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MMM2019 FP-03
The Interaction between
Two Permanent Magnets with
Significantly Different Permeance Coefficients
Hui Meng (a)*, Qifeng Wei (a), Guiping Tang (b), George Mizzell (c), and Christina H Chen (d)*
（a) Foresee Group, Zhejiang, 311500, China, (b) Quadrant at Hangzhou, Zhejiang, 311500, China,
(c) SuperMagnetMan, AL 35124, USA, (d) Quadrant at San Jose, CA 95131, USA,
*e-mail: hui.meng@foresee.xyz, c.chen@quadrant.us
FORESEE GROUP
Connect & Drive with Magnetics
Even though Gauss’ law for magnetic flux density (B-field) indicates there is no free magnetic charge,
we can still define the effective bound magnetic charges from the magnetization of magnetic material
[1]. The positive magnetic charge is called the “north pole”, and correspondingly, the negative magnetic
charge is called the “south pole”. The interaction between the magnetic charges is governed by
Coulomb’s law so that like poles repel and unlike poles attract [2]. However, experiment shows that
when two permanent magnets with significantly different permeance coefficients (Pc) were put together,
with their directions of magnetization (DOM) pointing against each other, instead of repelling, they can
attract to each other, especially when the coercivity of the big magnet is relatively low. This
phenomenon may lead people to think that Coulomb’s law for magnetic charges is not always right, and
in some cases, like poles attract.
In this work, we show that the above bizarre phenomenon is caused by the partial demagnetization in the
low Pcmagnet, rather than violation of Coulomb’s law. When the experiment is carried out using
sintered NdFeB magnet of N50 grade, the working point for the stand-alone low Pc magnet is very near
to the knee of its demagnetizing curve, so it’s very vulnerable to the external and its self-demagnetizing
field. Finite Element Analysis (FEA) shows that demagnetization happens obviously in the central
region of the magnet with low Pc,but the magnetization remains in the same direction all over the
magnet. FEA also gives an attractive force when the above low Pcand high Pcmagnets are close to each
other with opposite DOMs. Based on the magnetic charge model and Coulomb’s law, the numerical
integration of Coulomb’s force is carried out, which gives almost the same attractive force as FEA.
Abstract
Background
Knowledge from the secondary physics tells us that a magnet have a north
pole and a south pole, and like poles repel whereas unlike poles attract.
However, experiment shows that when two NdFeB magnets with
significantly different permeance coefficients (Pc) were put together, with
their directions of magnetization (DOM) pointing against each other as
shown in the figure below, instead of repelling, they will attract to each
other, especially when the coercivity of the large magnet is relatively low.
It seems that in some cases, like poles attract, is that true?
Research Method
Even though Gauss’ law for magnetic flux density (B-field) indicates there is no free magnetic charge,
we can still define the effective bound magnetic charges from the magnetization of magnetic material
[1]. The positive magnetic charge is called the “north pole”, and correspondingly, the negative
magnetic charge is called the “south pole”. The interaction between the magnetic charges is governed
by Coulomb’s law so that like poles repel and unlike poles attract [2],
𝑭𝟏𝟐 =𝟏
𝟒𝝅𝝁𝟎𝒎𝟏𝒎𝟐
|𝒓𝟏−𝒓𝟐|𝟐𝒓𝟏𝟐
For practical magnet, the magnetic charge is distributed around the magnet, therefore we should use
volume charge density ρ(r) (∇∙𝑀), or surface charge density σ(r) (𝑛∙𝑀)to replace the point charge m.
For most anisotropic rare earth magnet, the magnetization is uniform, therefore, σ(r) plays the key role.
Below we consider the magnetic force between two coaxial hollow circles with uniformly distributed
magnetic charge as shown in Fig. 2. After a series of simplification, the magnetic force between these
two circles can be written as,
𝑭𝟏𝟐 =𝟐
𝝁𝟎ඵ
𝒊𝒓𝟏,𝒊𝒓𝟐
𝒐𝒓𝟏,𝒐𝒓𝟐𝝈𝟏𝝈𝟐𝒍𝒓𝟏𝒓𝟐𝑬𝐥𝐥𝐢𝐩𝐭𝐢𝐜𝐄[ −𝟒𝒓𝟏𝒓𝟐
𝒍𝟐+ 𝒓𝟏−𝒓𝟐𝟐]
(𝒍𝟐+ 𝒓𝟏+𝒓𝟐𝟐) 𝒍𝟐+ 𝒓𝟏−𝒓𝟐𝟐ⅆ𝒓𝟏ⅆ𝒓𝟐
where EllipticE is the complete elliptic integral. When ir1=ir2=0, it gives the special case of magnetic
charge distributed in solid circles.
In the next section we use the equation
above to calculate the magnetic forces
between a small (D4mm*4mm) an a
large (D24mm*2mm) cylindrical magnet
with Br of 1.4T.
1. working point analysis
The magnet with higher Pc
will generate stronger
magnetic field near its
surface than the magnet with
lower Pc, as a result, the
tendency of demagnetization
for the large magnet will
increase when it is pushed
against the small magnet as
shown in Fig.3a.
For comparison, Fig.3b and
3c show the magnets with
the same Pc.
Fig. 3 →
The magnetic field distribution when
two magnets are pushed together with
their DOMs against each other (a) with
different Pc, (b) & (c) with the same Pc
Results and Discussions
Fig.4 Demagnetization curves for N50, N50M,
and N50H, and load lines for magnets with the
shape of D4*4 and D24*2.
For NdFeB grade with lower Hcj such as N50,
the working point for the low Pcmagnet is near
its knee as shown in Fig. 4, so it is more
vulnerable to demagnetization.
2. Perfect magnets
Perfect magnet means that the magnetization
inside both magnets is absolutely uniform
and equal the remanence.
Table 1 Interactive force between different
magnetic charge slices and the net force for
the case of Fig.5
3. Magnets with its intrinsic coercivity relatively weak
As is discussed in 1, for the N50 grade, the working point for the large magnet is very close to
the knee, therefore, the magnetic field generated by the small magnet will demagnetize the large
magnet locally and partially. We assume only the magnetization in the portion of the large
magnet which is located directly under the small magnet is weakened to 1.0T.
Fig.6 Case for the magnetization in the large magnet
being weakened in the central region
Table 2 Interactive force between different magnetic
charge slices and the net force for the case of Fig.6
The net force in this case
becomes attractive (negative)
even though the polarities of
the magnets remain the same.
Note that the interactive
force between each pair of
magnetic charge slices still
obeys the Coulomb’s law.
Conclusion
A numerical analysis base on Coulomb’s law is carried out
to interpret a bizarre magnetic phenomenon. The statement
that “like poles repel, unlike poles attract” still holds. The
phenomenon is caused by the partial demagnetization
(magnetic charge redistribution) in one of the magnet with
lower permeance coefficient.
References:
[1] J. M. D. Coey, Magnetism and Magnetic Materials, 2010,
Cambridge University Press, p.45.
[2] Soshin Chikazumi, Physics of Ferromagnetism, second
edition, 1997, Oxford University Press, p.3.
