Test3d27.dat, 27th 'test' file for CPO3DS
Cylindrical capacitor with dielectric in gap
Care must be taken in setting up dielectric simulations, so it is very important to read the guidance.
Here the inner and outer cylindrical conductors have radii r1 = 0.5 and r2 = 1.0mm, while the dielectric material has inner and outer radii s1 = 0.501 and s2 = 0.999mm.
The ends have been given larger segments than the middles.
The dielectric constant is K = 2.
The inner and outer conductors have potentials V1 = 1 and V2 = 0.
The charge per unit length on the outer conducter is
Q/l = 2*pi*epsilon0/(ln(s1/r1) + ln(s2/s1)/K + ln(r2/s2))
Therefore in the present case, Q/l = 1.59830E-10 coul/m.
To try to avoid end effects we look at the charge on the part of the outer cylinder between x = 0 and 1mm. Also we use 2 symmetry planes that include the axis.
Therefore the expected charge is 1E-3*(Q/l)/4 = 3.99575E-14 coul.
In fact in the present example it is 4.0055014E-14 (look for the cumulative charge of the 32nd segment), which is in error by 1.5%.
Higher accuracy can be achieved by increasing the total length of the system and of course by using more segments.
This again illustrates a general observation in the examples which we have tested and which involve curved electrodes: the dielectric calculations do not have the very high accuracy of the normal non-dielectric calculations. Also, dielectric calculations with CPO3D are always much slower than the analogous non-dielectric calculations. Furthermore, CPO3D/Di has been optimised to give the most accurate fields inside dielectrics (in preparation for the magnetic version) rather than being optimised for capacitance calculations.
test3d22 Spherical capacitor with dielectric in gap.
test3d23 Parallel plate capacitor with dielectric in gap.
test3d24 Field in a cavity inside a dielectric.
test3d25 Field inside a dielectric sphere.
test3d26 Field inside a dielectric cylinder.