Capacitance of spherical capacitor

A spherical capacitor is composed of two concentric spheres with the space between them filled with a dielectric medium. See Figure.

Links:

  1. Physics Bootcamp, formula 34.3.1.

capacitance

capacitance of the capacitor.

Symbol:

C

Latex:

\(C\)

Dimension:

capacitance

absolute_permittivity

absolute_permittivity of the medium between the spheres.

Symbol:

epsilon

Latex:

\(\varepsilon\)

Dimension:

capacitance/length

inner_radius

Radius of the inner sphere. See distance_to_origin.

Symbol:

r_in

Latex:

\(r_\text{in}\)

Dimension:

length

outer_radius

Radius of the outer sphere. See distance_to_origin.

Symbol:

r_out

Latex:

\(r_\text{out}\)

Dimension:

length

law

C = 4 * pi * epsilon * r_in * r_out / (r_out - r_in)

Latex:
\[C = \frac{4 \pi \varepsilon r_\text{in} r_\text{out}}{r_\text{out} - r_\text{in}}\]