Magnet

For other uses, see Magnet (disambiguation).

A magnet is material or object that produces a magnetic field. A "hard" or "permanent" magnet is one which stays magnetized for a long time, such as magnets often used in refrigerator doors. A "soft" or "impermanent" magnet is one which loses its memory of previous magnetizations. "Soft" magnetic materials are often used in electromagnets to enhance (often hundreds or thousands of times) the magnetic field of a wire that carries an electrical current and is wrapped around the magnet; the field of the "soft" magnet increases with the current. Permanent magnets occur naturally in some rocks, particularly lodestone, but are now more commonly manufactured. A magnet's magnetism decreases when it is heated and increases when it is cooled.

Iron filings in a magnetic field generated by a bar magnet

Two measures of a material's magnetic properties are its magnetic moment and its magnetization. A material without a permanent magnetic moment can, in the presence of magnetic fields, be attracted (paramagnetic), or repelled (diamagnetic). Liquid oxygen is paramagnetic; graphite is diamagnetic. Paramagnets tend to intensify the magnetic field in their vicinity, whereas diamagnets tend to weaken it. "Soft" magnets, which are strongly attracted to magnetic fields can be thought of as strongly paramagnetic; superconductors, which are strongly repelled by magnetic fields, can be thought of as strongly diamagnetic.

Quantities

The magnetic field, magnetic moment, and magnetization are vectors, meaning they have direction and magnitude. The magnetic moment and magnetization are properties only of the magnet, while the magnetic field it produces depends on the position relative to the magnet. The magnetic moment points from its south pole to its north pole. Also, its north pole points towards the Earth's geographic north pole, which is a magnetic south pole. A compass needle is approximately a bar magnet.

Magnetic field strength

A magnetic field can be measured using a good magnetic compass (this is a small permanent magnet). The direction of the field at a point in space is the direction in which the compass needle points when it passes through that point and is in equilibrium. The magnitude (or strength, usually denoted by the symbol B) of a magnetic field can also be measured using a compass, if the field is, like the Earth's, nearly uniform over the volume occupied by the needle. The needle is rotated about its center, and this makes it oscillate about its equilibrium position. The period t of oscillation is measured. For small oscillation angles, the frequency of the oscillation, 1/t, is proportional to the square root of B. This is a result from the theory of rotational motion and the theory of the torque on a magnet, and can be tested by creating an electromagnet, which makes a magnetic field proportional to the electric current that it carries. The common unit of magnetic field is the tesla, denoted "T", equal to one N/Amp-m (Force/Current-Distance), and about 20,000 times the Earth's magnetic field. Technically, B should be called the magnetic induction field, because changing B induces an electric field, by Faraday's Law of electromagnetic induction.

Magnetic moment

The magnetic moment μ of a magnet is the magnetic strength of the field at a distance r from the magnet. At large distances, the magnetic field B is proportional to μ and inversely proportional to r ^3. So, μ can be obtained by measuring B at a distance r. The common unit for magnetic moment is Amp-m^2. A wire in the shape of a circle with area A and carrying current I has a magnetic moment equal to IA.

Magnetization

Magnetization of an object is its magnetic moment per unit volume. It is usually denoted M and has the units Amp/m. A good bar magnet may have a magnetic moment of 0.1 Amp-m^2 and a volume of 1 cm^3, or 0.000001 m^3, and therefore a magnetization of 100,000 Amp/m. Iron can have a magnetization of around a million Amp/m.

Physical origin of magnetism

Magnetism ultimately is due to the motion of electric charge. For a macroscopic object, like a wire loop, an electric current flowing through it has a magnetic moment. Far from the loop there is a magnetic field proportional in strength to its magnetic moment.

For a microscopic object, the physical picture is more complex. An electron within an atom can have orbital angular momentum and a magnetic moment proportional to that orbital angular momentum; the electron also has intrinsic angular momentum, or spin, and a magnetic moment proportional to that spin angular momentum. The orbital and spin angular momentum of an electron are comparable in magnitude, as are their magnetic moments. Far from the electron there is a magnetic field proportional in strength to its magnetic moment.

In addition, within the atomic nucleus are both neutrons and protons, and these too have orbital and spin angular momentum, and associated magnetic moments. However, the nuclear magnetic moment typically is much smaller than the electron magnetic moment, because although the magnetic moment is proportional to its angular momentum (comparable to that of the electron) it is also inversely proportional to its mass. Nevertheless, it is the nucleus's relatively small nuclear magnetic moment that is responsible for nuclear magnetic resonance (NMR), which is the basis for magnetic resonance imaging (MRI).

Although most atoms and molecules have a net magnetic moment at temperatures well below room temperature, at room temperature they typically have no net magnetic moment. However, they can often be magnetized. If the orbital magnetic properties dominate, the response typically will be diamagnetic; if the intrinsic magnetic properties dominate, the response typically will be paramagnetic.

Solids are collections of atoms and molecules. At room temperature most solids are either diamagnetic or paramagnetic.

Although for many purposes it is convenient to think of a magnet as having magnetic poles, it must be remembered that no isolated magnetic pole has ever been observed. As indicated above, the proper description is ultimately one due to electrical currents. For a magnet, these currents should be thought of as circulating about its atoms, and flowing without any electrical resistance. This physical picture is due to André-Marie Ampère, and these atomic currents are known as Amperian currents. For a uniformly magnetized bar magnet in the shape of a cylinder, the net effect of the atomic currents is to make the magnet behave as if there is a sheet of current flowing around the cylinder, with local flow direction normal to the cylinder axis. A right-hand-rule due to Ampère tells us how the currents flow, for a given magnetic moment. Align the thumb of your right hand along the magnetic moment, and with that hand grasp the cylinder. Your fingers will then point along the direction of current flow.

Permanent magnets

A few elements -- especially iron, cobalt, and nickel -- are ferromagnetic at room temperature. When quantum mechanics and the Pauli Exclusion Principle are accounted for, the electrical energy within these atoms is found to be lower if the magnetic moments of the valence electrons are aligned. This makes them ferromagnetic. Every ferromagnet has its own individual temperature, called the Curie temperature, or Curie point, above which it loses its ferromagnetic properties. This is because the thermal tendency to disorder overwhelms the energy lowering due to ferromagnetic order. A perfectly aligned ferromagnet is said to have long-range order because all of its atoms have their magnetic moments pointing in the same direction. Real ferromagnets are not perfectly aligned, but rather contain perfectly aligned regions, called magnetic domains, which have their own magnetization directions.

A long bar magnet appears to have a north pole at one end and a south pole at the other. Near either end the magnetic field falls off inversely with the square of the distance from that pole.

For a magnet of any shape, at distances large compared to its size, the strength of the magnetic field falls off inversely with the cube of the distance from the magnet's center.

Electromagnets

Main article: electromagnet

An electromagnet in its simplest form, is a wire that has been coiled into one or more loops, known as a solenoid. When electric current flows through the wire, a magnetic field is generated. It is concentrated near the coil, and its field lines are very similar to those for a magnet. The orientation of this effective magnet is determined via the right hand rule. The magnetic moment and the magnetic field of the electromagnet are proportional to the number of loops of wire, to the cross-section of each loop, and to the current passing through the wire.

If the coil of wire is wrapped around a material with no special magnetic properties (i.e., cardboard), it will tend to generate a very weak field. However, if it is wrapped around a "soft" ferromagnetic material, such as an iron nail, then the net field produced can result in a several hundred- to thousand-fold increase of field strength.

Uses for electromagnets include particle accelerators, electric motors, junkyard cranes, and magnetic resonance imaging machines. Some applications involve configurations more than a simple magnetic dipole; for example, quadrupole magnets are used to focus particle beams.

Characteristics

Permanent magnets and dipoles

All magnets appear to have at least one north pole (reckoned positive) and at least one south pole (reckoned negative), and the net pole strength of every magnet is zero. Despite their apparent reality, as suggested by the image at the top of the page, where iron filings concentrate in regions of large magnetic field, poles are not physical objects on or in the magnet. They are, as we have stated repeatedly, a useful concept for describing magnets. Rather than poles being the fundamental unit, it is the magnetic dipole that is the fundamental unit. A magnetic dipole can be thought of as a combination of a positive and a negative pole that are microscopically close to one another and inseparable. This is not a bad description of the magnetic dipole of an electron in a magnetic material.

The effect of aligning many dipoles and placing them head-to-tail in a line is that there appears a north pole at one end and a south pole at the other, with all the intermediate north and south poles canceling out. The net effect is a very long dipole that appears to have poles only at its ends. Alternatively, aligning many dipoles and placing them on a sheet producing an object whose magnetic field is like that of a wire carrying current around the perimeter of the sheet. Again, although theories have been developed involving the possibility of north and south magnetic monopoles, no magnetic monopole has yet been found.

North-south pole designation and the Earth's magnetic field

See also: Earth's magnetic field, North Pole, South Pole, and Magnetic North Pole

A standard naming system for the poles of magnets is important. Historically, the terms north and south reflect awareness of the relationship between magnets and the earth's magnetic field. A freely suspended magnet will eventually orient itself north-to-south, because of its attraction to the north and south magnetic poles of the earth. The end of a magnet that points (approximately) toward the Earth's geographic North Pole is labeled as the north pole of the magnet; correspondingly, the end that points south is the south pole of the magnet. (The actual geographic north pole is in a slightly different ___location than the corresponding magnetic pole; see Magnetic North Pole.)

The Earth's present geographic north is thus actually its magnetic south. Confounding the situation further, magnetized rocks on the ocean floor show that the Earth's magnetic field has reversed itself in the past, so this system of naming is likely to be incorrect at some time in the future.

Fortunately, by using an electromagnet and the right hand rule relating the electromagnet's current and the magnetic field it produces, the orientation of the field of a magnet can be defined without reference to the Earth's geomagnetic field.

To avoid the confusion between geographic and magnetic north and south poles, the terms positive and negative are sometimes used for the poles of a magnet. The positive pole is that which seeks geographical north.

Common uses

 

Magnets have many uses in toys. M-tic uses magnetic rods connected to metal spheres for construction

• Magnetic recording media: Common VHS tapes contain a reel of magnetic tape. The information that makes up the video and sound is encoded on the magnetic coating on the tape. Common audio cassettes also rely on magnetic tape. Similarly, in computers, floppy disks and hard disks record data on a thin magnetic coating.

• Credit, debit, and ATM cards: All of these cards have a magnetic strip on one of their sides. This strip contains the necessary information to contact an individual's financial institution and connect with their account(s).

• Common televisions and computer monitors: TV and computer screens using vacuum tube technology employ an electromagnet to guide electrons to the screen, in order to produce an image -- see the article on cathode ray tubes. Plasma screens and LCDs use different technologies.

• Speakers and microphones: Most speakers employ a permanent magnet and a current-carrying coil to convert electric energy (the signal) into mechanical energy (the sound). The coil is wrapped around the speaker cone, and carries the signal, producing a changing magnetic field that interacts with the field of the permanent magnet. The low mass coil feels a magnetic force and in response moves the cone and the neighboring air, thus generating sound. Standard microphones employ the same concept, but in reverse. A microphone has a cone or membrane attached to a coil of wire. The coil rests inside a specially shaped magnet. When sound vibrates the membrane, the coil is vibrated as well. As the coil moves through the magnetic field, a voltage is generated in the coil (see Lenz's Law). This voltage drives current in the wire that is characteristic of the original sound.

 

Magnetic hand separator for heavy minerals

• Electric motors and generators: Some electric motors (much like loudspeakers) rely upon a combination of an electromagnet and a permanent magnet, and much like loudspeakers, they convert electric energy into mechanical energy. A generator is the reverse: it converts mechanical energy into electric energy.

• Transformers: Transformers are devices that transfer electric energy between two windings that are electrically isolated but are linked magnetically.

• Chucks: Chucks are used in the metalworking field to hold objects. If these objects can be held securely with a magnet then a permanent or electromagnetic chuck may be used. Magnets are also used in other types of fastening devices, such as the magnetic base, the magnetic clamp and the refrigerator magnet.

• Magic: Naturally magnetic Lodestones as well as iron magnets are used in conjunction with fine iron grains (called "magnetic sand") in the practice of the African-American folk magic known as hoodoo. The stones are symbolically linked to people's names and ritually sprinkled with magnetic sand to reveal the magnetic field. One stone may be utilized to bring desired things to a person; a pair of stones may be manipulated to bring two people closer together in love.

• Art: 1 mm or thicker vinyl magnet sheets may be attached to paintings, photographs, and other ornamental articles, allowing them to be stuck to refrigerators and other metal surfaces.

• Science Projects: Many topic questions are often based on magnets. For example; how is the strength of a magnet affected by glass, plastic, and cardboard?

• Magnets can be used to make jewelry. Necklaces and bracelets can have a magnetic clasp. Necklaces and bracelets can be made from small but strong, cylindrical magnets and slightly larger iron or steel balls connected in a pattern that is repeated until it is long enough to fit on the wrist or neck. These accessories may be fragile enough to accidentally come apart, but they also can be disassembled and reassembled with a different design. When connected as a necklace or a bracelet, magnets lose their attraction to other pieces of iron steel because they are already attached to their own iron and steel balls. Magnetic lip-rings and earrings are sometimes employed to avoid piercing.

• Most children enjoy playing with magnets; they usually try to attach the magnets to metallic objects to see if the objects are magnetic. The more children play with magnets, the more they learn.

• Magnets can pick up magnetic items (iron nails, staples, tacks, paper clips) that are either too small, too hard to reach, or too thin for fingers to hold.

• A recently developed use of magnetism is to connect portable computer power cables. Such a connection will occasionally break by accidentally pushing against the cable, but the computer battery prevents interruption of service, and the easy disconnection protects the cable from serious jerks or from being stepped on.

Magnetization and demagnetization

Ferromagnetic materials can be magnetized in the following ways:

• Placing the item in an external magnetic field will result in the item retaining some of the magnetism on removal. Vibration has been shown to increase the effect. Ferrous materials aligned with the earth's magnetic field and which are subject to vibration (e.g. frame of a conveyor) have been shown to acquire significant residual magnetism.
• Placing the item in a solenoid with a direct current passing through it.
• Stroking - An existing magnet is moved from one end of the item to the other repeatedly in the same direction.
• Placing a steel bar in a magnetic field, then heating it to a high temperature and then finally hammering it as it cools. This can be done by laying the magnet in a North-South direction in the Earth's magnetic field. In this case, the magnet is not very strong but the effect is permanent.

Permanent magnets can be demagnetized in the following ways:

• Heating a magnet past its Curie point will destroy the long range ordering.
• Contact through stroking one magnet with another in random fashion will demagnetize the magnet being stroked, in some cases; some materials have a very high coercive field and cannot be demagnetized with other permanent magnets.
• Hammering or jarring will destroy the long range ordering within the magnet.
• A magnet being placed in a solenoid which has an alternating current being passed through it will have its long range ordering disrupted, in much the same way that direct current can cause ordering.

In an electromagnet which uses a soft iron core, ceasing the flow of current will eliminate the magnetic field. However, a slight field may remain in the core material as a result of hysteresis.

Types of permanent magnets

 

A stack of ferrite magnets

• Rare Earth types:
  • Neodymium magnets - The second generation of rare-earth magnets are made from sintered neodymium, iron and small amounts of boron. These magnets have the highest energy product of any permanent magnetic material.
  • Samarium-cobalt magnets - A sintered rare-earth magnetic material made of samarium and cobalt. These magnets are corrosion and temperature resistant.
  • Ceramic magnets - A low cost sintered magnet made from a composite of iron oxide and barium/strontium carbonate.
  • Alnico magnets - magnet made from aluminum, nickel and cobalt.
  • Injection Molded/Bonded - A magnet made by the combination of resins and magnetic powder to form a soft and flexible magnetic material.
  • Plastic magnets

Magnetic behaviors

There are many forms of magnetic behavior, and all materials exhibit at least one of these behaviors. Magnets vary in the permanency of their magnetization and the strength of the magnetic field that is created.

Paramagnetism

Most popularly found in paper clips, paramagnetism is exhibited in substances which do not emit fields by themselves, but when exposed to a magnetic field, its electrons will begin to spin in such a manner that the substance emits a field of its own. A good analogy for this behavior can be found in a bucket of nails - if you pick up a single nail, you can expect that other nails will not follow. However, you can apply an intense magnetic field to the bucket, pick up one nail, and find that many will come with it.

Main article: Paramagnetism

Diamagnetism

Unscientifically referred to as 'non-magnetic,' diamagnets actually exhibit some magnetic behavior - just to very small magnitudes. While paramagnetism is affected more by the direction of the spin of electrons, diamagnetism is affected by electrons' centripetal forces. Under the influence of a field, electrons of opposite spin will see opposite effects to their centripetal force: one will increase and one will decrease. This results in a very small magnetic force. All materials exhibit this type of magnetism, however, when diamagnetism pairs with a stronger type of magnetic behavior, the diamagnetic effect is severely overshadowed.

Main article: Diamagnetism

Ferromagnetism

This is the 'popular' perception of a magnet. Ferromagnetic materials have a high retainment for magnetization, and a common example is a traditional refrigerator magnet. By technicality, ferromagnetism exists when all of the atoms contribute to the magnetic force emitted. The mechanical explanation of this is similar to that of paramagnetism - the electrons' spins align such it creates a magnetic force. However, unlike paramagnetic substances, a ferromagnet will retain this spin alignment.

Main article: Ferromagnetism

Ferrimagnetism

Like ferromagnetism, ferrimagnets retain their magnetization in the absence of a field. However, they are arranged such that some of its atoms oppose the magnetic moment. These atoms are said to be anti-aligned. The first discovered magnetic substance, magnetite, was originally believed to be a ferromagnet; Louis Néel disproved this, however, with the discovery of ferrimagnetism.

Main article: Ferrimagnetism

Antiferromagnetism

When all atoms are arranged in a substance so that they are anti-aligned, the substance is antiferromagnetic. Antiferromagnets have a zero net magnetic moment, meaning no field is emitted by them. Antiferromagnets are less common compared to the other types of behaviors, and are mostly observed at low temperatures. In varying temperatures, antiferromagnets can be seen to exhibit diamagnetic and ferrimagnetic properties.

Main article: Antiferromagnetism

Units in magnetism

Two sets of units are commonly employed in magnetism. How we write the laws of magnetism depends on which set of units we employ. We consider first the units known as SI (Système Internationale). The other set of units is actually two sets -- Gaussian and cgs-emu -- but these are the same for magnetic properties. Magnetic units is the subject of much frustration in the area of magnetism, as the SI units replace the older cgs-emu units; some magneticians have grown up on one set of units and some on the other.

In all units it is convenient to employ two types of magnetic field, B and H, as well as the magnetization M, defined as the magnetic moment per unit volume.

(1) The magnetic induction field B is given in SI units of T (tesla). B is the true magnetic field, whose time-variation produces, by Faraday's Law, circulating electric fields (which the power companies sell). B also produces a deflection force on moving charged particles (as in TV tubes). The tesla is equivalent to the magnetic flux (in webers) per unit area (in meters squared), thus giving B the unit of a flux density. In cgs-emu the unit of B is G (gauss). One T equals 10⁴ G.

(2) The magnetic field H is given in SI units of ampere-turns/meter (A-turn/m). The "turns" appears because when H is produced by a current-carrying wire, its value is proportional to the number of turns of that wire. In cgs-emu the unit of H is Oe (oersted). One A-turn/m equals ${\displaystyle 4\pi }$  x 10^-3 Oe.

(3) The magnetization M is given in SI units of ampere/meter (A/m). In cgs-emu the unit of M is emu. One A/m equals 10^-3 emu. A good permanent magnet can have a magnetization as large as a million A/m. Magnetic fields produced by current-carrying wires would require comparably huge currents per unit length, one reason we employ permanent magnets and electromagnets.

(4) In SI units, the relation B=${\displaystyle \mu _{0}}$ (H+M) holds, where ${\displaystyle \mu _{0}}$  is the permeability of space, which equals ${\displaystyle 4\pi }$  x 10^-7 tesla∙meter/ampere. In cgs-emu it is written as B=H+${\displaystyle 4\pi }$ M.

Materials that are not permanent magnets usually satisfy the relation M=χH in SI, where χ is the (dimensionless) magnetic susceptibility. Most non-magnetic materials have a relatively small χ (on the order of a millionth), but soft magnets can have χ's on the order of hundreds or thousands. For materials satisfying M=χH, we can also write B=${\displaystyle \mu _{0}}$ (1+χ)H=${\displaystyle \mu _{0}\mu _{r}}$ H=${\displaystyle \mu }$ H, where ${\displaystyle \mu _{r}}$ =1+χ is the (dimensionless) relative permeability and ${\displaystyle \mu =\mu _{0}\mu _{r}}$  is the magnetic permeability. Both hard and soft magnets have a more complex, history-dependent, behavior described by what are called hysteresis loops, which give either B vs H or M vs H. In cgs-emu M=χH, but ${\displaystyle \chi (SI)=4\pi \chi (cgs-emu)}$ , and ${\displaystyle \mu =\mu _{r}}$ .

Caution: In part because there are not enough Roman and Greek symbols, there is no commonly agreed upon symbol for magnetic pole strength and magnetic moment. The symbol m has been used for both pole strength (unit = A-m, where here "m is for meter") and for magnetic moment (unit = A-m²). The symbol μ has been used in some texts for magnetic permeability and in other texts for magnetic moment. We will use μ for magnetic permeability and m for magnetic moment. For pole strength we will employ q_m. For a bar magnet of cross-section A with uniform magnetization M along its axis, the pole strength is given by q_m=MA, so that M can be thought of as a pole strength per unit area.

Calculating the magnetic force

Calculating the attractive or repulsive force between two magnets is, in the general case, an extremely complex operation, as it depends on the shape, magnetization, orientation and separation of the magnets.

Force between two magnetic poles

The force between two magnetic poles is given by:

${\displaystyle F={{\mu q_{m1}q_{m2}} \over {4\pi r^{2}}}}$  [1]

where

F is force (SI unit: newton)

q_m1 and q_m2 are the pole strengths (SI unit: ampere-meter)

μ is the permeability of the intervening medium (SI unit: tesla meter per ampere or henry per meter)

r is the separation (SI unit: meter).

The pole description is useful to practicing magneticians who design real-world magnets, but real magnets have a pole distribution more complex than a single north and south. Therefore, implementation of the pole idea is not simple. In some cases, one of the more complex formulae given below will be more useful.

Force between two nearby attracting surfaces of area A and equal but opposite magnetizations M

${\displaystyle F={\frac {\mu _{0}}{2}}AM^{2}}$  [2]

where

A is the area of each surface, in m²

M is their magnetization, in ampere/m.

${\displaystyle \mu _{0}}$  is the permeability of space, which equals ${\displaystyle 4\pi }$  x 10^-7 tesla∙meter/ampere

Force between two bar magnets

The force between two identical cylindrical bar magnets placed end-to-end is given by:

${\displaystyle F=\left[{\frac {B_{0}^{2}A^{2}\left(L^{2}+R^{2}\right)}{\pi \mu _{0}L^{2}}}\right]\left[{\frac {1}{x^{2}}}+{\frac {1}{(x+2L)^{2}}}-{\frac {2}{(x+L)^{2}}}\right]}$  [3]

where

B₀ is the magnetic flux density very close to each pole, in T,

A is the area of each pole, in m²,

L is the length of each magnet, in m,

R is the radius of each magnet, in m, and

x is the separation between the two magnets, in m

B₀=${\displaystyle {\frac {\mu _{0}}{2}}}$ M relates the flux density at the pole to the magnetization of the magnet.

See also

• B-H Analyzer
• electromagnet
• electromagnetism
• electromagnetic field
• diamagnetism
• magnetic dipole
• magnetic monopole
• magnetism
• molecular magnet
• paramagnetism
• magnet therapy
• supermagnets

Online references

• HyperPhysics E/M, good complete tree diagram of electromagnetic relationships with magnets
• Maxwell's Equations and some history...
• Detailed Theory on Designing a Solenoid or a Coil Gun

Printed references

1. "positive pole n." The Concise Oxford English Dictionary. Ed. Catherine Soanes and Angus Stevenson. Oxford University Press, 2004. Oxford Reference Online. Oxford University Press.

2. Wayne M. Saslow, "Electricity, Magnetism, and Light", Academic (2002). ISBN 0-12-619455-6. Chapter 9 discusses magnets and their magnetic fields using the concept of magnetic poles, but it also gives evidence that magnetic poles don't really exist in ordinary matter. Chapters 10 and 11, following what appears to be a 19th century approach, use the pole concept to obtain the laws describing the magnetism of electric currents.

External links

• Joseph J. Stupak Jr., Template:PDFlink. Oersted Technology at the EMCW Coil Winding Show, 2000.
• Floating Magnet
• Magnets and Electromagnets - Video
• Magnet Technology Center Commercial source of information on permanent magnetic materials.
• Magnet Design Guide Commercial compilation on permanent magnet design.
• Research Papers on Magnetics Commercial company compilation of research papers related to permanent magnets.
• Answers to several questions from curious kids about magnets
• Magnetic units are discussed here
• [4]