# Magnetism

 Electrostatics Electromagnetism Electricity · Magnetism Electric charge Coulomb's law Electric field Gauss's law Electric potential Electric dipole moment Ampère's law Magnetic field Magnetic dipole moment Electric current Lorentz force law Electromotive force (EM) Electromagnetic induction Faraday-Lenz law Displacement current Maxwell's equations (EMF) Electromagnetic field (EM) Electromagnetic radiation Electrical conduction Electrical resistance Capacitance Inductance Impedance Resonant cavities Waveguides
Magnetic lines of force of a bar magnet shown by iron filings on paper

In physics, magnetism is one of the phenomena by which materials exert an attractive or repulsive force on other materials. Some well known materials that exhibit easily detectable magnetic properties are nickel, iron, some steels, and the mineral magnetite; however, all materials are influenced to greater or lesser degree by the presence of a magnetic field.

## History

In China, the earliest literary reference to magnetism lies in a 4th century BC book called Book of the Devil Valley Master (鬼谷子): "The lodestone makes iron come or it attracts it." The earliest mention of the attraction of a needle appears in a work composed between 20 and 100 AD (Louen-heng): "A lodestone attracts a needle." By the 12th century the Chinese were known to use the lodestone compass for navigation. Far earlier Magnetotactic bacteria had evolved to build miniature magnets inside themselves and use them to establish their orientation relative to the Earth's magnetic field .

## Physics of magnetism

Magnetic forces are forces that arise from the movement of electrical charge. Maxwell's equations and the Biot-Savart law describe the origin and behaviour of the fields that govern these forces. Thus, magnetism is seen whenever electrically charged particles are in motion. This can arise either from movement of electrons in an electric current, resulting in " electromagnetism", or from the quantum-mechanical spin and orbital motion of electrons, resulting in what are known as " permanent magnets". Electron spin is the dominant effect within atoms. The so-called 'orbital motion' of electrons around the nucleus is a secondary effect that slightly modifies the magnetic field created by spin.

The magnetic force is actually due to the finite speed (the speed of light) of a disturbance of the electric field which gives rise to forces that appear to be acting along a line at right angles to the charges. In effect, the magnetic force is the portion of the electric force directed to where the charge used to be. For this reason magnetism can be considered to be basically an electric force that is a direct consequence of relativity.

## Charged particle in a magnetic field

When a charged particle moves through a magnetic field B, it feels a force F given by the cross product:

$\vec{F} = q \vec{v} \times \vec{B}$

where $q\,$ is the electric charge of the particle, $\vec{v} \,$ is the velocity vector of the particle, and $\vec{B} \,$ is the magnetic field.

Because this is a cross product, the force is perpendicular to both the motion of the particle and the magnetic field. It follows that the magnetic force does no work on the particle; it may change the direction of the particle's movement, but it cannot cause it to speed up or slow down.

One tool for determining the direction of the velocity vector of a moving charge, the magnetic field, and the force exerted is labeling the index finger "V", the middle finger "B", and the thumb "F" with your right hand. When making a gun-like configuration (with the middle finger crossing under the index finger), the fingers represent the velocity vector, magnetic field vector, and force vector, respectively. See also right hand rule.

## Magnetic dipoles

Normally, magnetic fields are seen as dipoles, having a " South pole" and a " North pole"; terms dating back to the use of magnets as compasses, interacting with the Earth's magnetic field to indicate North and South on the globe. Since opposite ends of magnets are attracted, the 'north' magnetic pole of the earth must be magnetically 'south'.

A magnetic field contains energy, and physical systems stabilize into the configuration with the lowest energy. Therefore, when placed in a magnetic field, a magnetic dipole tends to align itself in opposed polarity to that field, thereby canceling the net field strength as much as possible and lowering the energy stored in that field to a minimum. For instance, two identical bar magnets normally line up North to South resulting in no net magnetic field, and resist any attempts to reorient them to point in the same direction. The energy required to reorient them in that configuration is then stored in the resulting magnetic field, which is double the strength of the field of each individual magnet. (This is, of course, why a magnet used as a compass interacts with the Earth's magnetic field to indicate North and South).

## Magnetic monopoles

The modern understanding of magnetism posits that all magnetic effects are actually due to relativistic effects caused by relative motion between the observer and the charged particles. Since all magnetism is caused by moving charges, all magnets are in fact electromagnets.

Even atoms have a tiny field. In the planetary model of an atom, the electrons orbit the nucleus and thus have a change in motion giving rise to a magnetic field. Permanent magnets have measurable magnetic fields because the atoms (and molecules) are arranged in a way that their individual tiny fields align and add up.

In this model, the lack of a single pole makes intuitive sense; cutting a bar magnet in half does nothing to the arrangement of the molecules within, and you end up with two bars with the same arrangement, and thus the same field. This also explains how heating or simply hitting a magnet made from a soft material will degauss it, as the molecules within are moved about.

Since all known forms of magnetic phenomena involve the motion of electrically charged particles, and since no theory suggests that "pole" is, in that context, a thing rather than a convenient fiction, it may well be that nothing that could be called a magnetic monopole exists or ever did or could.

Contrary to normal experience, some theoretical physics models predict the existence of magnetic monopoles. Paul Dirac observed in 1931 that, because electricity and magnetism show a certain symmetry, just as quantum theory predicts that individual positive or negative electric charges can be observed without the opposing charge, isolated South or North magnetic poles should be observable. In practice, however, although charged particles like protons and electrons can be easily isolated as individual electrical charges, magnetic south and north poles have never been found in isolation. Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain why the observed elementary particles carry charges that are multiples of the charge of the electron.

In modern elementary particle theory, the quantization of charge is realized in a spontaneous breakdown of a non- abelian gauge symmetry. Monopoles predicted in certain grand unified theories differ from the one originally thought of by Dirac. These monopoles, unlike elementary particles, are solitons, which are localized energy packets. If they exist at all, they contradict cosmological observations. A solution to this monopole problem in cosmology gave rise to the currently-interesting idea of inflation.

## Atomic magnetic dipoles

The physical cause of the magnetism of objects, as distinct from electrical currents, is the atomic magnetic dipole. Magnetic dipoles, or magnetic moments, result on the atomic scale from the two kinds of movement of electrons. The first is the orbital motion of the electron around the nucleus; this motion can be considered as a current loop, resulting in an orbital dipole magnetic moment along the axis of the nucleus. The second, much stronger, source of electronic magnetic moment is due to a quantum mechanical property called the spin dipole magnetic moment (although current quantum mechanical theory states that electrons neither physically spin, nor orbit the nucleus).

Dipole moment of a bar magnet.

The overall magnetic moment of the atom is the net sum of all of the magnetic moments of the individual electrons. Because of the tendency of magnetic dipoles to oppose each other to reduce the net energy, in an atom the opposing magnetic moments of some pairs of electrons cancel each other, both in orbital motion and in spin magnetic moments. Thus, in the case of an atom with a completely filled electron shell or subshell, the magnetic moments normally completely cancel each other out and only atoms with partially-filled electron shells have a magnetic moment, whose strength depends on the number of unpaired electrons.

The differences in configuration of the electrons in various elements thus determine the nature and magnitude of the atomic magnetic moments, which in turn determine the differing magnetic properties of various materials. Several forms of magnetic behaviour have been observed in different materials, including:

• Diamagnetism
• Paramagnetism
• Molecular magnet
• Ferromagnetism
• Antiferromagnetism
• Ferrimagnetism
• Metamagnetism
• Spin glass
• Superparamagnetism

Magnetars, stars with extremely powerful magnetic fields, are also known to exist.

## Types of magnets

### Electromagnets

Electromagnets are useful in cases where a magnet must be switched on or off; for instance, large cranes to lift junked automobiles.

For the case of electric current moving through a wire, the resulting field is directed according to the "right hand rule." If the right hand is used as a model, and the thumb of the right hand points along the wire from positive towards the negative side ("conventional current", the reverse of the direction of actual movement of electrons), then the magnetic field will wrap around the wire in the direction indicated by the fingers of the right hand. As can be seen geometrically, if a loop or helix of wire is formed such that the current is traveling in a circle, then all of the field lines in the centre of the loop are directed in the same direction, resulting in a magnetic dipole whose strength depends on the current around the loop, or the current in the helix multiplied by the number of turns of wire. In the case of such a loop, if the fingers of the right hand are directed in the direction of conventional current flow (i.e., positive to negative, the opposite direction to the actual flow of electrons), the thumb will point in the direction corresponding to the North pole of the dipole.

### Permanent and temporary magnets

Permanent and temporary magnets are alike in that they do not require another influence to create their magnetic field, they rely on magnetic poles. There are always two poles, a north and a south. Even by cutting a magnet in numerous pieces you will not get a magnetic monopole, you will get many abated magnets. A helpful way to think of it is to think of a line of pencils, all facing the same way. each has a sharp end and an eraser end, or a north and south end. If you diverse that line into two lines each line will still have a sharp side and eraser side. A permanent magnet differs from a temporary magnet in that a temporary magnet is simply temporary. Stroking a metal onto a magnetized material such as magnetite (a naturally magnetized mineral) would turn the metal into a ferromagnetic material. Permanent magnets that contain other materials such as those in strong magnets are difficult to magnetize, but tend to keep its magnetism for a greater period. Permanent magnets may be metals such as steel, and iron, natural minerals such as magnetite, or even plastic magnets. Although they are called permanent they are not comprehensively permanent, if dropped, heated, or struck against a hard object at a fast speed the magnetic domains within the magnet may shift out of alignment causing the magnet to become debilitated. There are two types of rare-earth magnets:

• Neodymium magnets - made from sintered neodymium, iron and small amounts of boron; the most powerful and affordable.
• Samarium-cobalt magnets (SmCo5) are less common than neodymium magnets, are not as strong, and are more expensive, but they have a higher curie point, making them more applicable for situations when they will be under intense heat.

#### Magnetic metallic elements

Many materials have unpaired electron spins, but the majority of these materials are paramagnetic. When the spins interact with each other in such a way that the spins align spontaneously, the materials are called ferromagnetic (what is often loosely termed as "magnetic"). Due to the way their regular crystalline atomic structure causes their spins to interact, some metals are (ferro)magnetic when found in their natural states, as ores. These include iron ore ( magnetite or lodestone), cobalt, zinc and nickel, as well the rare earth metals gadolinium and dysprosium (when at a very low temperature). Such naturally occurring (ferro)magnets were used in the first experiments with magnetism. Technology has since expanded the availability of magnetic materials to include various manmade products, all based, however, on naturally magnetic elements.

#### Composites

##### Ceramic or ferrite

Ceramic, or ferrite, magnets are made of a sintered composite of powdered iron oxide and barium/strontium carbonate ceramic. Due to the low cost of the materials and manufacturing methods, inexpensive magnets (or nonmagnetized ferromagnetic cores, for use in electronic component such as radio antennas, for example) of various shapes can be easily mass produced. The resulting magnets are noncorroding, but brittle and must be treated like other ceramics.

##### Alnico

Alnico magnets are made by casting or sintering a combination of aluminium, nickel and cobalt with iron and small amounts of other elements added to enhance the properties of the magnet. Sintering offers superior mechanical characteristics, whereas casting delivers higher magnetic fields and allows for the design of intricate shapes. Alnico magnets resist corrosion and have physical properties more forgiving than ferrite, but not quite as desirable as a metal.

##### Injection molded

Injection molded magnets are a composite of various types of resin and magnetic powders, allowing parts of complex shapes to be manufactured by injection molding. The physical and magnetic properties of the product depend on the raw materials, but are generally lower in magnetic strength and resemble plastics in their physical properties.

##### Flexible

Flexible magnets are similar to injection molded magnets, using a flexible resin or binder such as vinyl, and produced in flat strips or sheets. These magnets are lower in magnetic strength but can be very flexible, depending on the binder used.

#### Rare earth magnets

'Rare earth' ( lanthanoid) elements have a partially occupied f electron shell (which can accommodate up to 14 electrons.) The spin of these electrons can be aligned, resulting in very strong magnetic fields, and therefore these elements are used in compact high-strength magnets where their higher price is not a factor.

##### Samarium-cobalt

Samarium-cobalt magnets are highly resistant to oxidation, with higher magnetic strength and temperature resistance than alnico or ceramic materials. Sintered samarium-cobalt magnets are brittle and prone to chipping and cracking and may fracture when subjected to thermal shock.

##### Neodymium-iron-boron (NIB)

Neodymium magnets, more formally referred to as neodymium-iron-boron (NdFeB) magnets, have the highest magnetic field strength, but are inferior to samarium cobalt in resistance to oxidation and temperature. This type of magnet has traditionally been expensive, due to both the cost of raw materials and licensing of the patents involved. This high cost limited their use to applications where such high strengths from a compact magnet are critical. Use of protective surface treatments such as gold, nickel, zinc and tin plating and epoxy resin coating can provide corrosion protection where required. Beginning in the 1980s, NIB magnets have increasingly become less expensive and more popular in other applications such as controversial children's magnetic building toys. Even tiny neodymium magnets are very powerful and have important safety considerations.

#### Single-molecule magnets (SMMs) and single-chain magnets (SCMs)

In the 1990s it was discovered that certain molecules containing paramagnetic metal ions are capable of storing a magnetic moment at very low temperatures. These are very different from conventional magnets that store information at a "domain" level and theoretically could provide a far denser storage medium than conventional magnets. In this direction research on monolayers of SMMs is currently under way. Very briefly, the two main attributes of an SMM are:

1. a large ground state spin value (S), which is provided by ferromagnetic or ferrimagnetic coupling between the paramagnetic metal centres.
2. a negative value of the anisotropy of the zero field splitting (D)

Most SMM's contain manganese, but can also be found with vanadium, iron, nickel and cobalt clusters. More recently it has been found that some chain systems can also display a magnetization which persists for long times at relatively higher temperatures. These systems have been called single-chain magnets.

#### Nano-structured magnets

Some nano-structured materials exhibit energy waves called magnons that coalesce into a common ground state in the manner of a Bose-Einstein condensate.

See results from NIST published April 2005, or

## Units of electromagnetism

### SI units related to magnetism

SI electromagnetism units
Symbol Name of Quantity Derived Units Unit Base Units
I Magnitude of current ampere ( SI base unit) A A = W/V = C/s
q Electric charge, Quantity of electricity coulomb C A·s
V Potential difference or Electromotive force volt V J/C = kg·m2·s−3·A−1
R, Z, X Resistance, Impedance, Reactance ohm Ω V/A = kg·m2·s−3·A−2
ρ Resistivity ohm metre Ω·m kg·m3·s−3·A−2
P Power, Electrical watt W V·A = kg·m2·s−3
C Capacitance farad F C/V = kg−1·m−2·A2·s4
Elastance reciprocal farad F−1 V/C = kg·m2·A−2·s−4
ε Permittivity farad per metre F/m kg−1·m−3·A2·s4
χe Electric susceptibility (dimensionless) - -
G, Y, B Conductance, Admittance, Susceptance siemens S Ω−1 = kg−1·m−2·s3·A2
σ Conductivity siemens per metre S/m kg−1·m−3·s3·A2
H Magnetic field, magnetic field intensity ampere per metre A/m A·m−1
Φm Magnetic flux weber Wb V·s = kg·m2·s−2·A−1
B Magnetic flux density, magnetic induction, magnetic field strength tesla T Wb/m2 = kg·s−2·A−1 = N·A−1·m−1
Reluctance ampere-turn per weber A/Wb kg−1·m−2·s2·A2
L Inductance henry H Wb/A = V·s/A = kg·m2·s−2·A−2
μ Permeability henry per metre H/m kg·m·s−2·A−2
χm Magnetic susceptibility (dimensionless)
Π and Π * Electric and Magnetic hertzian vector potentials n/a n/a

### Other units

• gauss-The gauss, abbreviated as G, is the cgs unit of magnetic flux density or magnetic induction (B).
• oersted-The oersted is the CGS unit of magnetic field strength.
• maxwell-is the CGS unit for the magnetic flux.
• μo -common symbol for the permeability of free space (4πx10-7 N/(ampere-turn)2).