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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