Ferrofluids are strongly paramagnetic liquids. We study the behavior of fer
rofluid droplets confined between two parallel plates with a weak applied f
ield parallel to the plates. The droplets elongate under the applied field
to reduce their demagnetizing energy and reach an equilibrium shape where t
he magnetic forces balance against the surface tension. This elongation var
ies logarithmically with aspect ratio of droplet thickness to its original
radius, in contrast to the behavior of unconfined droplets. Experimental st
udies of a ferrofluid-water-surfactant emulsion confirm this prediction. [S
1063-651X(99)00210-X].