumed that quantity...he made a new unit.

 

[Naoki Shibuya]

Let me elaborate a bit. Let's suppose Coulomb assumed:

$$F= k q_1 q_2$$ (where r=1)

He could also decide the quantity q1 is 1c [coulomb] and k=1 as he created the unit of electricity. This way, if we know F, we know q2.

He would repeat this process using different charges in q2 while keeping q1=1c. Each time, he would measure F to arrive q2.

This gives him a way to measure quantity of electricity.

Then, he also supposed:

$$F\propto\frac{1}{r^2}$$

and to prove that he would adjust r = r1, r2, r3.. to see how F changes. He could do that with different electric charges and found no inconsistency.

So, he claimed his law is correct.

$$F= k \frac{q_1 q_2}{r^2}$$

***

Does anyone know any book or site that says this was actually what he did ?

 

[Naoki Shibuya]

According to the below article, Coulomb actually knew how to create equal electric charges without requiring his law.

http://www.jfinternational.com/ph/coulomb-law.html"

Coulomb used little spheres with different charges whose exact value he did not know, but the experiment allowed him to test the relation between the charges. Coulomb realized that if a charged sphere touches another identical not charged sphere, the charge will be shared in equal parts symmetrically. Thus, he had the way to generate charges equal to ½, ¼, etc., from the original charge. Keeping the distance constant between the charges he noticed that if the charge of one of the spheres was duplicated, the force was also duplicated; and if the charge in both spheres was duplicated, the force was increased to four times its original value. When he varied the distance between the charges, he found the force decreased in relation to the square of the distance; that is, if the distance was duplicated, the force decreased to the fourth part of the original value.

Also, he used cgs unit (http://http://en.wikipedia.org/wiki/Gaussian_units" ) where k becomes 1.

 

[Bob S]

I think one of the first Coulomb-meters was a gold-leaf in an electrometer inside a Leyden-jar like setup. Equal charge on the two halves of the gold leaf forced them apart, and the force could be calculated by measuring the angle between the two halves. See
http://en.wikipedia.org/wiki/Electrometer