Question

Obtain the Gravitational potential and field intensity at a point due to homogenous solid sphere of Inside point.

Answer 1

Potential at P due to the whole sphere may be treated as the sum of two potentials: The potential due to 

(i) Sphere of radius OP, V₁ and 

(ii) Hollow sphere of inner radius OP = r and outer radius R, V₂.

(i) Potential(V₁) due to sphere of radius OP.

Here P lies at the surface of this sphere. Hence

(ii) Potential(V₂) due to hollow sphere : The hollow sphere is assumed to be made up of spherical shells. One such shell,shown in the figure is producing potential at P given by

This is as function of r.The gravitational field intensity along radial direction denoted by. It is given by

The graphs of V(r) and g r are shown below. Mark that |g_r| is maximum at the surface of the sphere.