gravitational/electrical force within a shell

[johndoe3344]

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So I memorized that the gravitational force and the electrical field inside a uniformly dense sphere/ring is zero.

But why?

F is inversely proportional to r^2, so if it's off center, let's say closer to the top, then wouldn't the force from the top region of the ring be stronger and thus counteract the force from the bottom region of the ring?

 

[Bernoull]

So I memorized that the gravitational force and the electrical field inside a uniformly dense sphere/ring is zero.

But why?

F is inversely proportional to r^2, so if it's off center, let's say closer to the top, then wouldn't the force from the top region of the ring be stronger and thus counteract the force from the bottom region of the ring?

Explaining why the electric field is zero within a sphere is easy..

Say u have a neutral solid metal sphere, introduce a positive charge (+q) at its core - creating a net charge - adjacent electrons migrate towards +q, and the region they migrated from becomes positive, now electrons adjacent to those newly created + regions migrate towards them and what you have is a rippling out of positive charge - concentrically - from the core to the conductor's surface. Any spherical conductor is incapable of having a net charge anywhere BUT its surface. Since the interior has no net charge, electric field is zero.