Final answer:
The surface charge density on the inner surface of a spherical shell is calculated as the charge divided by the surface area of the shell. For the inner shell with radius R₁ and charge q₁, the density is q₁ / (4πR₁²), and for the outer shell with radius R₂ and charge q₂, the density is q₂ / (4πR₂²).
Step-by-step explanation:
Surface Charge Density on Spherical Shells
To determine the surface charge density on the inner and outer surfaces of concentric spherical shells, we apply concepts from electrostatics, specifically Gauss's Law. Let's consider a system with two spherical shells. The inner shell has radius R₁ and charge q₁, and the outer shell has radius R₂ and charge q₂. The surface charge density (σ) is the charge per unit area on the surface of a conductor.
(i) Inner Surface of the Inner Shell
Since the inner shell is conducting and of negligible thickness, all charge resides on the surface, and it's uniformly distributed. The surface charge density, σ₁, is given by σ₁ = q₁ / (4πR₁²).
(ii) Outer Surface of the Outer Shell
The outer surface of the outer shell similarly has its charge uniformly distributed. Thus, the surface charge density, σ₂, is given by σ₂ = q₂ / (4πR₂²).
It's important to note that if these shells were conductors and q₁ and q₂ have the same sign, charges in the inner shell would influence the distribution of charges on the inner surface of the outer shell. However, without additional information, we calculate densities assuming uniform distribution.