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The effect of the surface boundary between free space and a conducting medium on the excitation properties of neurons by magnetic fields is analyzed. The electric field and the spatial derivative of the induced field generated by a coil mounted both parallel and perpendicular to the surface of a semi-infinite conducting medium were calculated using the method of images. An imaginary axon is located in the same relative position from the coil in both configurations and the excitation properties are compared. The calculations are expressed in terms of the activating function for the electrical stimulation of axons. The calculations indicate that the activating function of magnetic stimulation is biphasic as opposed to triphasic for electrical stimulation. The large spatial extent of the magnetically induced electric field compared to the electric field generated by a point source electrode suggests a different mode of excitation for neuronal structures in the CNS. The field distribution has been verified experimentally.