  We re-examine the electrodynamic Casimir effect in a wedge defined by two
perfect conductors making dihedral angle \alpha=\pi/p. This system is analogous
to the system defined by a cosmic string. We consider the wedge region as
filled with an azimuthally symmetric material, with permittivity/permeability
\epsilon_1,\mu_1 for distance from the axis r<a, and \epsilon_2,\mu_2 for r>a.
The results are closely related to those for a circular-cylindrical geometry,
but with non-integer azimuthal quantum number mp. Apart from a zero-mode
divergence, which may be removed by choosing periodic boundary conditions on
the wedge, and may be made finite if dispersion is included, we obtain finite
results for the free energy corresponding to changes in 'a' for the case when
the speed of light is the same inside and outside the radius 'a', and for weak
coupling, |\epsilon_1- \epsilon_2| \ll 1, for purely dielectric media. We also
consider the radiation produced by the sudden appearance of an infinite cosmic
string, situated along the cusp line of the pre-existing wedge.
