  Magnetic confinement of stellar winds leads to the formation of
magnetospheres, which can be sculpted into Centrifugal Magnetospheres (CMs) by
rotational support of the corotating plasma. The conditions required for the
CMs of magnetic early B-type stars to yield detectable emission in H$\alpha$ --
the principal diagnostic of these structures -- are poorly constrained. A key
reason is that no detailed study of the magnetic and rotational evolution of
this population has yet been performed. Using newly determined rotational
periods, modern magnetic measurements, and atmospheric parameters determined
via spectroscopic modelling, we have derived fundamental parameters, dipolar
oblique rotator models, and magnetospheric parameters for 56 early B-type
stars. Comparison to magnetic A- and O-type stars shows that the range of
surface magnetic field strength is essentially constant with stellar mass, but
that the unsigned surface magnetic flux increases with mass. Both the surface
magnetic dipole strength and the total magnetic flux decrease with stellar age,
with the rate of flux decay apparently increasing with stellar mass. We find
tentative evidence that multipolar magnetic fields may decay more rapidly than
dipoles. Rotational periods increase with stellar age, as expected for a
magnetic braking scenario. Without exception, all stars with H$\alpha$ emission
originating in a CM are 1) rapid rotators, 2) strongly magnetic, and 3) young,
with the latter property consistent with the observation that magnetic fields
and rotation both decrease over time.
