Capacitance of Simple Systems
Calculating the capacitance of a system amounts to solving the Laplace equation ∇2φ=0 with a constant potential φ on the surface of the conductors. This is trivial in cases with high symmetry. There is no solution in terms of elementary functions in more complicated cases.
For quasi-two-dimensional situations analytic functions may be used to map different geometries to each other. See also Schwarz-Christoffel mapping.
| Type | Capacitance | Comment |
|---|---|---|
| Parallel-plate capacitor |
ε: Permittivity |
|
| Coaxial cable |
ε: Permittivity |
|
| Pair of parallel wires | ||
| Wire parallel to wall | a: Wire radius d: Distance, d > a : Wire length |
|
| Two parallel coplanar strips |
d: Distance w1, w2: Strip width ki: d/(2wi+d) k2: k1k2 |
|
| Concentric spheres |
ε: Permittivity |
|
| Two spheres, equal radius |
a: Radius d: Distance, d > 2a D = d/2a γ: Euler's constant |
|
| Sphere in front of wall | a: Radius d: Distance, d > a D = d/a |
|
| Sphere | a: Radius | |
| Circular disc | a: Radius | |
| Thin straight wire, finite length |
a: Wire radius : Length Λ: ln(/a) |
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