One embodiment of an enhanced flux-density magnet comprises a magnetic material with two magnetic poles and one magnetic pole-area smaller than the other magnetic pole-area. Because the magnetic field at both pole-areas is equal but the magnetic pole-areas are unequal, the magnetic flux-density is proportionally greater at the magnetic pole with a smaller area than the magnetic pole with the larger area and greater than if the magnetic pole-areas were equal.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application benefits from U.S. Pat. No. 8,487,486, filed 2013 Jul. 16 by the present inventor.

FEDERAL SPONSORED RESEARCH

Not applicable

SEQUENCE LISTING OF PROGRAM

Not applicable

BACKGROUND

Prior Art

US Patents

Electric motors and electric generators use magnets to either convert electricity into mechanical motion (motor) or mechanical motion into electricity (generator). The magnets in these devices can be permanent or electromagnetic and have a north-pole and a south-pole of equal area. Their magnetic field is invisible but is known to induce an electromotive force (EMF) in a wire coil when either the magnetic field of the magnet moves perpendicular (normal) to a stationary wire coil or the wire coil moves normal to the magnetic field of a stationary magnet. This EMF produces electrical power in a generator. Furthermore, an electric current in a wire coil creates a magnetic field that repels or attracts a magnet. This also is an EMF and produces the mechanical power to drive a motor.

Thus, motors and generators consist of two essential components: magnets to produce a magnetic field and wire coils to convert the magnetic field into mechanical power (motor) or electrical power (generator), and these two components contribute much of the cost, weight, and volume of a device. Therefore, reducing the amount of either or both components without reducing power can substantially lower cost, weight, and volume of a device. Furthermore, reducing wire decreases the electrical resistance of the device which increases operating efficiency. Studying the prior art reveals many attempts at reducing these components but without significant success.

SUMMARY

In accordance with the embodiments, an Enhanced Flux-Density Magnet (EFDM) comprises a magnetic material where the magnetic pole-areas of one magnetic polarity are smaller than the magnetic pole-areas of the other magnetic polarity. In proportion to the inequality of the magnetic pole-areas, the magnetic flux-density is greater at the smaller magnetic pole-areas than the larger magnetic pole-areas and greater than if the magnetic pole-areas were equal.

Advantages

Accordingly the greater magnetic flux-density of the EFDM enables less coil wire without reducing power from an electrical motor or generator. Less wire reduces cost, weight, and volume of the device. Furthermore, reducing wire decreases the electrical resistance of the device which increases operating efficiency. Also, the EFDM eliminates the need for magnetic iron without reducing power in electrical motors and generators. Eliminating magnetic iron reduces weight, cost, and volume of the device while removing power losses such as core saturation, eddy currents, and cogging.

DETAILED DESCRIPTION

The amount of EMF induced by the relative motion of the magnet and wire is determined by Faraday's law of induction which is as follows.
E=−NdΦB/dt
Where, E is the EMF (measured in volts) and ΦBis the magnetic flux through a single loop, N is the number of turns, and t is time. In more advanced physics, the magnetic flux is properly defined as the surface integral of the normal component of the magnetic field passing through a surface, i.e.
ΦB=B*S=BScosθ
where B is the magnitude of the magnetic field (the magnetic flux-density), S is the area of the surface, and θ is the angle between the magnetic field lines and the normal (perpendicular) to area S.

Thus, the introduction of more powerful magnets such as rare earth permanent magnets increases magnetic flux-density, but further increases of this type are not expected. More wire turns also produces higher EMF, but adds cost, weight, and volume with diminishing benefit as more turns are added. Furthermore, adding more wire increases the electrical resistance of the device which lowers the operating efficiency and increases device heat that limits output power.

To maintain a near normal angle between the magnetic field and the wire coils, motors and generators often use magnetic iron to guide the flux throughout the motor or generator. However, magnetic iron adds cost, weight, volume, and complexity while adding power losses such as core saturation, eddy currents, and cogging.

Sankar in U.S. Pat. No. 8,514,047 and Merritt in U.S. Pat. No. 5,705,902 discuss using Halbach arrays of magnets in electric machines to increase magnetic flux-density. The Halbach array consists of multiple magnets arranged perpendicular to each other such that the magnetic field exits mostly on only one side of the array. While this arrangement is useful for refrigerator magnets and magnetically levitated locomotives, it is not particularly useful in electric devices. This is because it does not channel or transfer magnetic flux-density any better than arrangements of magnetic iron while adding complexity and magnetic field losses.

Flux focusing shaped permanent magnets as discussed by McClellan in U.S. Pat. Nos. 8,299,672 and 7,994,674 also redirect the flux to a preferred side of the magnet but do not increase the magnetic flux-density at the magnetic poles where it would be useful by increasing EMF in a motor or generator.

Thus, prior art attempts to significantly reduce the cost, weight, and volume of magnets or wire in motors and generators have failed, and motor and generator design has remained essentially the same for over 100 years.

In contrast to prior art, the EFDM has greater magnetic flux-density that enables less coil wire without reducing power from an electrical motor or generator. Less wire reduces cost, weight, and volume of the device. Furthermore, reducing wire decreases the electrical resistance of the device which increases operating efficiency.

First-embodiment EFDM10is illustrated inFIGS. 1, 2, 4, 6(isometric views) andFIGS. 3, 5(side views). EFDM10consists of magnetic material12that has been magnetized to create its own persistent, magnetic field14, such that magnetic material12is a permanent magnet. Some examples of magnetic materials12are ceramic, iron, nickel, cobalt, some alloys of rare-earth metals, and some naturally occurring minerals such as lodestone. Magnet material12has one or more north magnetic pole-areas16where magnetic field14leaves magnetic material12and one or more south magnetic pole-areas18where magnetic field14enters magnetic material12.

Because magnetic field14is created from dipole microstructures in magnetic material12, the magnitude of magnetic field14exiting north magnetic pole-areas16is the same magnitude of magnetic field14entering south magnetic pole-areas18. Magnetic flux-density is defined as the magnitude of magnetic field14through a finite area. Therefore, when the sum of one or more magnetic pole-areas of one polarity is smaller than the sum of one or more magnetic pole areas of the other polarity, the magnetic flux-density is proportionally greater at the smaller magnetic pole-areas since magnetic field14is the same at both magnetic pole-areas. In this embodiment, the sum of one or more north magnetic pole-areas16is smaller than the sum of one or more south magnetic pole-areas18.

InFIG. 1, north magnetic pole-area16is smaller than south magnetic pole-area18. Therefore, the magnetic flux-density at north magnetic pole-area16is greater than the magnetic flux-density at south magnetic pole-area18. Furthermore, the magnetic flux-density at north magnetic pole-area16is greater that if north magnetic pole-area16and south magnetic pole-area18were equal.

The path of magnetic field14at the magnetic pole-areas and within the magnet is determined when magnet material12is magnetized. Therefore, by conservation of energy the following equations apply:By definition: MFDn=MFn/PAnand therefore MFn=MFDn*PAnwhere MFDnis the magnetic flux-density at north magnetic pole-area16; MFnis magnetic field14at north magnetic pole-area16; and PAnis north magnetic pole-area16.By definition: MFDs=MFs/PAsand therefore MFs=MFDs*PAswhere MFDsis the magnetic flux-density at south magnetic pole-area18; MFsis magnetic field14at south magnetic pole-area18; and PAsis south magnetic pole-area18.By definition: MFn=MFsand therefore MFDn*PAn=MFDn*PAsThus: MFDn=MFDs*(PAs/PAn) and MFDs=MFDn*(PAn/PAs) Therefore, if one magnetic pole-area is smaller than the other magnetic pole-area than the flux-density at that smaller magnetic pole-area is proportionally greater than the magnetic flux-density at the larger magnetic pole-area. Furthermore, that flux-density is greater at the smaller magnetic pole-area than if the magnetic pole-areas were equal. These formulas apply for one or more magnetic pole-areas for each polarity. This surprising discovery of enhanced flux-density by unequal magnet pole-areas is a feature consistent through all embodiment of the EFDM.

Experiments were conducted to prove enhanced flux-density with a magnet having unequal magnetic pole-areas. One end of the magnet was much larger in area (about 1 square inch) than the other end (about 0.1 square inch). A gauss meter measured the magnetic flux-density at about 10 times greater at the smaller area end of the magnet than the larger area end, validating the mathematical formula above.

InFIG. 2, north magnetic pole-area16is smaller than south magnetic pole-area18and substantially perpendicular such that magnetic field14must bend inside magnetic material12. Therefore, magnetic field14enters magnetic material12through the larger south magnetic pole-area18and exits through the smaller north magnetic pole-area18.FIG. 3is a side view showing magnetic field14bending inside magnetic material12.

InFIG. 4, two first-embodiments EFDMs10are positioned such that their smaller north magnetic pole-areas16are substantially touching and larger south magnetic pole-areas18are at opposite ends of contiguous surface19.FIG. 5shows magnetic field14entering magnetic material12through the larger south magnetic pole-areas18approaching contiguous surface19and bending to exit the smaller north magnetic pole-areas16.

InFIG. 6, magnetic field14enters into magnetic material12passing through the larger south magnetic pole-areas18at opposite ends of magnetic material12, and magnetic field14exits magnetic material12passing through the smaller north magnetic pole-area16at the center of magnetic material12.

Second-embodiment EFDM20is illustrated inFIGS. 7, 8, 10, and 12(isometric views) andFIGS. 9 and 11(side views). EFDM20consists of magnetic material12that has been magnetized to create its own persistent, magnetic field14, such that magnetic material12is a permanent magnet. Some examples of magnetic materials12are ceramic, iron, nickel, cobalt, some alloys of rare-earth metals, and some naturally occurring minerals such as lodestone. Magnet material12has one or more north magnetic pole-areas16where magnetic field14leaves magnetic material12and one or more south magnetic pole-areas18where magnetic field14enters magnetic material12. In this embodiment, the sum of one or more south magnetic pole-areas18is smaller than the sum of one or more north magnetic pole-areas16.

InFIG. 7, south magnetic pole-area18is smaller than north magnetic pole-area16such that the magnetic flux-density at south magnetic pole-area18is greater than the north magnetic pole-area16. Furthermore, the magnetic flux-density at south magnetic pole-area18is greater that if south magnetic pole-area18and north magnetic pole-area16were equal.

InFIG. 8, south magnetic pole-area18is smaller than north magnetic pole-area16and substantially perpendicular such that magnetic field14must bend inside magnetic material12. Therefore, magnetic field14enters magnetic material12through the smaller south magnetic pole-area18and exits through the larger north magnetic pole-area16.FIG. 9is a side view showing magnetic field14bending inside magnetic material12.

InFIG. 10, two second-embodiments EFDMs20are positioned such that their smaller south magnetic pole-areas18are substantially touching and larger north magnetic pole-areas16are at opposite ends of contiguous surface19.FIG. 11shows magnetic field14entering magnetic material12through the smaller south magnetic pole-area18substantially parallel to contiguous surface19and bending to exit the larger north magnetic pole-areas16.

InFIG. 12, magnetic field14enters into magnetic material12passing through the smaller south magnetic pole-area18at the center of magnetic material12, and magnetic field14exits magnetic material12passing through the two larger north magnetic pole-areas16at opposite ends of magnetic material12.

Third-embodiment EFDM30is illustrated inFIGS. 13, 14, and 16(isometric views) andFIG. 15(side view). Magnetic material12is magnetized only when electric current32is passed through electric wire34surrounding magnetic material12, such that magnetic material12is an electromagnet. Some examples of magnetic materials12that work as electromagnets are iron, nickel, cobalt, some alloys of rare-earth metals, and lodestone. Magnet material12has one or more north magnetic pole-areas16where magnetic field14leaves magnetic material12and one or more south magnetic pole-areas18where magnetic field14enters magnetic material12. According to the well-known right-had rule, the direction of current32in electric wire34determines which end of material12will be a north magnetic pole area16and which end will be a south magnetic pole area18. In this embodiment, the sum of one or more north magnetic pole-areas16is smaller than the sum of one or more south magnetic pole-areas18.

InFIG. 13, north magnetic pole-area16is smaller than south magnetic pole-area18. Therefore, the magnetic flux-density at north magnetic pole-area16is greater than the magnetic flux-density at south magnetic pole-area18. Furthermore, the magnetic flux-density at north magnetic pole-area16is greater that if north magnetic pole-area16and south magnetic pole-area18were equal.

InFIG. 14, two third-embodiments EFDMs30are positioned such that their smaller north magnetic pole-areas16are substantially touching and larger south magnetic pole-areas18are at opposite ends of contiguous surface19.FIG. 15shows magnetic field14entering magnetic material12through the larger south magnetic pole-areas18approaching contiguous surface19and bending to exit the smaller north magnetic pole-areas16. Magnetic field14bends because it follows the path of microstructure alignment of magnetic material12when electric current32passes through electric wire34. That path is determined by the arrangement of electric wire34, and in this embodiment, electric wire34is arranged such that magnetic field14bends towards north magnetic pole areas16.

InFIG. 16, magnetic field14enters into magnetic material12passing through the larger south magnetic pole-areas18at opposite ends of magnetic material12, and magnetic field14exits magnetic material12passing through the smaller north magnetic pole-area16at the center of magnetic material12.

Fourth-embodiment EFDM40is illustrated inFIGS. 17, 18, and 20(isometric views) andFIG. 19(side view). Magnetic material12is magnetized only when electric current32is passed through electric wire34surrounding magnetic material12, such that magnetic material12is an electromagnet. Some examples of magnetic materials12that work as electromagnets are iron, nickel, cobalt, some alloys of rare-earth metals, and lodestone. Magnet material12has one or more north magnetic pole-areas16where magnetic field14leaves magnetic material12and one or more south magnetic pole-areas18where magnetic field14enters magnetic material12. According to the well-known right-had rule, the direction of current32in electric wire34determines which end of material12will be a north magnetic pole area16and which end will be a south magnetic pole area18. In this embodiment, the sum of one or more south magnetic pole-areas18is smaller than the sum of one or more north magnetic pole-areas16.

InFIG. 17, south magnetic pole-area18is smaller than north magnetic pole-area16such that the magnetic flux-density at south magnetic pole-area18is greater than the magnetic flux-density at north magnetic pole-area16. Furthermore, the magnetic flux-density at south magnetic pole-area18is greater that if south magnetic pole-area18and north magnetic pole-area16were equal.

InFIG. 18, two fourth-embodiments EFDMs40are positioned such that their smaller south magnetic pole-areas18are substantially touching and larger north magnetic pole-areas16are at opposite ends of contiguous surface19.FIG. 19shows magnetic field14entering magnetic material12through the smaller south magnetic pole-area18substantially parallel to contiguous surface19and bending to exit the larger north magnetic pole-areas16. Magnetic field14bends because it follows the path of microstructure alignment of magnetic material12when electric current32passes through electric wire34. That path is determined by the arrangement of electric wire34, and in this embodiment, electric wire34is arranged such that magnetic field14bends towards north magnetic pole areas16.

InFIG. 20, magnetic field14enters into magnetic material12passing through the smaller south magnetic pole-area18at the center of magnetic material12, and magnetic field14exits magnetic material12passing through the two larger north magnetic pole-areas16at opposite ends of magnetic material12.

A common method of magnetizing said magnetic material12into a permanent magnet is using electromagnets50to inject a magnetic field14into magnetic material12, aligning the internal microstructure such that magnetic material12remains magnetized.

FIG. 21shows an example of this manufacturing method. The north polarity of one electromagnet50is substantially touching the larger, future south magnetic pole-area18of a first-embodiment EFDM10, and the south polarity of a second electromagnet50is substantially touching smaller, future north magnetic pole-area16of first-embodiment EFDM10. When electric current32is applied to electromagnets50, a magnetic field14is produced through magnetic material12, aligning the microstructure of magnetic material12to the same orientation as magnetic field14passing through magnetic material12. When electromagnets50are removed, magnetic material12remains magnetized, and its magnetic field14follows the same path as magnetic field14of electromagnets50.

FIG. 22shows how the same magnetic material12inFIG. 21can be made into a second-embodiment EFDM20. Electromagnets50are turned around such that their magnetic field14enters the smaller, future south magnetic pole-area18and exits the larger, future north magnetic pole-area16of magnetic material12. When electromagnets50are removed, magnetic material12remains magnetized, and its magnetic field14follows the same path as magnetic field14of electromagnets50.

Operation in Motors and Generators—FIGS. 23 through 26

One of the many applications for this new technology will be in motors and generators.FIGS. 23 through 26illustrate a few of a plurality of motor and generator arrangements where first-embodiment EFDMs10and second-embodiment EFDMs20are attached to a hub62and wire coils64are attached to support66. Hub62can rotate relative to a fixed support66, or support66can rotate relative to a fixed hub62. Furthermore, a plurality of other motor or generator arrangements (not shown) could have wire coils64attached to hub62and first-embodiment EFDMs10and second-embodiment EFDMs20attached to support66where hub62rotates relative to a fixed support66or support66rotates relative to a fixed hub62. Furthermore, first-embodiment EFDMs10and second-embodiment EFDMs20inFIGS. 23 through 26could be replaced with third-embodiment EFDMs30and fourth-embodiment EFDMs40electromagnets (not shown).

Magnetic flux14produced by each adjacent pair of first-embodiment EFDMs10and second-embodiment EFDMs20, exits north pole-area16of first-embodiment EFDM10, passes through wire coils64, enters south pole-area18of second-embodiment EFDM20, passes through second-embodiment EFDM20and through first-embodiment EFDM10to continuously repeat this circular path of magnetic flux14. Because the outer-diameter pole areas are smaller than the internal pole-areas, their magnetic flux density is greater than if the outer and inner pole-areas were equal. Since the greater magnetic flux density of the outer-diameter poles is what enters wire coils64, those coils can be smaller without reducing motor or generator power. This feature of reduced wire coil64without reducing power is consistent in all four motor/generator configurations shown inFIGS. 23 through 26.

In a motor, an electric current32in wire coil64creates a magnetic field that repels or attracts first-embodiment EFDMs10and second-embodiment EFDMs20converting electricity into mechanical power. In a generator, relative motion of first-embodiment EFDMs10and second-embodiment EFDMs20and wire coils64converts mechanical motion into electrical power.

FIG. 25shows a side-view of an electrical motor or generator80with four, first-embodiment EFDMs10and four, second-embodiment EFDMs20attached to hub62and surrounded by wire coils64attached to support66. Magnetic iron spacers82fill the space between first-embodiment EFDMs10and second embodiment EFDMs20to assist transfer of magnetic flux14.

FIG. 26shows a side-view of an electrical motor or generator90with four, first-embodiment EFDMs10contiguous with four, second-embodiment EFDMs20attached to hub62and surrounded by wire coils64attached to support66. Contiguous surface19can be a real division of adjacent first-embodiment EFDM10and second-embodiment EFDM20such that magnetic material12is segmented, or contiguous surface19can be an imaginary division of adjacent first-embodiment EFDM10and second-embodiment EFDM20such that magnetic material12is a solid ring.

Advantages

From the description above, a number of advantages of some of my embodiments of my enhanced flux-density magnet become evident:

(a) The greater magnetic flux-density of the EFDM enables less coil wire without reducing power from an electrical motor or generator. Less wire reduces cost, weight, and volume of the device. This reduction in coil wire is possible because the greater magnetic flux density of the EFDM enables a smaller surface area for the magnetic field to pass through while producing the same power. Ina motor or generator, the smaller magnetic pole-area of the EFDM can be arranged to face the coil wire such that the wire volume can be reduced while not changing the power output of the electric motor or generator. In other words, the magnitude of magnetic flux entering the coil is the same even though the amount of wire is less because the magnetic flux density is proportionally greater,

(b) Reducing wire decreases the electrical resistance of the device. Since efficiency is the ratio of load resistance divided by the sum of load resistance and device resistance, significantly reducing the device resistance greatly improves efficiency.

(c) Reducing wire also decreases heat in an electrical device and excess heat is most often what limits the output power of motors and generators. The largest contributor of device heat is electrical resistance in the wire cods. If there is less wire, then there is less heat, and the electrical device can achieve more power before overheating.

(d) The ability of EFDMs to efficiently bend the magnetic field enables an ideal match to the contour of a Folded Electromagnetic Coil (U.S. Pat. No. 8,847,846) such that the average angle of deviation between the magnetic field and the coil-surface normal is near zero, further increasing the magnetic flux-density in the wire coils which enables even less wire without reducing power from an electric motor or generator.

(e) Since the EFDM bends the magnetic field directly normal into the Folded Electromagnetic Cods, magnetic iron can be eliminated because the magnetic field does not need to be transferred; it is already where it needs to be—in the coil. Eliminating magnetic iron reduces weight, cost, volume, and complexity of the device while removing power losses such as iron-core saturation and eddy currents.

(f) Without the weight of magnetic iron, direct-drive wind turbines will become a more practical choice over geared wind turbines. By eliminating the costly and high maintenance gearboxes, the cost of wind energy will be significantly lower. With wind power costing less, it will replace fossil fuel power sources more often, resulting in less green house gases and pollutants that damage our environment.

(g) Since there is no magnetic iron for the magnets to attract, cogging is eliminated. Consequently, motors and generators with EFDMs and ironless wire coils such as Folded Electromagnetic Coils do not lose power to reduce cogging as necessary in many electric devices using magnetic iron. Also, the instability, noise, and damage associated with cogging are avoided.

(h) Some embodiments of the EFDM are ideally suited for magnetically levitating locomotives and other levitated vehicles since the magnetic field is channeled in one direction that is substantially perpendicular to a linear arrangement of magnets.

(i) With EFDM reducing cost, weight, volume, complexity, device resistance, and operating losses, motors and generators can service mankind better and more efficiently while reducing global warming.

Conclusions, Ramifications, and Scope

Accordingly, the reader will see that the enhanced flux-density magnet in its various embodiments uses unequal magnetic pole-areas to enable a greater flux-density than would be possible if the magnetic pole-areas were equal. Furthermore, the magnetic pole-areas can be arranged at various angles relative to each other such that EFDMs can be efficient used in electric motors and generators. For example, EFDMs are arranged such that the smaller magnetic pole-areas with greater magnetic flux-density are positioned close to the wire coils of a motor or generator while the larger magnetic pole-areas with less magnetic flux-density are used to transfer magnetic field from one EFDM to another EFDM. This arrangement of EFDMs provides greater magnetic flux-density at the wire coils which enables less wire to produce the same electromotive force (power). Less wire reduces cost, weight, and volume of the device. Furthermore, the EFDM has the additional advantages in that:

(a) it reduces the electrical resistance of the device. Since efficiency is a ratio of load resistance divided by the sum of load resistance and device resistance, significantly reducing the device resistance greatly improves efficiency. More efficient motors need less electrical input, more efficient generators produce more power, and these benefits on a global scale could greatly reduce world energy consumption.

(b) it lowers the heat generated in the device which most often is what limits the output power of electric motors and generators. If there is less wire then there is less heat, and the device can achieve more power before overheating.

(c) it provides a smaller average-deviation angle between the magnetic flux and the coil-surface normal such that almost all the magnetic flux is effective in the coil, further enabling less wire without reducing power from an electric motor or generator.

(d) it bends the magnetic flux to match the contour of a Folded Electromagnetic Coils such that the average-deviation angle between the magnetic flux and the coil-surface normal are nearly zero, and almost all the magnetic flux is effective in the coil, further enabling less wire without reducing power from an electric motor or generator.

(e) it bends the magnetic flux such that magnetic iron is not necessary to transfer the flux because it is already where it needs to be—in the coil. Eliminating magnetic iron reduces weight, cost, volume, and complexity of the device while removing power losses such as iron-core saturation and eddy currents.

(f) it significantly reduces weight of motors and generators because it eliminates magnetic iron which often is half the device weight. With less generator weight, gearless, direct-drive wind turbines become more practical. Eliminating gears lowers the price of clean wind energy, making it a more likely choice over dirty fuels that pollute the environment and cause global warming.

(g) it eliminates cogging which is a drag force between magnets and magnetic iron. When EFDMs are paired with ironless wire coils such as Folded Electromagnetic Coils, there is no magnetic iron for the magnets to attract and cogging is eliminated. Consequently, motors and generators with EFDMs and ironless wire coils do not lose power to reduce cogging as is necessary in many electric devices using magnetic iron. Also, the instability, noise, and damage associated with cogging are avoided.

(h) it bends magnetic flux such that the magnetic flux can exit and enter on only one side of an array of EFDMs. This can be useful for magnetically levitating locomotives above only one side of a long line of magnets.

Although the description above contains many specificities, these should not be construed as limiting the scope of the embodiment but as merely providing illustrations of some of several embodiments. For example, the EFDM can have other shapes, such as square, rectangular, circular, oval, trapezoidal, triangular, etc.; the bending of the magnetic field inside the magnetic material can have other shapes such as straight, bowed, perpendicular, parallel, sinusoidal, etc.; the magnetic pole-areas can be positioned at various angles relative to each other; the magnetic pole-areas can have any shape such as square, rectangular, circular, oval, trapezoidal, triangular, etc.; the area of the poles can vary greatly or vary just by a few percent, and the magnetic pole areas of a given polarity do not have to be the same size.

Thus, the scope of the embodiment should be determined by the appended claims and their legal equivalents, rather than by examples given.