The capacitance of an isolated sphere can be calculated using the formula:
=
4
0
,
C=4ĻĻµ
0
ā
R,
where:
C is the capacitance of the sphere,
Ļ (pi) is the mathematical constant approximately equal to 3.14159,
0
Ļµ
0
ā
(epsilon naught) is the vacuum permittivity, a fundamental constant related to the properties of free space, approximately
8.854
Ć
1
0
ā
12
ā
F/m
8.854Ć10
ā12
F/m,
R is the radius of the sphere.
This formula assumes that the sphere is a perfect conductor (idealized case) and that the charge is distributed uniformly over the surface of the sphere.
Keep in mind that capacitance is a measure of the ability of a conductor to store electric charge when a potential difference (voltage) is applied across it. The larger the capacitance, the more charge the sphere can store for a given voltage.
It's important to note that for more complex geometries or non-uniform charge distributions, the calculation of capacitance might involve more intricate methods, such as using calculus or numerical techniques. However, for an isolated sphere with uniform charge distribution, the above formula is sufficient.