Question

A hollow metallic sphere has inner and outer radii a and b

Answer 1

A hollow metallic sphere has inner and outer radii aa and bb respectively. How to calculate its resistance between two a points AA (on the inner surface) and a point BB (on the outer surface)? The resistivity of the metal is rr.

If you really mean "points", see the answer to this question. Basically, the logic is as follows:

If you try to inject a finite current at a "point" in a bulk, it will necessarily lead to a divergent current density J⃗ J→ in a neighborhood of that point, proportional to r−2r−2 (where rr is the distance from the injection point.)

A divergent current density J⃗ J→ implies a divergent electric field E⃗ E→, via the microscopic Ohm's Law J⃗ =σE⃗ J→=σE→.

E⃗ =−∇VE→=−∇V. Since the electric field is proportional to r−2r−2, the potential will diverge as we go to the injection point (proportionally to r−1r−1).

Thus, the potential difference VV between the points is infinite for a finite current II.

Thus, R=V/IR=V/I is infinite.