Final answer:
To calculate the capacitance of a spherical capacitor, use the formula involving the radii of the inner and outer shells and the permittivity of free space; the capacitance is independent of which sphere is positively or negatively charged.
Step-by-step explanation:
To calculate the capacitance of a spherical capacitor with two concentric spherical conducting shells separated by a vacuum, we use the formula derived from Gauss's Law. The capacitance (C) is given by:
C = 4πε0R1R2 / (R2 - R1)
where:
- ε0 is the permittivity of free space,
- R1 is the radius of the inner spherical shell,
- R2 is the radius of the outer spherical shell.
This equation assumes that the potential difference between the two spheres creates an electric field, which in turn causes the shells to store electric charge.
Note that the capacitance of a spherical capacitor does not depend on which sphere is charged positively or negatively, as it is only concerned with the absolute values of radii and the potential difference.