Dependence of size on electrical permittivity

[notknowing]

Imagine that one could alter the electrical permittivity or the magnetic permeability of the vacuum. How would this affect for instance the size of an atom or the size/length of a piece of material ?

 

[Gokul43201]

What do you think?

This looks like it might be a homework/textbook problem, so we require you to first show us what you think.

 

[notknowing]

What do you think?

This looks like it might be a homework/textbook problem, so we require you to first show us what you think.

If it was so simple as a homework/textbook problem, I would not have asked for help (being a physicist). I know about all kinds of different bonds, Lennard-Jones potential, Van der Waals forces and all that stuff. I could not find out however how the interatomic distance in a solid for instance depends on the electrical permittivity (E). What I expect (but could not prove) is that the atom size or atomic distance depends always in the same way on E, such that if one could change the permittivity (thought experiment) of the vacuum that all distances would scale in exactly the same way, independent of the type of bond (or the atom considered). So, it would be nice if some of the experts in this forum could come with a simple, founded, scaling formula.

My motivation for this question is based on cosmological considerations, but this is another story (which I don't want to mix with this more down to Earth question).