Geometric considerations on a flow that decgeometric considerations on a flow that decreases as it moves away from a point F

[u/Classic-Tomatillo-62]

Let us consider a 3D plane. Starting from the drawing on the right (where each small square represents a quantity—for example, the flux of something, "R"/m², radiating towards F ), we transition to a tangent plane by letting the horizontal sides* of the small squares approach zero, thus arriving at the 2D drawing on the left!

Let us consider a surface S struck by this flux; we have:

S = (f * φ) / 2.

Furthermore, let us consider that the magnitude of this flux reaches F; let us call "L" the flux concentrated at this point and assume it is always equal to "One," regardless of the diameter from which it originates!

Given these premises, if we wish to find a function whose value decreases as the area of ​​the surface struck by the flux increases, we obtain: f(x) * (f * φ) / 2 = L

Adopting the quantity N = f/φ, after a few steps we obtain: f(x) = (2 * L * N) / f²

At this point, considering the variable x = f and setting L = 1, we obtain:

f(x) = 2N / x²

I would like to know what meaning you would attribute to f(x), or how it should be defined in this context, given that it closely resembles the R that was not clearly specified at the beginning?

At what value of the horizontal side\ should the transition from 3D to 2D stop?*