{  Box.PDE  }
 {
    This problem computes the field in a metal box, with the lid at a fixed potential
    relative to the remaining sides.  (See example 4-7 in Cheng)
 }
 
Title 'Box Capacitor'
 
Variables
     V   ! The electrostatic potential
 
Definitions
     a=2	! Box width
     b=1	! Box Height
 
     V0=1	! Lid Voltage
 
     eps0=8.854e-12	! Free-space permittivity
     eps=eps0		! permittivity variable used in calculations
 
   { Here we find the charge and capacitance }
    Qt=eps*LINE_INTEGRAL(Normal(grad(V)),'lid')
    Cbox =Qt/V0
 
Equations
     DIV(-eps*GRAD(V)) = 0	! Laplace's equation
 
Boundaries
   REGION 1    'box'
     eps=eps0
     Start(0,b)
     Value(V)=0 Line to (0,0) to (a,0) to (a,b)	! The grounded sides
     Value(V)=1 Line to Finish			! The lid
 
      { Now define a path across the lid, used to find the charge}
      START "lid" (0,b) LINE TO (a,b) FINISH
 
Plots
   Contour(V)   Report(Cbox)
End