  We revisit the description of the magnetic field around antiferromagnetic
magnetoelectrics in the context of recent developments regarding
magnetoelectric monopoles. Using Maxwell's equations, we calculate the magnetic
and electric fields associated with a free charge in a bulk uniaxial
magnetoelectric, as well as in a finite sphere of magnetoelectric material. We
show that a charge in the prototypical magnetoelectric Cr$_2$O$_3$, which is
uniaxial with a diagonal magnetoelectric response, induces an internal magnetic
field with both monopolar and quadrupolar components, but that only the
quadrupolar contribution extends beyond the sample surface. We discuss the
behavior of the external quadrupolar field and compare its magnitude to those
of magnetic fields from other sources.
