The forces acting on a magnetic particle during nonrelativistic motion parallel to the surface of a homogeneous medium with a frequency dispersion of magnetic permeability are considered. General expressions are obtained for the normal (attractive) and lateral (braking) forces acting on a small dipole particle and an extended probe. It is shown that for an arbitrary orientation of the vector of the dipole magnetic moment of the particle, along with the force of attraction and the stopping force, there also appears a velocity-dependent lateral force perpendicular to the velocity vector. The possibility of using the results to study the frequency-dependent magnetic permeability of nanostructured materials and films in the dynamic scanning mode of magnetic force microscopy (MCM) with magnetic probes is discussed. Numerical estimates are given for the magnitude of the expected forces, friction coefficients, and changes in the quality factor of the MFM oscillators in the case of frequency dispersion of relaxation-type magnetic permeability.
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