Attractive force of magnets and magnetic fields
Strength and range of impact by the attractive force of magnets
H. Yamaguchi1,2, M. Takahashi2, G. Togawa2 and Y. Takada2
1
2

Division of Advanced Prosthetic Dentistry, Tohoku University Graduate School of Dentistry
Division of Dental Biomaterials, Tohoku University Graduate School of Dentistry

Introduction
Most of dental magnetic attachments used in Japan utilize a closed magnetic circuit1). They show
excellent attractive force because the magnetic flux density is enhanced within the yoke. On the other hand,other countries utilize some magnetic attachments that utilize open magnetic circuit such as that of a basic
magnet2). The attractive force generated in open magnetic circuit attachments is weak compared with thatof closed magnetic attachments. Open magnetic circuit attachments are still used in some countries, andmay have some advantages.

Objective
The aim of this study was to investigate the influence combining similar and different type of magnets
has on attractive force and extent of magnetic fields.

Materials and Methods
Cylindrical neodymium magnets (4 mm in diameter and 2 mm in height, Trusco) and ferrite magnets (5mm in diameter and 3 mm in height, Trusco) were used in this study. Multiple magnets made of the twodifferent materials (neodymium and ferrite) were combined and arranged in various fashions as shown inFig 1. Each magnet was fixed using cyanoacrylate adhesive. The keeper (4 mm in diameter and 12 mm inlength) made of SUS XM27 stainless steel was used in all setups. The attractive force between the magnetsand keeper was measured using a measuring device at a crosshead speed of 2 mm/min. The measuring
device used in this study matched ISO 13017 specifications3,4) and was connected to a digital force gauge(ZPS, Imada). A typical curve of the attractive force generated is shown in Fig. 2. The attractive force ofmagnets [C, Fig.2] is acquired by subtracting weight of the mobile part of measuring device and friction
during movement [B, Fig. 2] from peak of the curve [A] which is the value of magnetic attachments
attractive force, weight of the magnet and movable part of measuring device as well as friction duringmovement. Point “A” [Fig. 2] signifies the time scenario when the magnet is in contact with keeper justbefore separation begins.
C＝A-B (A: initial separation point value, B: weight of device and friction, C: attractive force)
The range of influence by magnetic fields that resulted in an attractive force between keeper and magnet
was derived from the attractive force curve and is represented as “S0”, [Fig 2]. Additionally, the patterns
formed by iron powder around the magnets was observed.

NNNNNNNNNN

N1N2N3N4NFFNF
NF
NFF
NNFNNFFFFFFFFFFFF1F2F3F4NF
NFNNFFN: neodymium magnet

F: ferrite magnet: keeperM1M2M3M4M5M6

Measured value

Fig. 1 Combination of magnets

Distance

Fig. 2 Attractive force curve

Results
The measured attractive force generated by multiple neodymium magnets and the range of impact by theattractive force is shown in Fig. 3, whereas that of ferrite magnets is shown in Fig. 4. The attractive force
value and range of impact by attraction force increased with increase in the number of magnets. The
dependency relationship was not linear and the increase diminished with increase in number of magnets.
The attractive force of combined neodymium and ferrite magnets in different arrangements and the rangeof impact by the attractive forces are shown in Figs. 5 and 6. When a neodymium magnet was in directcontact with the keeper (conditions M1-3), the attractive forces ranged between 3.5 and 4.0 N. The order ina descending manner was M3, M2 and M1 respectively. The range of impact of the attractive force wasapproximately 6-10 mm with no significant difference across the different setup conditions.
When a ferrite magnet is in contact with the keeper (conditions M4-6), the attractive forces measured
were 0.5-0.7 N. The highest was M6, followed by M5, and M4 in descending order. Their extent ofmagnetic fields was approximately 6-7 mm with no significance difference across the various setup
conditions.

63.0

542.0

32

1.0

12100.6

80.4

640.2

2

1

0.00N2N30.0

N4Fig. 3 Attractive force values and range ofimpact by the magnetic fields ofmultiple neodymium magnets

Attractive force
Range

Attractive force (N)

4.0

1.0

100.8

8
3.0
6

2.0
4
1.0

0.0

2M1

M2

M3F2F3F4

Fig. 4 Attractive force values and range ofimpact by the magnetic fields ofmultiple ferrite magnets

12Range of impact (mm)5.00F1

Attractive force (N)N1

12Attractive force
Range

1080.660.4
40.2

20.000M4

Fig. 5 Attractive force and range of impact of
combined neodymium and ferrite
magnets (neodymium magnet is incontact with keeper)

Range of impact (mm)74.0

14Range

0.8

Attractive force (N)816

Attractive force

Range of impact (mm)1.09Range5.0

Attractive force (N)10

Attractive force

Range of impact (mm)

6.0

M5

M6

Fig. 6 Attractive force and range of impact of
combined neodymium and ferrite
magnets (ferrite magnet is in contactwith keeper)

Discussion
1. Multiple magnets of similar typeThe demagnetizing field is the magnetic field generated by the magnetization in a magnet1). The term
demagnetizing field reflects its tendency to act on the magnetization so as to reduce the internal magnetic
field, otherwise known as attractive force. The demagnetizing field of a magnet is inversely proportional to
the square of the distance between the magnetic poles. The distance between the magnetic poles increases
as the number of magnets increases. An increase in the distance between magnetic poles causes a
significant change (decrease) in demagnetizing field. Consequently, the attractive force and extent or rangeof impact by the attractive force increased because demagnetizing field decreased with increase in numberof magnets combined. Since the demagnetizing field becomes negligibly small when the distance between
the magnetic poles is very large, the attractive force stagnates at a certain value.
2. Combinations of different types of magnets
When different type of magnets was combined and the magnet in contact with the keeper wasneodymium; the attractive force increased as the number of ferrite magnets between the neodymium ones
reduced. The attractive force of a setup involving different types of magnets with a pair of consecutive
neodymium magnets in contact with the keeper (M3) was equal to the attractive force of two (similar)

neodymium magnets (N2). A setup that involves ferrite magnets sandwiched between a pair of neodymium
magnets attenuates the attractive force. The range of impact by the attractive force measured in setups
M1-3 also was equal to that of N2.
When the magnet in contact with the keeper was ferrite (M4-6), it was expected that neodymium
magnets would enhance the attractive force of ferrite magnets. However, the obtained results differed fromthe expectation. The amount of magnetic flux which can pass through a ferrite magnet is much less thanthat of a neodymium magnet. A ferrite magnet placed adjacent to the keeper would therefore interfere withthe flow of magnetic flux from neodymium magnet to the keeper. The attractive force of mixed type ofmagnets whereby two consecutive ferrite magnets were in contact with keeper (M6) was relatively higher
than that of neodymium sandwiched between ferrite or one ferrite adjacent to keeper M4-5. Possibly, a partof the magnetic flux from the neodymium magnet leaked through the sides of the cylindrical keeper.
Although the attractive force of M4-6 was equal to or higher than that of F2-4, the range of impact by theattractive force for M4-6 setups was smaller than that of F2-4. It is desirable of magnets for intraoral
applications to have a small range of impact by the magnetic fields1). This study demonstrated that it ispossible to control the extent of magnetic fields without changing attractive force through combination ofdifferent kinds of magnets.
Setups denoted as M3 and M6 constitute of two consecutive neodymium and ferrite magnets. Excluding
the keeper, M3 is the reverse setup of M6 whereas M2 is the reverse of M5. However, the attractive force
when neodymium contacts keeper (M2 or M3) was higher than that of ferrite in contacts with keeper (M5or M6). Even if the magnetic composition was the same, the force of the magnet structure changed basedon the side which contacts with a keeper. This is because the amount of the magnetic flux which can passthrough a ferrite and neodymium material differs, as shown in Fig. 7. From these results, we may be able todevelop a magnetic application with which the attractive force differs depending on the side which contacts
with.

FF
NN

M3: 3.97 NNNFFneodymiumsideferriteside

M6: 0.63 N

Influence of the magnetic pole in contact
with keeper on attractive force value

Pattern of magnetic fields (M3, M6)

Fig. 7 Features of combined magnets of different types

Conclusion
Similar or different type of magnets combined in various fashions showed unique features with regard to
the strength value of attractive force and the range of impact. This study suggests that the attractive force
value and range of impact by the magnetic fields can be controlled through combination of different kindsof magnets.

Acknowledgments
The authors are pleased to acknowledge the assistance of Dr. Mary Wambui KANYI in proofreading andediting the English version.

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