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Coulomb's Law states that : $$F_e = K_e \dfrac{q_1q_2}{d^2}$$ where $F_e$ means the electrostatic force between two charges of magnitude $q_1$ and $q_2$ and $d$ is the distance between them.
Scientist Charles Augustine de Coulomb derived it in the following manner:

He observed that $F_e$ was directly proportional to the product of the charge of the particles. So, $$F_e \propto q_1q_2$$ He also observed that $F_e$ is inversely proportional to the square of the distance between the particles (inverse-square law). So, $$F_e \propto \dfrac{1}{d^2}$$ Using these two proportions hence obtained, he concluded that :$$F_e \propto \dfrac{q_1q_2}{d^2}$$ which can be expressed in the form of an equation like this : $$F_e = K_e \dfrac{q_1q_2}{d^2}$$ where $K_e$ is the constant of proportionality and is commonly known as Coulomb's Constant or the Electric Constant.

Now, Coulomb observed two factors that affect the force of attraction between any two charged particles. But how did he conclude that there were only $2$ factors that affected the electrostatic force between particles? Could there not be a third factor which affects it too?
Or are we still not sure about the existence of any other factor?

Thanks!

Rajdeep Sindhu
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2 Answers2

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Controlled experimentation/observation is generally the best way to go when setting up a mathematical equation for the phenomenon.

So in case of the electric force, while experimenting they considered various parameters that the force could potentially depend on and tested for it. All of that ultimately led to the form Coulomb got.

Like in all of science, the laws that we have are actually hypothesis that are continuously tested. And so far, Coulomb’s law holds in all those cases.

See this answer for regime where it is violated.

Superfast Jellyfish
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Check Casimir force. It is a force due to quantized electromagnetic fields, and it is a mutual force between particles, static or not. So, Coulomb did understandably miss this.

naijing
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