# Why does k vary in Coulomb's law depending on the medium?

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Coulombs law is F=kq1q2/r^2, where F is the force of repulsion between two charged objects, r is the distance between them, q1 and q2 are the objects' respective charges, and k is a constant whose value is dependent upon the medium between the 2 objects.

The larger k is, the greater the force, and the smaller k is the smaller the force. k is at its greatest in a vacuum. In contrast, in water it is an eightyth as large. In the body it is about eighth as large. In rubber it is about half to a third. Etc etc. My question is why?

I suspect it might have something to do with induction.

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If by "induction" you mean that the surrounding material reacts to the presence of a charge and becomes electrically polarized, you are correct. This should indeed also alter the net force between two charged objects in such a medium. However, I have my doubts that the relation $F=k q_1q_2/r^2$ holds true in water at all. Are you sure it's not a $k®$ (or that the "1/80 the value in vacuum" refers to a given distance) in the source where you have that from?

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I think what you want to investigate is the polarizability ($\epsilon$, rather than $\epsilon_0$ for vacuum) of materials. A dielectric in an electric field will become polarized, and the electric field from that reduces the overall field present in the medium.

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• 2 weeks later...

I think what you want to investigate is the polarizability ($\epsilon$, rather than $\epsilon_0$ for vacuum) of materials. A dielectric in an electric field will become polarized, and the electric field from that reduces the overall field present in the medium.

Nice response! That's my thought too, except I couldn't think of how to put it as elegantly as you have.

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