  Semi-analytic expressions for the static limit of the T-matrix for
electromagnetic scattering are derived for a circular torus, expressed in bases
of both toroidal and spherical harmonics. The scattering problem for an
arbitrary static excitation is solved using toroidal harmonics and the extended
boundary condition method to obtain analytic expressions for auxiliary Q and
P-matrices, from which the T-matrix is given by their division. By applying the
basis transformations between toroidal and spherical harmonics, the
quasi-static limit of the T-matrix block for electric multipole coupling is
obtained. For the toroidal geometry there are two similar T-matrices on a
spherical basis, for computing the scattered field both near the origin and in
the far field. Static limits of the optical cross-sections are computed, and
analytic expressions for the limit of a thin ring are derived.
