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A model is presented for the electromagnetic interaction between a carbon nanotube and an electrically-small sphere, such as a plasmonic metal particle. The sphere is characterized by its dipole moment, which is coupled to an integral equation for the nanotube. The model can be easily adapted to other systems consisting of electrically-small objects coupled to larger objects requiring a full-wave treatment. It is found that the presence of a non-plasmonic electrically-small sphere has a small effect on observed system properties, but that a plasmonic nanosphere in close proximity to a carbon nanotube leads to pronounced coupling, and may be useful as a way to excite carbon nanotube antennas. Furthermore, backscattering from a plasmonic nanosphere-carbon nanotube system is dominated by the nanosphere response. An approximate analytical solution is provided for the current induced on a nanotube in the presence of a plasmonic nanosphere.