The definition of the magnetization of the spherical magnetic medium in the uniform background magnetic field H _o is as shown in Fig. 4. A diameter d _o Pa magnetization of the magnetization M in the ball uniform background magnetic field, the magnetic field strength of the outer surface of the ball represented by the following formula:
H _r =(H _o +Ï€/3Md _O /r ³ )cosθ
H _θ =(-H _o +Ï€/6Md _O /r ³ )sinθ (11)

As can be seen from the figure, the magnetic force that causes the selected magnetic particles to adhere to the surface of the sphere is the radial magnetic force F _mr :

Where V———particle volume;
Xp and Xm—the magnetic susceptibility of solid particles and carrier media. [next]

The cross section of the cylindrical filament magnetic medium is shown in Fig. 5. Background field radius b of the non-ferromagnetic particles in the magnetic field intensity _{H o (μ o H o>} M s) is the radius of a, a saturation magnetization M _s of the ferromagnetic cylinder suction, in this case The radial component of the magnetic field near the cylinder is given by:

When θ=0 and (Xp-Xm) are positive (ie for paramagnetic particles), the particles will receive the maximum magnetic attraction F _mr
F ^p _mr =-4Ï€(Xp-Xm)M _s a ² (b ³ /3r ³ )(M _s a ² /μ _o r ² +H _o )
=-4Ï€(Xp-Xm)(M _s H _o /3)[Kx ⁴ /(1+x) ⁵ +x ² /(1+x) ³ ]b ² (14)
Where K = M _s /2μ _o H _o ;
X=a/b.
If (Xp-Xm) is negative (ie for diamagnetic particles), the maximum magnetic attraction occurs at θ = π/2:
F ^D _m r=4Ï€(Xp-Xm)(M _s H _o /3)[Kx ⁴ /(1+x) ⁵ -x ² /(1+x) ³ ]b ² (15)
It can be seen from equations (14) and (15) that if H _o and M _s are constant values, the magnetic force is only related to x=a/b. For any given b value of the opponent, F _m varies with x as shown in Figure 6. It is calculated that F _{m is} maximum when x = 2.34 (paramagnetic particles) or x = 1.35 (antimagnetic particles).

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