  The amplitude of the magnetic field surrounding the Galactic Centre (GC) on
large scales (> 100 pc) has been uncertain by two orders of magnitude for
several decades: different analyses report fields as weak as ~6 microG on the
one hand and 1 mG on the other. Here I report on our recent work which shows
that the field on 400 pc scales has a firm lower limit of about 50 microG. To
obtain this result we compiled existing (mostly single dish) radio data to
construct the spectrum of the GC region on these size scales. This spectrum is
a broken power law with a down-break (most conservatively) attributable to a
transition from bremsstrahlung to synchrotron cooling of the in-situ cosmic-ray
electron population. The lower limit on the magnetic field arises through the
consideration that the synchrotron-emitting electrons should not produce too
much gamma-ray emission given existing constraints from the EGRET instrument.
