Magnetism

For other senses of this word, see magnetism (disambiguation).

In physics, magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well known materials that exhibit easily detectable magnetic properties (called magnets) are nickel, iron and their alloys; however, all materials are influenced to greater or lesser degree by the presence of a magnetic field.

Magnetism also has other manifestations in physics, particularly as one of the two components of electromagnetic waves such as light.

Brief and qualitative explanation of magnetism

Every electron is, by its nature, a small magnet (see Electron magnetic dipole moment). Ordinarily, the countless electrons in a material are randomly oriented in different directions, leaving no effect on average, but in a magnet the electrons tend to face the same way, so they all pull together, thus creating a strong total magnetic force.

Physics of magnetism

Magnetism, electricity, and special relativity

Main article: Electromagnetism

As a consequence of Einstein's theory of special relativity, electricity and magnetism are understood to be fundamentally interlinked. Both magnetism without electricity, and electricity without magnetism, are inconsistent with special relativity, due to such effects as length contraction, time dilation, and the fact that the magnetic force is velocity-dependent. However, when both electricity and magnetism are taken into account, the resulting theory (electromagnetism) is fully consistent with special relativity. In particular, a phenomenon that appears purely electric to one observer may be purely magnetic to another, or more generally the relative contributions of electricity and magnetism are dependent on the frame of reference. Thus, special relativity "mixes" electricity and magnetism into a single, inseparable phenomenon called electromagnetism (analogously to how special relativity "mixes" space and time into spacetime).

Magnetic fields and forces

Magnetic lines of force of a bar magnet shown by iron filings on paper

Main article: magnetic field

The phenomenon of magnetism is "mediated" by the magnetic field -- i.e., an electric current or magnetic dipole creates a magnetic field, and that field, in turn, imparts magnetic forces on other particles that are in the fields.

To an excellent approximation (but ignoring some quantum effects---see quantum electrodynamics), Maxwell's equations (which simplify to the Biot-Savart law in the case of steady currents) describe the origin and behavior of the fields that govern these forces. Therefore magnetism is seen whenever electrically charged particles are in motion---for example, from movement of electrons in an electric current, or in certain cases from the orbital motion of electrons around an atom's nucleus. They also arise from "intrinsic" magnetic dipoles arising from quantum effects, i.e. from quantum-mechanical spin.

The same situations which create magnetic fields (charge moving in a current or in an atom, and intrinsic magnetic dipoles) are also the situations in which a magnetic field has an effect, creating a force. Following is the formula for moving charge; for the forces on an intrinsic dipole, see magnetic dipole.

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. The magnitude of the force is

$F=qvB\sin \theta \,$

where $\theta \,$ is the angle between the ${\vec {v}}\,$ and ${\vec {B}}\,$ vectors.

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.

Lenz's law gives the direction of the induced electromotive force (emf) and current resulting from electromagnetic induction. German physicist Heinrich Lenz formulated it in 1834.

Magnetic dipoles

Main article: magnetic dipole

A very common source of magnetic field seen in nature is a 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 placed side-to-side normally line up North to South, resulting in a much smaller 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).

An alternative, equivalent formulation, which is often easier to apply but perhaps offers less insight, is that a magnetic dipole in a magnetic field experiences a torque and a force which can be expressed in terms of the field and the strength of the dipole (i.e., its magnetic dipole moment). For these equations, see magnetic dipole.

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. 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).

File:Magnetic dipole moment.png

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 behavior have been observed in different materials, including:

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

Magnetic monopoles

Main article: Magnetic monopole

Since a bar magnet gets its ferromagnetism from microscopic electrons distributed evenly throughout the bar, when a bar magnet is cut in half, each of the resulting pieces is a smaller bar magnet. Even though a magnet is said to have a north pole and a south pole, these two poles cannot be separated from each other. A monopole — if such a thing exists — would be a new and fundamentally different kind of magnetic object. It would act as an isolated north pole, not attached to a south pole, or vice versa. Monopoles would carry "magnetic charge" analogous to electric charge. Despite systematic searches since 1931, as of 2006, they have never been observed, and could very well not exist.

Nevertheless, some theoretical physics models predict the existence of these 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. Using quantum theory Dirac showed that if magnetic monopoles exist, then one could explain the quantization of electric charge---that is, why the observed elementary particles carry charges that are multiples of the charge of the electron.

Certain grand unified theories predict the existence of monopoles which, unlike elementary particles, are solitons (localized energy packets). Using these models to estimate the number of monopoles created in the big bang, the initial results that contradicted cosmological observations---the monopoles would have been so plentiful and massive that they would have long since halted the expansion of the universe. However, the idea of inflation (for which this problem served as a partial motivation) was successful in solving this problem, creating models in which monopoles existed but were rare enough to be consistent with current observations.

Types of magnets

Electromagnets

Main article: Electromagnet

An electromagnet is a magnet made from electrical wire wound around a magnetic material, such as iron. This form of magnet is 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 center 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

Main article: Magnet

A permanent magnet retains its magnetism without an external magnetic field whereas a temporary magnet is only magnetic while within another magnetic field. Inducing magnetism in steel results in a permanent magnet but iron loses its magnetism when the inducing field is withdrawn. A temporary magnet such as iron is thus a good material for electromagnets. Magnets are made by stroking with another magnet, tapping while fixed in a magnetic field or placing inside a solenoid coil supplied with a direct current. A permanent magnet may be de-magnetised by subjecting it to heating or sharp blows or placing it inside a solenoid supplied with a reducing alternating current.

Units of electromagnetism

SI units related to magnetism

SI electromagnetism units

Symbol	Name of quantity	Unit name	Symbol	Base units
E	energy	joule	J = C⋅V = W⋅s	kg⋅m2⋅s−2
Q	electric charge	coulomb	C	A⋅s
I	electric current	ampere	A = C/s = W/V	A
J	electric current density	ampere per square metre	A/m2	A⋅m−2
U, ΔV; Δϕ; E, ξ	potential difference; voltage; electromotive force	volt	V = J/C	kg⋅m2⋅s−3⋅A−1
R; Z; X	electric 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	electric power	watt	W = V⋅A	kg⋅m2⋅s−3
C	capacitance	farad	F = C/V	kg−1⋅m−2⋅A2⋅s4
ΦE	electric flux	volt metre	V⋅m	kg⋅m3⋅s−3⋅A−1
E	electric field strength	volt per metre	V/m = N/C	kg⋅m⋅A−1⋅s−3
D	electric displacement field	coulomb per square metre	C/m2	A⋅s⋅m−2
ε	permittivity	farad per metre	F/m	kg−1⋅m−3⋅A2⋅s4
χe	electric susceptibility	(dimensionless)	1	1
p	electric dipole moment	coulomb metre	C⋅m	A⋅s⋅m
G; Y; B	conductance; admittance; susceptance	siemens	S = Ω−1	kg−1⋅m−2⋅s3⋅A2
κ, γ, σ	conductivity	siemens per metre	S/m	kg−1⋅m−3⋅s3⋅A2
B	magnetic flux density, magnetic induction	tesla	T = Wb/m2 = N⋅A−1⋅m−1	kg⋅s−2⋅A−1
Φ, ΦM, ΦB	magnetic flux	weber	Wb = V⋅s	kg⋅m2⋅s−2⋅A−1
H	magnetic field strength	ampere per metre	A/m	A⋅m−1
F	magnetomotive force	ampere	A = Wb/H	A
R	magnetic reluctance	inverse henry	H−1 = A/Wb	kg−1⋅m−2⋅s2⋅A2
P	magnetic permeance	henry	H = Wb/A	kg⋅m2⋅s-2⋅A-2
L, M	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
χ	magnetic susceptibility	(dimensionless)	1	1
m	magnetic dipole moment	ampere square meter	A⋅m2 = J⋅T−1	A⋅m2
σ	mass magnetization	ampere square meter per kilogram	A⋅m2/kg	A⋅m2⋅kg−1

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.
• μ_o -common symbol for the permeability of free space (4πx10^-7 N/(ampere-turn)²).

See also

• Earth's magnetic field
• Electrostatics
• Magnetostatics
• Electromagnetism
• Lenz's law
• Plastic magnet
• Magnet
• Magnetar
• Magnetic field
• Magnetic bearing
• Magnetic cooling
• Magnet therapy
• Magnetic circuit
• Magnetization
• Michael Faraday
• Micromagnetism
• James Clerk Maxwell
• Coercivity
• Spin wave
• Spontaneous magnetization
• Sensor
• Magnetic stirrer

References

• Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X.
• Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
• Furlani, Edward P. (2001). Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications. Academic Press. ISBN 0-12-269951-3.

External links

• Electromagnetism - a chapter from an online textbook
• Magnetic Force and Field on Project PHYSNET
• On the Magnet, 1600 First scientific book on magnetism by the father of electrical engineering. Full English text, full text search.