dielectric

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{  DIELECTRIC.PDE

 

   This problem shows the electrostatic potential and the electric field

   in a rectangular domain with an internal region in which the dielectric

   constant is fifty times that of the surrounding material.

   The electric field E is -grad(V), where V is the electrostatic potential.

   

   See also FIELDMAP.PDE

}  

 

title 'Electrostatic Potential'  

 

variables V  

 

definitions  

 eps = 1  

 

equations  

 div(eps*grad(V)) = 0    

 

boundaries  

region 1  

  start (0,0)  

  value(V) = 0   line to (1,0)  

  natural(V) = 0 line to (1,1)  

  value(V) = 100 line to (0,1)  

  natural(V) = 0 line to close  

region 2  

   eps = 50  

  start (0.4,0.4)  

  line to (0.8,0.4) to (0.8,0.8)  

        to (0.6,0.8) to (0.6,0.6)  

        to (0.4,0.6) to close  

 

monitors  

contour(V) as 'Potential'  

 

plots  

grid(x,y)  

contour(V) as 'Potential'  

vector(-dx(V),-dy(V)) as 'Electric Field'  

 

end