How to prove that field inside a hollow sphere is zero anywhere inside that sphere using solid angle concept?

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One possible (well known) proof is based on Coulomb's law.

For any given point inside a hollow sphere, the fields produced by patches of charge, subtending the equal solid angles on the opposite sides of the sphere, will cancel each other, because the charge magnitudes of the patches will be proportional to the square of their distances to the point of interest, while their fields will be inversely proportional to the square of the same distances.

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  • $\begingroup$ K, I was thinking about that, any other proof $\endgroup$ – user199996 Jul 7 '18 at 13:09
  • $\begingroup$ @user199996 Not off the top of my head. $\endgroup$ – V.F. Jul 7 '18 at 13:12

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