Ladder
Gauss law — the ladder
2 distinct arguments against one idea, from the one that introduces it to the one that assumes the rest.
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Counting what comes out, and never looking inside
Draw any closed surface. The field crossing it depends only on the charge enclosed — not on where that charge sits, not on its shape, not on anything outside.
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The shape decides the falloff, and the force law never changes
A point charge gives an inverse square, a line gives an inverse, a plane gives a constant. All three come from the same law, and the exponent belongs to the geometry of the source rather than to the physics.