# Gravitational field intensity inside a hollow sphere

It is quite easy to derive the gravitational field intensity at a point within a hollow sphere. However, the result is quite surprising. The field intensity at any point within a hollow sphere is zero.

What exactly is the reason behind this? Except for, of course, the mathematics behind it. Is there any logic why the field intensity should be zero within a sphere? For example, it is logical to say that the field intensity would be zero at the center, as all the intensities cancel out. However, this cannot be the case for any point within the sphere.

• Note that this proof only works because the angles between the "line of sight" and the surface normal for each of the patches are the same; so both patches are "foreshortened" by the same factor of $\cos \theta$. Otherwise you could make this argument for the interior of any closed surface with a uniform charge density. – Michael Seifert Jul 9 '18 at 18:48