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Integral quantities in Electrostatics

Generally the integral quantities of interest in electrostatic analysis are: electric charge, potential difference, mechanical force and torque, field energy.
The following notations are used in formulas:

U - electric potential;
E - electric field strength;
D - vector of electric flux density (electric displacement).

Name, ActiveField constant	Formula and Description
Electric charge qfInt_KGrad_n_ds	\[ Q_s = \oint(\mathbf D ·\mathbf n)ds \] According to the Gauss theorem, total electric charge in a particular volume can be calculated as a flux of electric displacement over its closed boundary.
Electric field energy qfInt_ElectrostaticEnergy	\[ W = \frac{1}{2}\int(\mathbf E ·\mathbf D)dv \] Electric field energy in a particular volume.
Mechanical force qfInt_MaxwellForce	\[ \mathbf f = \frac{1}{2}\oint\left( \mathbf E(\mathbf n · \mathbf D) + \mathbf D(\mathbf n · \mathbf E) - \mathbf n(\mathbf E · \mathbf D) \right) ds \] Total electric force acting on bodies contained in a particular volume. The integral is evaluated over the volume's boundary.
Mechanical torque qfInt_MaxwellTorque	\[ \mathbf T = \frac{1}{2}\oint\left( (\mathbf r × \mathbf E)(\mathbf n · \mathbf D) + (\mathbf r × \mathbf D)(\mathbf n · \mathbf E) - (\mathbf r × \mathbf n)(\mathbf E · \mathbf D) \right) ds \] Electric force torque acting on bodies contained in a particular volume, 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.

Name, ActiveField constant	Formula and Description
Average surface potential qfInt_Potential_ds	\[ U = \frac{1}{S}\int U ds \]
Average volume potential qfInt_Potential_dv	\[ U = \frac{1}{V}\int U dv \]
Root mean square value of the surface strength	\[ E = \sqrt {\frac{1}{S}\int \|\mathbf E\|^2 ds } \]
Root mean square value of the volume strength	\[ E = \sqrt {\frac{1}{V}\int \|\mathbf E\|^2 dv } \]
Root mean square value of the surface displacement	\[ D = \sqrt {\frac{1}{S}\int \|\mathbf D\|^2 ds } \]
Root mean square value of the volume displacement	\[ D = \sqrt {\frac{1}{V}\int \|\mathbf D\|^2 dv } \]