Where does the epsilon in Gauss's law come from

[semc]

Hi, I have been trying to find out the derivation of Gauss's law but can't seem to find any derivations. May I know how the differential form of Gauss's law is derived and where does the epsilon come from? Does it have to do with the displacement field definition?

 

[clamtrox]

What would you like to derive it from? Which laws are your starting point?

The epsilon in Gauss's law is related to the strength of electromagnetic interactions, and basically it tells you how easy it is for the electric field to penetrate the medium.

 

[semc]

I have no idea the starting point. From the differential form of Gauss's law you get the epsilon but what's the law before that? Does the epsilon come from experimental data in Coulomb's law?

 

[rude man]

All electromagnetic theory is based on experimental evidence.

This is probably not the place for me to enumerate the 9 experiments that form the basis of e-m theory.

 

[clamtrox]

You can try proving Gauss's law from Coulomb's law, if you like. They are not logically equivalent, but Gauss holds whenever Coulomb holds.