  Effective magnetic penetration depth and microwave surface impedance are
derived for anisotropic layered superconductors in the shape of spheres and
long cylinders, where the external magnetic field is applied in the plane of
the highly conducting layers to induce out-of-plane screening currents. The
results are extended by analytic continuation to highly anisotropic conductors
and to lossy superconductors at high frequency. The electrodynamics for the
general case of a superconductor or metal with arbitrary anisotropy are
presented. The treatment is then specialized to layered materials with
unixaxial anisotropy, in which the penetration depth for currents flowing
perpendicular to the layers, lambda_c, is much greater than that for in-plane
currents, lambda_a. Exact solutions are found in the limit lambda_a goes to
zero, and are expected to provide an accurate representation of many
experiments on cuprates and other layered superconductors, particularly on
grain-aligned powders.
