C magnetic force and r are linear relationship magnetic pole When k=2, the magnetic field theory can be used to prove that the magnetic force of this magnetic pole has a linear relationship with r (the proof is omitted).
When k=2, its equal magnetic potential equation is:
The absolute value of the relative sin2θ is the largest (equal to 1), and the absolute value of r is the smallest. When writing r0, there is
Therefore, the equipotential equation can be rewritten as:
r 2 sin2θ=r 0 2 (8)
With r 0 selected, the corresponding pole shape can be determined, as shown in Figure 4. In fact, the equipotential surface family at this time is the isometric hyperbolic family. [next]
It can be seen from Equation 6 and Figure 4(a) that the magnetic field in which the magnetic force is linear with r is formed by two pairs of magnetic poles I, II and I', II'. in On several straight lines, the magnetic potential φ = 0. Therefore, in practice, the zero magnetic pole (neutral magnetic pole) II can be used (see Fig. 4(b) instead of the pair of magnetic poles I', II'.
Figure 4(b) The magnetic field between I, II, and III, because the equations and boundary conditions are the same as those in Figure 4(a), the magnetic field distribution will be exactly the same as the same spatial magnetic field distribution in Figure 4(a).
However, such a magnetic pole requires a neutral pole, which is located at the upper ends of the other two magnetic poles, which causes a lot of inconvenience to the operation. For this reason, it is best to remove the neutral pole. After testing, after removing the neutral pole, The relationship with the Y-axis is as shown in Fig. 5, except for the upper part of the magnetic pole, which changes substantially linearly and basically satisfies the requirements.
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