Final answer:
The potential due to a uniformly charged sphere is the same as that of a point charge outside the sphere, r > R, and different inside the sphere, r < R. For a non-uniformly charged sphere, the electric potential generally differs from that of a point charge except possibly at large distances.
Step-by-step explanation:
In What Region of Space is the Potential Due to a Uniformly Charged Sphere the Same as That of a Point Charge?
The electric potential due to a uniformly charged sphere is the same as that of a point charge at distances outside the sphere (r > R, where R is the radius of the sphere). According to the principle of superposition and Gauss's law, the electric field outside the sphere behaves as if the entire charge were concentrated at a point at the center of the sphere. Thus, the potential at any point outside the sphere is identical to that which would be caused by a point charge located at the sphere's center.
However, inside the sphere (r < R), the situation is different. Here, the potential is not the same as that of a point charge. The potential inside the sphere is influenced by the specific distribution of charge within that region, and it varies linearly from the center to the surface of the sphere, unlike the potential of a point charge which would continue decreasing towards the center. Therefore, the correct answer is c) Different inside, same outside.
Can the Potential of a Non-Uniformly Charged Sphere be the Same as That of a Point Charge?
For a non-uniformly charged sphere, the potential generally cannot be the same as that of a point charge at all points because the charge distribution affects the electric potential differently at various points in space. However, at a sufficiently large distance from such a sphere, the non-uniformities in the charge distribution may not significantly affect the potential, making it approximately the same as that of a point charge at those distant points.