Calculated physical quantities in Electrostatics

For electrostatic problems the QuickField postprocessor calculates the following set of local and integral physical quantities.

Local quantities:

• Scalar electric potential U;

• Vector of electric field intensity E = –gradU

  Ex = -dU/dx , Ey = -dU/dy	- for planar case;
  Ez = -dU/dz , Er = -dU/dr	- for axisymmetric case;

• Tensor of the gradient of electric field intensity G = gradE

  Gxx = dEx /dx , Gyy = dEy /dy , Gxy = (dEx /dy + dEy /dx) / 2	- for planar case;
  Gzz = dEz /dz , Grr = dEr /dr , Gzr = (dEz /dr + dEr /dz) / 2	- for axisymmetric case;

  and also its principal components G₁ and G₂.

• Vector of electric induction D = εE, where ε is electric permittivity tensor.

Integral quantities:

• Total electric charge in a particular volume

  q = ∫ D·n ds,
  where integral is evaluated over the boundary of the volume, and n denotes the vector of the outward unit normal;

• Total electric force acting on bodies contained in a particular volume

  F = ½∫ (E(D·n) + D(E·n) - n(E·D)) ds.

• Total torque of electric forces acting on bodies contained in a particular volume

  T = ½∫ ((r×E)(D·n) + (r×D)(E·n) - (r×n)(E·D)) 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.

• Energy of electric field

  W = ½∫ (E·D) dV.

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.