{  ParallelPlate.PDE  }
 {
    This problem computes the field in an ideal parallel-plate capacitor
    Remember: this is infinitely long in the z direction (out of the page), so we are actually
    computing the capacitance per unit length
 }
 
Title 'Parrallel-Plate Capacitor'
 
Variables
     V   ! The electrostatic potential
 
Definitions
     a=2	! width
     b=1	! Height
 
     V0=1	! Voltage across capacitor
 
     eps0=8.854e-12	! Free-space permittivity
     er=1			! Dielectric constant of filled region
     eps=er*eps0		! permittivity variable used in calculations
 
   { Here we find the charge and capacitance per unit length }
    Qt=eps*LINE_INTEGRAL(Normal(grad(V)),'top')
    Cbox =Qt/V0
 
Equations
     DIV(-eps*GRAD(V)) = 0	! Laplace's equation
 
Boundaries
   REGION 1    'box'
     Start(0,b)   Natural(V)=0 Line to (0,0)
     Value(V)=0 Line to (a,0)
     Natural(V)=0 Line to (a,b)	
     Value(V)=1 Line to Finish			! The top plate
 
     { Now define a path across the lid, used to find the charge}
      START "top" (0,b) LINE TO (a,b) FINISH
 
Plots
   Contour(V)   Report(Cbox)
End