  We consider the interaction of two perfectly conducting plates of arbitrary
shape that are inside a non-simply connected cylinder with transverse section
of the same shape. We show that the existence of transverse electromagnetic
(TEM) modes produces a Casimir force that decays only as $1/a^2$, where $a$ is
the distance between plates. The TEM force does not depend on the area of the
plates and dominates at large distances over the force produced by the
transverse electric (TE) and transverse magnetic (TM) modes, providing in this
way a physical realization of the 1+1 dimensional Casimir effect. For the
particular case of a coaxial circular cylindrical cavity, we compute the TE, TM
and TEM contributions to the force, and find the critical distance for which
the TEM modes dominate.
