ABSTRACT
Combining Equation 4.5 and Equation 4.3, the force on a small spherical weakly magnetic particle placed in the external magnetic field can be written as
Fm 5 [m0kV/(1 1 k/3)](H=)H (4.6)
or in a simplified form (assuming that k << 1),
Fm 5 (1/2)m0kV=(H2) (4.7)
If a paramagnetic particle (volume magnetic susceptibility: kp) is immersed in the fluid (volume magnetic susceptibility:kf), the magnetic force per unit volume acting on a particle is given by Equation 4.7 (using k 5 kp – kf). For practical calculations it is sometimes advantageous to replace the magnetic field strength by the magnetic induction B. Then, Equation 4.7 reads as follows:
Fm 5 (k/m0)VB=B (4.8)
Here B is considered as the external magnetic induction, and =B is the gradient of the magnetic induction. Thus, in the direction of x, the magnetic force Fmx can be written by the following equation (where B 5 moH and magnetization kHx 5 Ix),
Fmx 5 m0Vk(Hx · dHx/dx) 5 m0VIx · dHx/dx (4.9)
Magnetic force is proportional to the product of the external magnetic field and the field gradient and has the direction of the gradient. In a homogeneous magnetic field, in which =B 5 0 or dHx/dx 5 0, the force to change the position of a particle is zero.
