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?

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    $\begingroup$ 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. $\endgroup$ – Kevin Oct 19 '15 at 0:35
  • $\begingroup$ @HDE226868 are you saying that Gauss's law depends on the number of dimensions? $\endgroup$ – Anders Gustafson Oct 19 '15 at 1:04
  • $\begingroup$ @AndersGustafson The mathematical framework differs slightly, so technically, yes, but the result is the same, if I remember correctly. $\endgroup$ – 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.

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  • $\begingroup$ Would electromagnetic waves also scale with 1/r or would they still scale with 1/r^2 in this situation? $\endgroup$ – Anders Gustafson Oct 19 '15 at 5:48
  • $\begingroup$ Can you prove the assertions you make in the last sentence? I don't follow how the universe would have "shot apart". $\endgroup$ – HDE 226868 Oct 19 '15 at 15:36
  • $\begingroup$ 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). $\endgroup$ – user6511 Oct 19 '15 at 20:02
  • $\begingroup$ @AndersGustafson, I think so, but I don't know for sure, sorry. $\endgroup$ – user6511 Oct 25 '15 at 22:06

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