For magnetostatic problems the QuickField postprocessor calculates the following set of local and integral physical quantities.
Local quantities:
Vector magnetic potential A (flux function rA in axisymmetric case);
Vector of the magnetic flux density B = curl A
Bx = dA/dy , By = -dA/dx |
- for planar case; |
Bz = (1/r)·(d(rA)/dr) , Br = -dA/dz |
- for axisymmetric case; |
Vector of magnetic field intensity
H = μ-1·B,
where μ is the magnetic permeability tensor.
Integral quantities:
Total magnetostatic force acting on bodies contained in a particular volume
F = ½∮ (H(B·n) + B(H·n) - n(H·B)) ds,
where integral is evaluated over the boundary of the volume, and n denotes the vector
of the outward unit normal.
Total torque of magnetic forces acting on bodies contained in a particular volume
T = ½∮ ((r×H)(B·n) + (r×B)(H·n) - (r×n)(H·B)) ds,
where r is a radius vector of the point of integration. The torque vector is parallel to z-axis in the planar case, and is identically equal to zero in the axisymmetric one. The torque is considered relative to the origin of the coordinate system. The torque relative to any other arbitrary point can be obtained by adding extra term of F × r0, where F is the total force and r0 is the radius vector of the point.
Magnetic field energy
W = ½∫ (H·B) dV. |
- linear case; |
W = ½∫
|
- nonlinear case. |
Flux linkage per one turn of the coil
Ψ = 1/S · ∮A ds |
- for planar case; |
Ψ = 1/S · 2π∮rA ds |
- for axisymmetric case; |
the integral has to be evaluated over the cross section of the coil, and S is the area of the cross section.
For planar problems all integral quantities are considered per unit length in z-direction.
The domain of integration is specified in the plane of the model as a closed contour consisting of line segments and circular arcs.