Capacitance matrix

Where problems involving multiple surfaces are concerned, it is normal to replace the scalar capacitance with a capacitance matrix. Here individual rows correspond with individual surfaces. The same thing is true for columns. They correspond in the same way with the same surfaces. The element in a given row and column then represents the capacitance between the two corresponding surfaces. The surface charges can be obtained by premultiplying the voltage vector by the capacitance matrix. The question of determining the surface charges that would give rise to the specified voltages is therefore equivalent to determination of the capacitance matrix.