The relation of the structure of a cylindrical coil used on the receiver side of an inductive power system to the level of power that can be delivered is investigated. It is found that for a given fixed receiver coil size, an optimum design can be defined in which the cross sectional area of the core equals that of the winding. Results of circuit simulation, Finite Element Analysis and measurements of five test coils are presented to verify the proposed theory for the case of coils having 5 mm diameter and 10 mm length.