  The $T$-matrix formally describes the solution of any electromagnetic
scattering problem by a given particle in a given medium at a given wavelength.
As such it is commonly used in a number of contexts, for example to predict the
orientation-averaged optical properties of non-spherical particles. The
$T$-matrix for electromagnetic scattering can be divided into four blocks
corresponding physically to coupling between either magnetic or electric
multipolar fields. Analytic expressions were recently derived for the
electrostatic limit of the electric-electric $T$-matrix block $\mathbf T^{22}$,
of prolate spheroids. In such an electrostatic approximation, all the other
blocks were zero. We here analyse the long-wavelength limit for the other
blocks ($\mathbf T^{21}$, $\mathbf T^{12}$, $\mathbf T^{11}$) corresponding to
electric-magnetic, magnetic-electric, and magnetic-magnetic coupling
respectively. Analytic expressions (finite sums) are obtained in the case of
spheroidal particles by expressing the fields with solutions to Laplace's
equation, expanding the fields in terms of spheroidal harmonics and applying
the boundary conditions. Similar expressions are also presented for the
auxiliary matrices in the extended boundary condition method, often used in
conjunction with the $T$-matrix formalism.
