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.
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It comes from geometry. That’s like saying the areal of a square isn’t length^2, but length^(2.0001)
The short answer is we did the math.
A lot of concepts in physics rely on the 1/r^2 law, gravity, electromagnetic, acoustics and optics.
The idea is this, if you have a square in front of you 1 unit away with 1 unit sides. The square has an area of 1 square units. Now move the square to be 2 units away from you. Now, the sides of the square look like they became half as small, .5 units. Making the “area” of the square appear to be .25 units squared, or 1/r^2 = 1/4.
So as objects get further away from each other, the “area” seen by each object decreases with 1/r^2. The official derivation for the physics equations can be done by using the conservation of energy and calculus. 🙂
We don’t, despite other answers claiming so. It just fits our theoretical explanations for lots of things extremely neatly, and it matches all experimental data so far. But nothing _really_ prevents it from being 2.00[a billion zeros]001 instead. It would be silly, ugly, and a joke of nature/god/whatever, and we might never even notice.
a few others have already answered with where the inverse square comes from from a mathematical perspective, but there is another aspect:
there are experimental physicists who work with this very question. basically they design experiments to measure that exponent and add ever more zeroes before that maybe existing 00001
by now, we are up to like 20 0’s iirc, but take that number with a grain of salt, I didn’t look it up again for this.
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.
1/r^2 is an approximation. All of our physics calculations are an approximation. Even when we use pi, it’s an approximation.
But these approximations are super super accurate and they are so accurate that we can use them generally for anything in our universe without issue even if they may be some tiny inconsequential, infinitesimally small difference at some scale.
So when we say that this is the value. We understand it may not be ultra ultra perfect, but it’s so close to perfect that there isn’t any difference we care about.
I haven’t seen anyone share the actual reason yet, but not incorrect statements, just not reasonings.
The reason why it’s true is because we live in a world with (supposedly) three spatial dimensions. If we lived in a world with a different number of spatial dimensions then the inverse square law wouldn’t hold. This means that the energy is spread out over an area instead of some other geometry at a particular distance, and as others have said this mathematically translates to an inverse square law.
As for how we know this? Well I said supposedly for a reason. We only think we are in a 3+1 spacetime. We have very good reason to think this, of course, but it is possible we live in a 3.0000000000002+1 dimensional spacetime which would be incredibly weird and makes no sense to our 3+1 evolved brains. If this were the case then it would be an inverse power of 2.0000000000002 law, which looks like an inverse square law down to very small tolerances. The general rule is 1^-(x-1) where x is the number of dimensions that exist. Additionally, micro dimensions, dimensions coiled up on themselves that we can’t perceive, are one hypothesis to explain the weakness of gravity. There’s a lot going on in dimensional studies.
> … Edit: I was assuming correctness of maxwells equations, how flux remains same in absense of additional charge. …
Assuming that Maxwell’s equations hold is a lot like assuming 1/r^2 is correct, though you’d technically need some extra assumptions about stuff like space-time being flat and electromagnetism not having a preferred orientation to get from one to the other.
The 1/r^2 is how a force changes with distance, when the source of the force is a point. If it’s a plane or other object, it’s different.
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