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New equations are derived for voltage and current on two parallel conductors terminated with arbitrary impedances and immersed in external fields. By examining several pertinent static boundary-value problems, it is shown that the source terms of the equations can be split into two parts; one part is directly proportional to the transverse components of the magnetic and electric fields of the incident wave, and the other part is attributable to the unequal size of the two conductors. It is also shown that only one two-dimensional static boundaryvalue problem need be solved for the determination of the coefficients and source terms in the new equations. Detailed calculations are given for two parallel terminated cylinders. Some simple examples are worked out, and the results based on the new equations are contrasted with those derived from the conventional theory.