Final answer:
The potential difference between two concentric hollow spheres of radii r and 4r with equal surface charge densities can be found using Coulomb's law and the definition of electric potential, considering the charges on each sphere and their radii.
"The correct option is approximately option C"
Step-by-step explanation:
The student's question pertains to the electric potential difference between two concentric hollow metal spheres with respect to their surface charge densities and radii.
Given that the surface charge densities of the two concentric spheres are equal, and the radii are r and 4r, with charges Q1 and Q2 respectively, we are to find the potential difference V(r) - V(4r). Since the surface charge density is given by σ = Q/(4πR²), and for two surfaces with the same charge density, Q1/R² = Q2/(4R)². From this ratio, we can find a relation between Q1 and Q2, and then express the potential difference using the formula V = kQ/R, where k is Coulomb's constant and R is the radius.
By equating the charge densities and solving for the charges in terms of the known variables, we can calculate the potential at the surfaces of both spheres. Finally, we find the difference in potential to determine the potential difference, V(r) - V(4r). In such a scenario, the answer would involve an expression of the form V = kQ/R, applied to each sphere independently and according to the charges Q1 and Q2 settled by the equality of the surface charge densities across the spheres.