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In this paper, we derive a quantitative model for the manipulation of superparamagnetic particles by superposition of a homogeneous magnetic field and magnetic field gradients. Our results show that by this combination, the magnitude as well as the sign of the force on a magnetic particle can be controlled. By quantitatively modeling the magnetic force on a representative superparamagnetic particle, we find that for a common lab-on-chip scenario large repulsive forces can be achieved by adding a homogeneous field perpendicular to the plane of the chip. This offers new perspectives for the on-chip manipulation of magnetic particles. As a first example, in-plane positioning of particles with an accuracy of \(\sim 1 \mu \) m is experimentally demonstrated. [ABSTRACT FROM AUTHOR]