Spherical capacitor Formula

The capacitance for spherical conductors can be obtained by evaluating the voltage difference between the conductors for a given charge on each. It depends then on the inner and outer radius of each sphere.

Capacitance = 4 * π * (relative permittivity) * (permittivity of space) / (1/(inner radius) – 1/(outer radius) )

The equation is:

C =4 π k ϵ / (1/ri -1/ro)

Where:

C: Capacitance

ri: inner radius

ro: outer radius

k: relative permittivity

ϵ: permittivity of space

Spherical capacitor Formula Questions:

1) A spherical capacitor filled with air is formed by to cylinders with inner radius 1 cm, and outer radius 5 cm. What is its capacitance?

Answer:

From the cylinder capacitance formula, we substitute the permittivity, equals to one for air, and both radius:

C =4 π k ϵ /(1/ri-1/ro) = 4 π (8.854 *10^(-12) F/m) /(1/(1cm) – 1/(5 cm))

C = 139.07*10^(-12) F

2) A spherical capacitor filled with paper is formed by to cylinders with inner radius 2 cm, and outer radius 5 cm. What is its capacitance?

Answer:

From the cylinder capacitance formula, we substitute the permittivity, equals to 3.85 for paper, and both radius:

C =4 π k ϵ /(1/ri-1/ro) = 4 π * 3.85*(8.854 *10^(-12) F/m) /(1/(2cm) – 1/(5 cm))

C = 1427.87*10^(-12) F