What if gauss's law was different?

Gauss's Law states that the electric field enclosed by a sphere, or any other surface is the same as the charge divided by the electric constant. What if in another universe Gauss's law was, "The Electric Flux enclosed by a sphere is equal to the charge multiplied by Radius of the sphere divided by the electric constant"?

What effect would this have on electromagnetism?

• It's been a few years since I had to deal with that sort of thing, but I'm pretty sure that "law" is mathematically derived; you'll have to change something much more fundamental. And do make sure the units match up, just adding "times the radius" just makes physicists cry. – Kevin Oct 19 '15 at 0:35
• @HDE226868 are you saying that Gauss's law depends on the number of dimensions? – Anders Gustafson Oct 19 '15 at 1:04
• @AndersGustafson The mathematical framework differs slightly, so technically, yes, but the result is the same, if I remember correctly. – HDE 226868 Oct 19 '15 at 1:48

What effect would this have on electromagnetism?

Forces on charges will now scale with $1/r$, not $1/r^2$

The universe will have shot apart shortly after the Big Bang. No stars would form.

• Would electromagnetic waves also scale with 1/r or would they still scale with 1/r^2 in this situation? – Anders Gustafson Oct 19 '15 at 5:48
• Can you prove the assertions you make in the last sentence? I don't follow how the universe would have "shot apart". – HDE 226868 Oct 19 '15 at 15:36
• Can't really 'prove' it per-say. But now that coulombic forces are stronger, like-charges are going to push each other apart far stronger. I highly suspect this would overcome gravity (which will still scale with $1/r^2$ as per the rest of the laws of nature). – user6511 Oct 19 '15 at 20:02
• @AndersGustafson, I think so, but I don't know for sure, sorry. – user6511 Oct 25 '15 at 22:06