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In systems involving inductive coupling between an external coil or coils and an internal coil, an improvement in the efficiency of energy transport is usually realized when a suitable ferrite core is utilized for the implanted coil. A detailed theoretical analysis, with particular emphasis upon hollow spherical and oblate spheroidal cores indicates the manner in which the improvement is related to the geometry of the core and the electrical and magnetic parameters of the ferrite. For a system with a low initial value of efficiency, the insertion of a suitable core results in a several-fold improvement in energy transport efficiency. The analysis indicates that unless the almost field-free region within the ferrite shell can be utilized to advantage, increased efficiency of energy transport can probably be achieved more easily by increasing the diameter of a coreless coil than by using a ferrite core.