  We have experimentally investigated field induced aggregation of nonmagnetic
particles confined in a magnetic fluid layer when rotating magnetic fields were
applied. After application of a magnetic field rotating in the plane of the
fluid layer, the single particles start to form two-dimensional (2D) clusters,
like doublets, triangels, and more complex structures. These clusters
aggregated again and again to form bigger clusters. During this nonequilibrium
process, a broad range of cluster sizes was formed, and the scaling exponents,
$z$ and $z'$, of the number of clusters $N(t)\sim t^{z'}$and average cluster
size $S(t)\sim t^{z}$ were calculated. The process could be characterized as
diffusion limited cluster-cluster aggregation. We have found that all sizes of
clusters that occured during an experiment, fall on a single curve as the
dynamic scaling theory predicts. Hovewer, the characteristic scaling exponents
$z',\: z$ and crossover exponents $\Delta$ were not universal. A particle
tracking method was used to find the dependence of the diffusion coefficients
$D_{s}$ on cluster size $s$. The cluster motions show features of
\textit{\emph{Brownian}} motion. The average diffusion coefficients $<D_{s}>$
depend on the cluster sizes $s$ as a power law $<D_{s}>\propto s^{\gamma}$
where values of $\gamma$ as different as $\gamma=-0.62\pm0.19$ and
$\gamma=-2.08\pm0. were found in two of the experiments.
