  We present a comparative investigation of two-dimensional tractor magnet
configurations, analyzing both theoretical predictions and experimental results
with a focus on the minimal tractor magnet. The minimal tractor magnet consists
of a rigid assembly of one attracting magnet (attractor), two repelling magnets
(repulsors), and a fourth magnet (follower) that is magnetically stabilized in
a local energy minimum. The theoretical framework relies on magnetostatics and
stability analysis of stationary equilibria. To calculate the magnetostatic
force and energy, we use a multipole method. In a first approximation, we
derive analytical results from the point dipole approximation. The point dipole
analysis defines an upper bound criterion for the magnetic moment ratio and
provides analytical expressions for stability bounds in relation to geometry
parameters. Our experimental results are consistent with the predictions from
the fourth-order multipole expansion. Beyond the minimal tractor magnet, we
introduce a more advanced configuration that allows for a higher magnetic
binding energy and follower capture at larger distances.
