It's not about the formula. The formula comes from the geometry.
1/r^2 falls out as the formula, starting from the geometry of "flux" and "field lines", along with "conservation of flux", in 3d space.
That's the idea that the force acts like something that's radiated in all directions, that doesn't fade with distance, instead it just spreads out so it seems weaker at individual points. The amount of spreading out, if it's uniform in 3d, turns out to be exactly 1/r^2.
You get the same 1/r^2 if you measure the flow of water in a 3d volume with a point source of water in the centre, or electric current in a 3d block of metal with a point source of electric current in the centre. (In both cases, presumably through a thin pipe or cable to the centre).
In 2d space, you get a different formula from the geometry, 1/r. If you see a force, or flow, reducing by 1/r^2 in a system you thought was 2d, you might ask "is there a third dimension involved here which I haven't accounted for?"
In 1d, the force or flow doesn't reduce with distance. For example, current in an electrical wire is the same all along the wire.
And if you see 1/r^3 in 3d, you might speculate about a hidden fourth dimension to explain it.
1/r^2 falls out as the formula, starting from the geometry of "flux" and "field lines", along with "conservation of flux", in 3d space.
That's the idea that the force acts like something that's radiated in all directions, that doesn't fade with distance, instead it just spreads out so it seems weaker at individual points. The amount of spreading out, if it's uniform in 3d, turns out to be exactly 1/r^2.
You get the same 1/r^2 if you measure the flow of water in a 3d volume with a point source of water in the centre, or electric current in a 3d block of metal with a point source of electric current in the centre. (In both cases, presumably through a thin pipe or cable to the centre).
In 2d space, you get a different formula from the geometry, 1/r. If you see a force, or flow, reducing by 1/r^2 in a system you thought was 2d, you might ask "is there a third dimension involved here which I haven't accounted for?"
In 1d, the force or flow doesn't reduce with distance. For example, current in an electrical wire is the same all along the wire.
And if you see 1/r^3 in 3d, you might speculate about a hidden fourth dimension to explain it.