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boundary conditions in an equivalent plane capacitor

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For a mathematical study, I want to modelize a checkerboard in 2D, in electrostatics.
The checkerboard is filled with 2 materials with complex permittivities (eps1=1 eps2=1+100i for example). The checkerboard is a square of dimensions : 1 * 1 , the 2 materials are randomly distributed.
When I impose an electrical potential on bottom side (V=1V) and Ground on top side (electric symmetry on the 2 other sides), I should find the norm of the electric field equal to 1. It's not the case : normE is superior to 1.
Where is the problem with my boundary conditions?
I need to integrate on checkerboard normE*normE : the value is bigger (3 or more...).
What have I to change in my boundary conditions to obtain normE=1?

The idea is to simulate a plane capacitor with the checkerboard inside the two armatures, to find an equivalent homogenous material to the checkerboard. If I add 2 copper armatures on the top and bottom sides with electrical potentials on bottom and top, the problem remains the same.
Thank you for your help.

0 Replies Last Post 21 avr. 2016, 10:40 UTC−4
COMSOL Moderator

Hello Sophie Lasquellec

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