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.
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, e0 , 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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