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
We don’t. We basically made a guess that has held up for a few hundred years. But that guess was based on many other guesses that have held up for even longer (e.g. the concept of the inverse square law) so it’s not like we were just shooting in the dark.
As for what if we were off by just a bit? It’s possible, but in practical terms, it hasn’t mattered. I vaguely recall an anecdote that we only need pi to around 15 decimal places in order to send a probe to the other side of the galaxy usefully. And if you want even more egregious intentional fudging, check out amplifier linearity.
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