Magnetic force field paramagnetic particles

The magnetic force exerted on a small magnetizable paramagnetic particle of volume rtip/pp) in a magnetic field of strength ff (unit, amp/m) and volume susceptibility/p in vacuo is... 

Figure 3.1.2F. Simplified cross-sectional view of the magnetic forces acting on a paramagnetic particle flowing past a magnetized ferromagnetic wire in a background field H. (After Dobby and Finch (1977).)...

The magnetic force on a spherical paramagnetic (linearly polarizable) particle of radius in a paramagnetic solution exposed to a nonuniform magnetic field having a local field intensity vector of ff in vacuo is given by (Jones, 1995)... 

A spherical paramagnetic particle in a paramagnetic solution is subjected to a magnetic force due to a local magnetic field intensity H (in vacuum). Consider the situation where the magnetic permeabilities of the particle and the solution are related to the corresponding susceptibilities Xp and Xs via... 

The ponderomotive force affecting particle is proportional to the particle volume, to the gradient of the squared magnetic field strength, and to the difference between the magnetic susceptibility of the particles and en-vironment. Paramagnetic particles subjected to this force would be drawn... 

Paramagnetic polystyrene beads assembled into 2D arrays at the water/air or water/glass interface by application of a magnetic field. The beads assembled from 6 to 10 particle diameters apart due to dipole-dipole and electrostatic repulsion Magnetic and electrostatic forces pm 58... 

A magnetic field was utilized as a driving force for split-flow thin (SPLITT) fractitMiation by Fuh and co-workers. This technique allowed the complete separation of paramagnetic icm-labeled particles from non-labeled particles. Zborowski et al. constmcted a cylindrically symmetric SPLITT fractionation channel that used a quadmpole magnetic field. In SPLITT fractionation, the separation axis is the thin dimension of the channel. 

In order to make some numerical estimates, Berman et al. considered an array of paramagnetic moments in a non-magnetic host material, with the impurity atoms separated by a = 50 A, arranged at a distance d = 100 A beneath the surface of the material. This is also the distance from the cantilever tip, which possesses a ferromagnetic particle with radius /f = 50 A. In these conditions, the normal component of the magnetic field acting on the electronic moment is Bj = 5.4 x 10 T, which corresponds to an electronic resonance shift of 1.5 GHz, approximately (see Problems with solutions). Under resonance condition, the force on the cantilever, estimated as 10 N, produces a vibration with amplitude of approximately 1.2 A, much above the estimate of 0.3 A due to the thermal noise, at a temperature of 1 K. 

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