plate_capacitor

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plate_capacitor

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{  PLATE_CAPACITOR.PDE  

 

 This problem computes the field around a plate capacitor.

 (adapted from "Fields of Physics on the PC" by Gunnar Backstrom)

 

}  

 

title 'Plate capacitor'  

 

variables  

 u  

 

definitions  

 Lx=1      Ly=1  

 delx=0.5  d=0.2  

 ddy=0.2*d  

 Ex=-dx(u)     Ey=-dy(u)  

 Eabs=sqrt(Ex^2+Ey^2)  

 eps0=8.854e-12  

 eps  

 DEx=eps*Ex    DEy=eps*Ey  

 Dabs=sqrt(DEx^2+DEy^2)  

 zero=1.e-15  

 

equations  

 u : div(-eps*grad(u)) = 0  

 

boundaries  

Region 1  

   eps=eps0  

  start "V0" (-Lx,-Ly)  

      Load(u)=0  

  line to (Lx,-Ly) to (Lx,Ly) to (-LX,Ly) to close  

 

  start "V1" (-delx/2,-d/2)  

      value(u)=0  

  line to (delx/2,-d/2) to (delx/2,-d/2-ddy) to (-delx/2,-d/2-ddy)  

        to close  

 

  start(-delx/2,d/2+ddy)  

      value(u)=1  

  line to (delx/2,d/2+ddy) to (delx/2,d/2) to(-delx/2,d/2)  

        to close  

 

Region 2  

   eps = 7.0*eps0  

  start(-delx/2,-d/2)  

  line to (delx/2,-d/2) to (delx/2,d/2) to(-delx/2,d/2)  

        to close  

 

monitors  

  contour(u)  

 

plots  

  contour(u)  

  surface(u)  

  vector(dx(u),dy(u))  

  fieldmap(u) on "V1" fieldlines=40 as "Field Map"

  contour fieldmap(u) on "V1" fieldlines=40 points=400 as "Potential and Field Map"

 

end