32nd benchmark test for CPO3D, shielding by a spherical dielectric shell
Derived from test3d25, field in a dielectric sphere.
See also test3d24.dat, field in a cavity inside a dielectric.
Care must be taken in setting up dielectric simulations, so it is veryimportant to read the guidance given in Help.
A uniform field of 1V/mm is created by applying a linear field to a sphere.
A spherical shell of inner and outer radii 0.04 and 0.05mm is put at thecentre of the system. It has a dielectric constant K = 10.
The inaccuracy used for evaluation of the fields at the dielectric interfacesis 1.E-7 (but see below).
The ratio of the internal field to the external far-field is (see J D Jackson,Classical Electrodynamics, Wiley, 1998)
s = 9K/((2K+1)*(K+2)-2(A/B)**3*(K-1)**2)
where a and b are the inner and outer radii
In the present simulation, with the present number of segments in the outersphere, E_ext is 0.998664, slightly different from the 1V/mm. Therefore we should have, for K = 10, s = 0.5324, E_cavity = 0.5317. The program gives 0.5285, which is in error 0.6%.