For the following discussion we have to differentiate between the physics of the Coulomb interaction in vacuum and that in a medium. A "medium" is some kind of material that contains atoms or ions and electrons. We will later see that in particular the electrons have a tendency to rearrange themselves in the presence of other charges or electrical fields.
So let's get started with the discussion of the vacuum, and on the next page we will cover a medium.
We have seen that the value of the force constant k in Coulomb's law has the vacuum value of
There is also an alternative way to proceed. To this end we define the permittivity of the vacuum:
Definition:
The permittivity of the vacuum,$\epsilon$ 0 , is defined to have the numerical value:
This value is chosen to obtain the following relationship between the Coulomb constant and the permittivity of the vacuum:
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