Double layer spherical capacitor with foil

QuickField simulation example

Problem Type
3D problem of electrostatics.

Geometry

R = 200 mm, R=100 mm, a=150 mm

Given
Relative permittivity of dielectric: ε' = 2, ε'' = 6.
Foil electric potential U = 1 V
Conductors electric potential - 0 V

Task
Find the capacitance of spherical capacitor and compare it with analytical solution:
C = 4π·ε·ε₀ · r·R / ( R_ext - r_int ), [F]. *

Solution
Foil subdivides the capacitor into two capacitors. Capacitance of each capacitor can be calculated from charge q or energy W:
C = q/U.
C = 2*W/U².

Results
Electric field strength distribution inside the double layer spherical capacitor with foil is shown below.

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