  This paper studies the electrostatic responses of a polarly radially
anisotropic cylinder and a spherically radially anisotropic sphere. For both
geometries, the permittivity components differ from each other in the radial
and tangential directions. We show that choosing the ratio between these
components in a certain way, these rather simple structures can be used in
cloaking dielectric inclusions with arbitrary permittivity and shape in the
quasi-static limit. For an ideal cloak, the contrast between the permittivity
components has to tend to infinity. However, only positive permittivity values
are required and a notable cloaking effect can already be observed with
relatively moderate permittivity contrasts. Furthermore, we show that the
polarly anisotropic cylindrical shell has a complementary capability of
magnifying the response of an inner cylinder.
