  We show, by solving Maxwell's equations, that an electric charge on the
surface of a slab of a linear magnetoelectric material generates an image
magnetic monopole below the surface provided that the magnetoelectric has a
diagonal component in its magnetoelectric response. The image monopole, in
turn, generates an ideal monopolar magnetic field outside of the slab. Using
realistic values of the electric- and magnetic- field susceptibilties, we
calculate the magnitude of the effect for the prototypical magnetoelectric
material Cr$_2$O$_3$. We use low energy muon spin rotation to measure the
strength of the magnetic field generated by charged muons as a function of
their distance from the surface of a Cr$_2$O$_3$ films, and show that the
results are consistent with the existence of the monopole. We discuss other
possible routes to detecting the monopolar field, and show that, while the
predicted monopolar field generated by Cr$_2$O$_3$ is above the detection limit
for standard magnetic force microscopy, detection of the field using this
technique is prevented by surface charging effects.
