Abstract: Motivated by electrodynamic space tethers we consider the statics problem of a conducting rod in a uniform magnetic field. This problem has close analogies with that of a spinning top in rigid-body dynamics. We show that some cases are integrable while others are nonintegrable. For the latter we use a (Hamiltonian) Melnikov approach that highlights problems with similar Melnikov applications in rigid-body dynamics in the literature as well as ways around these problems.