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Chapter 10 Theoretical Description
Neumann condition is defined by the following equations:
jn = j
 at outward boundaries,
jn+ - jn- = j
 at inner boundaries,
where jn is a normal component of the current density vector, "+" and "−"
superscripts denote quantities to the left and to the right side of the boundary, and j at
right hand side is a density of the external current. If j value is zero, the boundary
condition is called homogeneous. This kind of boundary condition is used at an
outward boundary of the region that is formed by the symmetry plane of the problem.
The homogeneous Neumann condition is the natural one; it is defaulted at all outward
boundary parts where no explicit boundary condition is specified.
If the surface-bound current density is to be specified at the plane of problem
symmetry and this plane is the outward boundary of the region, the surface current
density has to be halved.
Constant potential boundary condition is used to describe surface of a conductor
having much greater conductivity than the surrounding medium. This conductor is
assumed to have constant but unknown potential value.
Note. The edge described as possessing constant potential should not have common
points with any Dirichlet edge. In that case the constant potential edge has to be
described by the Dirichlet condition with an appropriate potential value.
Calculated Physical Quantities
For ac conduction problems, the QuickField postprocessor calculates the following
set of local and integral physical quantities.
Local quantities:
•
•
Complex amplitude of electric potential U;
Complex vector of electric field intensity E = −gradU
Ex = −
Ez = −
∂U
∂x
∂U
∂z
,
Ey = −
,
Er = −
∂U
∂y
∂U
∂r
 for planar case;
 for axisymmetric case;