  Nonmagnetic spheres confined in a ferrofluid layer (magnetic holes) present
dipolar interactions when an external magnetic field is exerted. The
interaction potential of a microsphere pair is derived analytically, with a
precise care for the boundary conditions along the glass plates confining the
system. Considering external fields consisting of a constant normal component
and a high frequency rotating in-plane component, this interaction potential is
averaged over time to exhibit the average interparticular forces acting when
the imposed frequency exceeds the inverse of the viscous relaxation time of the
system. The existence of an equilibrium configuration without contact between
the particles is demonstrated for a whole range of exciting fields, and the
equilibrium separation distance depending on the structure of the external
field is established. The stability of the system under out-of-plane buckling
is also studied. The dynamics of such a particle pair is simulated and
validated by experiments.
