
Problem Type:
A plane problem of electrostatics.
Geometry:
The problem's region is bounded by ground from the bottom side and extended to infinity on other three sides.
Given:
Relative permittivity of air ε = 1;
Relative permittivity of dielectric ε = 2.
Problem:
Determine self and mutual capacitance of conductors.
Solution:
To avoid the influence of outer boundaries, we'll define the region as a rectangle large enough
to neglect side effects. To calculate the capacitance matrix we set the voltage U = 1 V
on one conductor and U = 0 on the another one.
Self capacitance: C_{11} = C_{22} = Q_{1} / U_{1};
Mutual capacitance: C_{12} = C_{21} = Q_{2} / U_{1};
where charge Q_{1} and Q_{2} are evaluated on rectangular contours around conductor 1 and 2 away from their edges. We chose the contours for the C_{11} and C_{12} calculation to be rectangles –6 ≤ x ≤ 0, 0 ≤ y ≤ 4 and 0 ≤ x ≤ 6, 0 ≤ y ≤ 4 respectively.
Comparison of Results:
C_{11} (F/m) 
C_{12} (F/m) 

Reference: 
9.2310–^{11} 
–8.5010–^{12} 
QuickField 
9.43 10–^{11} 
–8.5710–^{12} 
Reference:
A. Khebir, A. B. Kouki, and R. Mittra, "An Absorbing Boundary Condition for QuasiTEM Analysis of Microwave Transmission Lines via the Finite Element Method", Journal of Electromagnetic Waves and Applications, 1990.
See the Elec2.pbm problem in the Examples folder.