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Magnetic field integral equation (MFIE) and Calderón preconditioned electric field integral equation (EFIE) operators applied to toroidal surfaces have nontrivial nullspaces in the static limit. The nature of these nullspaces is elucidated and a technique for generating a basis for them presented. In addition, the effects of these nullspaces on the numerical solution of both frequency and time-domain MFIE and Calderón preconditioned EFIEs are investigated. The theoretical analysis is accompanied by corroborating numerical examples that show how these operators' nullspaces affect real-world problems. Index Terms-Boundary integral equations, Calderon preconditioned electric field integral equation (EFIE), magnetic field integral equation (MFIE), nullspace.

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