I've recently become interested in Nikola Tesla's resonant inductive coupling method of wireless power transfer. I saw an experiment online and the resonant coils seemed to be on axis, or facing each other. I was just wondering if the coils can transmit power when perpendicular to each other.
To maximize the power transfer between two coils you want to maximizes the faction of flux from coil 1 that passes through coil 2 (parallel to the axis of symmetry). The coils might be coaxial or they might be wound on a loop of ferromagnetic material. If one coil were perpendicular (and centered on the other), the flux linkage would be zero.
Generally the coupling (mutual inductance) is maximized if the coils are coaxial. This is related to the fact that, for a given separation, the field along the axis of a small coil or magnet is twice the field on its equatorial plane. The dipole-dipole interaction (which relates to small coils with relatively large separation) gives some insight into how the coupling can vary. Interestingly, there are positions and angles where the coupling is exactly zero - which is sometimes a useful feature.
For two small coils at right angles, the coupling is maximized when the line joining their centers is at 45 degrees to either coil.