How did Coulomb measure charges?

Question

I was studying some Electrodynamics when suddenly this question popped into my mind :

The whole of Electrodynamics is based on the Coulomb's Law. There is no derivation of this law because it is an empirical law. So Mr.Coulomb somehow $experimentally$ measured the force between two charges. . I do not doubt that Mr.Coulomb was a very intelligent person. My question is : How did he manage to put forward a law based on charges without actually knowing what a charge means or represents ? Coulomb's law contains the product of two charges. How does one measure magnitude of charges with some (more) fundamental truths of Physics without invoking any sort of Electro or Magneto concepts ?

Forgive me if this question seems very silly. I am just a beginner at this subject.

Answer 1

Coulomb did not know the absolute value of the charge but what he was able to do was to reduce the charge on one of his spheres by a known ratio.

He charged a metal sphere and used it in his experiment.
He then removed that metal sphere and touched it with an identical uncharged metal sphere.
He assumed that the final charge of the initially charged sphere was half of what had been initially because the initially uncharged sphere has removed half the charge from the initially charged sphere.
He could then use that initially charged sphere with half its initial charge to take a second set of readings.

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You should note that defining the coulomb as the unit of charge is rather recent.
The electrostatic unit (esu) of charge was defined using Coulomb's law, $F = \dfrac {q_1\,q_2}{r^2}$, where $F$ is the force of attraction/repulsion in dynes (the force required at accelerate $1$ gramme at $1\, \rm cm \,s^{-2}$), $r$ the separation in centimetres and the charge was then in esu or statCoulomb or franklin.

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There have been many who have tried to reproduce Coulomb's original experiments to try and evaluate the sort of accuracy that Coulomb might have been able to achieve and even as to whether Coulomb actually got his "results" experimentally.
The paper The Material Intricacies of Coulomb’s 1785 Electric Torsion Balance Experiment and the links therein may be of interest?

Answer 2

[Finally, in 1785, the French physicist Charles-Augustin de Coulomb] published his first three reports of electricity and magnetism where he stated his law. This publication was essential to the development of the theory of electromagnetism. He used a torsion balance to study the repulsion and attraction forces of charged particles, and determined that the magnitude of the electric force between two point charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them.

It is worth reading the history.

Experiments generate a lot of equations that have to be fulfilled for the given measurements, changing the distances and measuring, and assuming the $1/r^2$ attraction will fit the charges to a measured within errors value.

Answer 3

Once the Coulomb force law has been established, with three charges you can decide the values by measuring the three forces between them.

Answer 4

You can measure an effect, and draw tentative conclusions, without a total understanding of its cause. You don't need to know what a charge is, to detect that there is some property, and when it is doubled, other things happen, or when the object changes distance more other things happen. A lot of science happens that way.

As for how they actually found that charge was quantified - it appeared in discrete "amounts" - that was Millikan's oil drop experiment. I've already commented on that, at chemistry stack exchange, but it's relevant here as well (see https://chemistry.stackexchange.com/questions/87803/how-do-they-ensure-there-is-one-electron-on-an-oil-drop-in-millikans-oil-drop-e/87820).

To quote (because it's on a different SE site):

The experiment showed all the drops had discrete amounts of charge. That means, the charges weren't all over the place (any random value). They only had specific values. Some had $2$ or $3$ or $4$ times the charge of others, but it was always some specific value that they had multiples of.

The conclusion was that oil drops didn't seem to pick up "any random amount" of charge, and the reason seemed likely to be because electric charge couldn't be just "any value". There seemed to be some basic unit of a "single electric charge", the smallest value that was found. Some oil drops had $1\times$ or $2\times$ or $5\times$ that charge, but no oil drops had (say) $3.77\times$ or $1.628\times$ that value.

(This isn't strictly correct, because the formula used for friction/viscosity wasn't exactly right, but it gives a good idea how they found the answer. In fact the results led to corrections in that formula.)