Two theorems related to electrical systems containing rapidly rotating conducting bodies are presented and proved. A system of harmonic components of such a system is defined. The first theorem states that each harmonic component is physically realizable. The second and more important theorem follows from the first and states that, under certain conditions which can always be satisfied, the field distribution external to the rotating body is identical to the field that would be there if the currents in the body flowed in a certain determinable pattern. This pattern has the two characteristics: (i) the currents flow entirely on the surface of the rotating conductor; (ii) there is no field within the rotating conductor. The analogy with a.c. skin currents is pointed out. The general conditions under which the second theorem applies are discussed, together with some examples of its application to rotors with current carrying brushes.