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Electromagnetic free oscillations in the presence of two conducting spheres

We consider the electromagnetic fields which can exist in the presence of two perfectly conducting spheres in free space in the absence of external sources, i.e. the free oscillations. An asymptotic analytical solution for the natural frequencies and natural modes is presented, which is exact in the limit of infinite sphere separation. To our knowledge this is the first analytical treatment of the free oscillations of a two-body geometry. The transcendental equation for the natural frequencies is solved numerically for a representative example. We examine the physical content, especially the feedback mechanism between the current on the two spheres which sustains the free oscillation (apart from radiation damping). This leads to the establishment of a physically logical link between a natural mode and its corresponding natural frequency.