How do we surely know that electric force is 1/r²? If it is just because “it works” then why can’t it be 1/r^(2.0000001) or something, how do we know?

Question

Edit 1:
I was assuming the correctness of maxwells equations, how flux remains same in the absence of additional charge. So is it to say that that is 100% correct or just simple it can be a really really good approximation and we dont know?

Edit 2:
The best explanation I got till now: We simply do not know if it is really 1/r^2, but experimentally we have found that this model is very accurate to several decimal points(2.0000…). The 1/r^2 and maxwells equations are same, they are correct or wrong together. And in my opinion, the divergence equation for electric field seems very simple, and we found its high accuracy through experiments, so I have a feeling that it must all be exact 1/r^2. But still, I don’t think we have a way to find out because the equations are themselves the starting point which describes the experiments very well, we don’t have derivation for them and I don’t think we will ever have, and on the other hand, our only way to check is by experiments which won’t give 100% confidence accuracy.

Edit 3:
Another perception is about unit-dimentions. Like ( c^2 ) * e0*u0 = 1, which binds the units of e0 and u0, so electric and magnetic formulas must together be right or wrong. I can’t think or anything more right now, but there can be some other unit-dimension constraints that I am missing which will complete the picture.

In: 40

Answer 1

Pretty much everything in physics is “This is true as far as we’re able to measure it right now, and the math works out.”

Inverse square relationships seem to work to the degree that we’re capable of measuring them (which is quite a bit more than seven decimals), and assuming that they’re true allows us to make other mathematical formulas that correctly describe the universe, as far as we can measure it.

If, at some future point, we’re able to measure things better, and it turns out to be some other exponent, then that means that our math is pretty much all wrong, and we’ll have to start over. That’s happened several times over the years.

For a long time, Newton’s laws of motion were correct, but then we found out that they were just a tiny bit off, and Einstein (and others) worked out how relativity fit into the equations.

A big part of science is taking stuff we “know” and figuring out whether it’s right or not. It’s possible that Maxwell was wrong, too, but if he was, then somebody will have to prove it, and come up with a new set of equations that work better.