My question is regarding gravitational potential If you take a spherical shell, say of mass $M$, and then you split the shell in 2 portions by a plane other than the median plane....say that the larger portion is A and the smaller portion is B....Now consider a point C, which is the centre of the circular common interface of both portions A and B.
Could you compare the gravitational field and potential by both the portions A and B at C.
Please provide a suitable explanation for your answer.
 A: This is a straightforward application of Newton's Shell theorem. The gravitational field of the two portions exactly cancels out, and C does not have to be the centre of the common interface. I have given a proof in the caption of Figure 8.4 of Structures of the Sky


Figure 8.4: Newton’s shell theorem (part I). It is a well known theorem of Euclidean
geometry that, for points A, B, C & D on a circle centre O, angle A equals angle C
and angle B equals angle D. So, triangles BAX and DCX are similar (the same shape but
different sizes). Then the length of the small arcs AB and CD are proportional to their
distance from X. On a sphere, similar areas at AB and at CD are proportional to the
square of their distances from X. With a uniform spherical shell and an inverse square
law, the gravitational force due to matter in a small region at AB is equal and opposite to
the gravitational force due to matter at a similar region at CD. Since gravity cancels out
for all such regions, there is no net gravitational force inside the shell.

Since there is no gravitational force inside the shell, the gravitational potential is constant inside the shell.
