Final answer:
The electric potential inside a hollow conducting sphere with surface charge +Q and radius R is constant throughout the interior. At any distance inside, including at r=R/3 from the center, the potential is the same as on the surface: V = kQ/R.
Step-by-step explanation:
Electric Potential Inside a Hollow Conducting Sphere
When considering a hollow conducting sphere with radius R and a surface charge +Q, the electric potential within the sphere is uniform. Due to the spherical symmetry and the properties of a conductor in electrostatic equilibrium, the charges reside on the outer surface, and the electric field inside the sphere is zero. Therefore, by integrating the electric field to find the electric potential, the potential at any point within the sphere is the same as on the surface.
At a distance r=R/3 from the center, the electric potential is still equal to the potential at the surface, which is V = kQ/R where k is Coulomb's constant k = 1 / (4πε0). The reason for this is because the integrating path from the surface to any interior point crosses no electric field lines, as the field inside is zero. Hence, there is no change in potential within the sphere, and the value remains constant.
For this particular problem, the numeric calculation of the potential is not required. Instead, the key concept is understanding the potential within a hollow conducting sphere is constant and equal to the potential on its surface.