The capacitance of a conductor has a boundary integral equation formula as the product of the embedding medium dielectric permittivity, the area of the conductor, and the inverse of the squared norm of a given Eigen function of the Neumann-Poincaré operator. The result leads to a class of capacitors in which the outer electrode has the shape of an equipotential surface generated by the equilibrium charge of the inner electrode. We show that co focal spheroid capacitors belong to this class. The thin capacitors of the same class have a planar-like capacitor formula that may be used to estimate the membrane capacitance in living cells.
