The respective posts where this mistake propagates has been changed.
From the post "Opps! Lucky Me", we suggested that,
F=−dEdr=−ψA
where E is the energy in a infinitely thin spheric shell passing through a point r, r distance from a point particle center. And
dEdr
is the change in E along the radial line.
This is again wrong. This force must be divided by 4πr2, as this total force is redistributed over the surface area of the sphere, to obtain F, the force along a radial line.
F=−14πr2dEdr=−ψA4πr2
and we have,
F=−ψ
when
ψA=ψ.4πr2
And for F to have a inverse square law dependence,
ψ∝1r2
This hopefully is the last of the issue.