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Magnetic field

A magnetic field (sometimes called B-field ) is a physical field that describes the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. A permanent magnet's magnetic field pulls on ferromagnetic materials such as iron, and attracts or repels other magnets. In addition, a nonuniform magnetic field exerts minuscule forces on "nonmagnetic" materials by three other magnetic effects: paramagnetism, diamagnetism, and antiferromagnetism, although these forces are usually so small they can only be detected by laboratory equipment. Magnetic fields surround magnetized materials, electric currents, and electric fields varying in time. Since both strength and direction of a magnetic field may vary with location, it is described mathematically by a function assigning a vector to each point of space, called a vector field (more precisely, a pseudovector field).

In electromagnetics, the term magnetic field is used for two distinct but closely related vector fields denoted by the symbols $B$ and $H$. In the International System of Units, the unit of $B$, magnetic flux density, is the tesla (in SI base units: kilogram per second2 per ampere), which is equivalent to newton per meter per ampere. The unit of $H$, magnetic field strength, is ampere per meter (A/m). $B$ and $H$ differ in how they take the medium and/or magnetization into account. In vacuum, the two fields are related through the vacuum permeability, $$\mathbf{B}/\mu_0 = \mathbf{H}$$; in a magnetized material, the quantities on each side of this equation differ by the magnetization field of the material.

Magnetic fields are produced by moving electric charges and the intrinsic magnetic moments of elementary particles associated with a fundamental quantum property, their spin. Magnetic fields and electric fields are interrelated and are both components of the electromagnetic force, one of the four fundamental forces of nature.

Magnetic fields are used throughout modern technology, particularly in electrical engineering and electromechanics. Rotating magnetic fields are used in both electric motors and generators. The interaction of magnetic fields in electric devices such as transformers is conceptualized and investigated as magnetic circuits. Magnetic forces give information about the charge carriers in a material through the Hall effect. The Earth produces its own magnetic field, which shields the Earth's ozone layer from the solar wind and is important in navigation using a compass.

Description
The force on an electric charge depends on its location, speed, and direction; two vector fields are used to describe this force. The first is the electric field, which describes the force acting on a stationary charge and gives the component of the force that is independent of motion. The magnetic field, in contrast, describes the component of the force that is proportional to both the speed and direction of charged particles. The field is defined by the Lorentz force law and is, at each instant, perpendicular to both the motion of the charge and the force it experiences.

There are two different, but closely related vector fields which are both sometimes called the "magnetic field" written $B$ and $H$. While both the best names for these fields and exact interpretation of what these fields represent has been the subject of long running debate, there is wide agreement about how the underlying physics work. Historically, the term "magnetic field" was reserved for $H$ while using other terms for $B$, but many recent textbooks use the term "magnetic field" to describe $B$ as well as or in place of $H$. There are many alternative names for both (see sidebars).

The B-field
The magnetic field vector $B$ at any point can be defined as the vector that, when used in the Lorentz force law, correctly predicts the force on a charged particle at that point:

Here $H$ is the force on the particle, $B$ is the particle's electric charge, $H$, is the particle's velocity, and × denotes the cross product. The direction of force on the charge can be determined by a mnemonic known as the right-hand rule (see the figure). Using the right hand, pointing the thumb in the direction of the current, and the fingers in the direction of the magnetic field, the resulting force on the charge points outwards from the palm. The force on a negatively charged particle is in the opposite direction. If both the speed and the charge are reversed then the direction of the force remains the same. For that reason a magnetic field measurement (by itself) cannot distinguish whether there is a positive charge moving to the right or a negative charge moving to the left. (Both of these cases produce the same current.) On the other hand, a magnetic field combined with an electric field can distinguish between these, see Hall effect below.

The first term in the Lorentz equation is from the theory of electrostatics, and says that a particle of charge $H$ in an electric field $H$ experiences an electric force: $$\mathbf{F}_{\text{electric}} = q \mathbf{E}.$$

The second term is the magnetic force: $$\mathbf{F}_{\text{magnetic}} = q(\mathbf{v} \times \mathbf{B}).$$

Using the definition of the cross product, the magnetic force can also be written as a scalar equation: $$F_{\text{magnetic}} = q v B \sin(\theta)$$ where $B$, $v$, and $B$ are the scalar magnitude of their respective vectors, and $θ$ is the angle between the velocity of the particle and the magnetic field. The vector $H$ is defined as the vector field necessary to make the Lorentz force law correctly describe the motion of a charged particle. In other words,

"[T]he command, 'Measure the direction and magnitude of the vector $H$ at such and such a place,' calls for the following operations: Take a particle of known charge $B$. Measure the force on $F$ at rest, to determine $q$. Then measure the force on the particle when its velocity is $v$; repeat with $q$ in some other direction. Now find a $E$ that makes the Lorentz force law fit all these results—that is the magnetic field at the place in question."

The $F_{magnetic}$ field can also be defined by the torque on a magnetic dipole, $B$.

The SI unit of $B$ is tesla (symbol: T). The Gaussian-cgs unit of $q$ is the gauss (symbol: G). (The conversion is 1 T ≘ 10000 G. ) One nanotesla corresponds to 1 gamma (symbol: γ).

The H-field
The magnetic $q$ field is defined:

where $$\mu_0$$ is the vacuum permeability, and $E$ is the magnetization vector. In a vacuum, $v$ and $v$ are proportional to each other. Inside a material they are different (see H and B inside and outside magnetic materials). The SI unit of the $B$-field is the ampere per metre (A/m), and the CGS unit is the oersted (Oe).

Measurement
An instrument used to measure the local magnetic field is known as a magnetometer. Important classes of magnetometers include using induction magnetometers (or search-coil magnetometers) which measure only varying magnetic fields, rotating coil magnetometers, Hall effect magnetometers, NMR magnetometers, SQUID magnetometers, and fluxgate magnetometers. The magnetic fields of distant astronomical objects are measured through their effects on local charged particles. For instance, electrons spiraling around a field line produce synchrotron radiation that is detectable in radio waves. The finest precision for a magnetic field measurement was attained by Gravity Probe B at $5 aT$ ($5 T$).

Visualization
The field can be visualized by a set of magnetic field lines, that follow the direction of the field at each point. The lines can be constructed by measuring the strength and direction of the magnetic field at a large number of points (or at every point in space). Then, mark each location with an arrow (called a vector) pointing in the direction of the local magnetic field with its magnitude proportional to the strength of the magnetic field. Connecting these arrows then forms a set of magnetic field lines. The direction of the magnetic field at any point is parallel to the direction of nearby field lines, and the local density of field lines can be made proportional to its strength. Magnetic field lines are like streamlines in fluid flow, in that they represent a continuous distribution, and a different resolution would show more or fewer lines.

An advantage of using magnetic field lines as a representation is that many laws of magnetism (and electromagnetism) can be stated completely and concisely using simple concepts such as the "number" of field lines through a surface. These concepts can be quickly "translated" to their mathematical form. For example, the number of field lines through a given surface is the surface integral of the magnetic field.

Various phenomena "display" magnetic field lines as though the field lines were physical phenomena. For example, iron filings placed in a magnetic field form lines that correspond to "field lines". Magnetic field "lines" are also visually displayed in polar auroras, in which plasma particle dipole interactions create visible streaks of light that line up with the local direction of Earth's magnetic field.

Field lines can be used as a qualitative tool to visualize magnetic forces. In ferromagnetic substances like iron and in plasmas, magnetic forces can be understood by imagining that the field lines exert a tension, (like a rubber band) along their length, and a pressure perpendicular to their length on neighboring field lines. "Unlike" poles of magnets attract because they are linked by many field lines; "like" poles repel because their field lines do not meet, but run parallel, pushing on each other.

Magnetic field of permanent magnets
Permanent magnets are objects that produce their own persistent magnetic fields. They are made of ferromagnetic materials, such as iron and nickel, that have been magnetized, and they have both a north and a south pole.

The magnetic field of permanent magnets can be quite complicated, especially near the magnet. The magnetic field of a small straight magnet is proportional to the magnet's strength (called its magnetic dipole moment $B$). The equations are non-trivial and depend on the distance from the magnet and the orientation of the magnet. For simple magnets, $m$ points in the direction of a line drawn from the south to the north pole of the magnet. Flipping a bar magnet is equivalent to rotating its $B$ by 180 degrees.

The magnetic field of larger magnets can be obtained by modeling them as a collection of a large number of small magnets called dipoles each having their own $Φ_{B}$. The magnetic field produced by the magnet then is the net magnetic field of these dipoles; any net force on the magnet is a result of adding up the forces on the individual dipoles.

There are two simplified models for the nature of these dipoles: the magnetic pole model and the Amperian loop model. These two models produce two different magnetic fields, $B$ and $H$. Outside a material, though, the two are identical (to a multiplicative constant) so that in many cases the distinction can be ignored. This is particularly true for magnetic fields, such as those due to electric currents, that are not generated by magnetic materials.

A realistic model of magnetism is more complicated than either of these models; neither model fully explains why materials are magnetic. The monopole model has no experimental support. The Amperian loop model explains some, but not all of a material's magnetic moment. The model predicts that the motion of electrons within an atom are connected to those electrons' orbital magnetic dipole moment, and these orbital moments do contribute to the magnetism seen at the macroscopic level. However, the motion of electrons is not classical, and the spin magnetic moment of electrons (which is not explained by either model) is also a significant contribution to the total moment of magnets.

Magnetic pole model

Historically, early physics textbooks would model the force and torques between two magnets as due to magnetic poles repelling or attracting each other in the same manner as the Coulomb force between electric charges. At the microscopic level, this model contradicts the experimental evidence, and the pole model of magnetism is no longer the typical way to introduce the concept. However, it is still sometimes used as a macroscopic model for ferromagnetism due to its mathematical simplicity.

In this model, a magnetic $H$-field is produced by fictitious magnetic charges that are spread over the surface of each pole. These magnetic charges are in fact related to the magnetization field $M$. The $B$-field, therefore, is analogous to the electric field $H$, which starts at a positive electric charge and ends at a negative electric charge. Near the north pole, therefore, all $H$-field lines point away from the north pole (whether inside the magnet or out) while near the south pole all $m$-field lines point toward the south pole (whether inside the magnet or out). Too, a north pole feels a force in the direction of the $m$-field while the force on the south pole is opposite to the $m$-field.

In the magnetic pole model, the elementary magnetic dipole $m$ is formed by two opposite magnetic poles of pole strength $m$ separated by a small distance vector $H$, such that $B$. The magnetic pole model predicts correctly the field $H$ both inside and outside magnetic materials, in particular the fact that $H$ is opposite to the magnetization field $M$ inside a permanent magnet.

Since it is based on the fictitious idea of a magnetic charge density, the pole model has limitations. Magnetic poles cannot exist apart from each other as electric charges can, but always come in north–south pairs. If a magnetized object is divided in half, a new pole appears on the surface of each piece, so each has a pair of complementary poles. The magnetic pole model does not account for magnetism that is produced by electric currents, nor the inherent connection between angular momentum and magnetism.

The pole model usually treats magnetic charge as a mathematical abstraction, rather than a physical property of particles. However, a magnetic monopole is a hypothetical particle (or class of particles) that physically has only one magnetic pole (either a north pole or a south pole). In other words, it would possess a "magnetic charge" analogous to an electric charge. Magnetic field lines would start or end on magnetic monopoles, so if they exist, they would give exceptions to the rule that magnetic field lines neither start nor end. Some theories (such as Grand Unified Theories) have predicted the existence of magnetic monopoles, but so far, none have been observed.

Amperian loop model
In the model developed by Ampere, the elementary magnetic dipole that makes up all magnets is a sufficiently small Amperian loop with current $H$ and loop area $E$. The dipole moment of this loop is $H$.

These magnetic dipoles produce a magnetic $H$-field.

The magnetic field of a magnetic dipole is depicted in the figure. From outside, the ideal magnetic dipole is identical to that of an ideal electric dipole of the same strength. Unlike the electric dipole, a magnetic dipole is properly modeled as a current loop having a current $H$ and an area $H$. Such a current loop has a magnetic moment of $$m = Ia ,$$ where the direction of $m$ is perpendicular to the area of the loop and depends on the direction of the current using the right-hand rule. An ideal magnetic dipole is modeled as a real magnetic dipole whose area $qm$ has been reduced to zero and its current $d$ increased to infinity such that the product $m = qm d$ is finite. This model clarifies the connection between angular momentum and magnetic moment, which is the basis of the Einstein–de Haas effect rotation by magnetization and its inverse, the Barnett effect or magnetization by rotation. Rotating the loop faster (in the same direction) increases the current and therefore the magnetic moment, for example.

Force between magnets
Specifying the force between two small magnets is quite complicated because it depends on the strength and orientation of both magnets and their distance and direction relative to each other. The force is particularly sensitive to rotations of the magnets due to magnetic torque. The force on each magnet depends on its magnetic moment and the magnetic field of the other.

To understand the force between magnets, it is useful to examine the magnetic pole model given above. In this model, the $H$-field of one magnet pushes and pulls on both poles of a second magnet. If this $H$-field is the same at both poles of the second magnet then there is no net force on that magnet since the force is opposite for opposite poles. If, however, the magnetic field of the first magnet is nonuniform (such as the $M$ near one of its poles), each pole of the second magnet sees a different field and is subject to a different force. This difference in the two forces moves the magnet in the direction of increasing magnetic field and may also cause a net torque.

This is a specific example of a general rule that magnets are attracted (or repulsed depending on the orientation of the magnet) into regions of higher magnetic field. Any non-uniform magnetic field, whether caused by permanent magnets or electric currents, exerts a force on a small magnet in this way.

The details of the Amperian loop model are different and more complicated but yield the same result: that magnetic dipoles are attracted/repelled into regions of higher magnetic field. Mathematically, the force on a small magnet having a magnetic moment $B$ due to a magnetic field $I$ is:

$$\mathbf{F} = \boldsymbol{\nabla} \left(\mathbf{m}\cdot\mathbf{B}\right),$$

where the gradient $A$ is the change of the quantity $m = IA$ per unit distance and the direction is that of maximum increase of $B$. The dot product $I$, where $a$ and $m$ represent the magnitude of the $a$ and $I$ vectors and $m = Ia$ is the angle between them. If $B$ is in the same direction as $H$ then the dot product is positive and the gradient points "uphill" pulling the magnet into regions of higher $H$-field (more strictly larger $H$). This equation is strictly only valid for magnets of zero size, but is often a good approximation for not too large magnets. The magnetic force on larger magnets is determined by dividing them into smaller regions each having their own $H$ then summing up the forces on each of these very small regions.

Magnetic torque on permanent magnets
If two like poles of two separate magnets are brought near each other, and one of the magnets is allowed to turn, it promptly rotates to align itself with the first. In this example, the magnetic field of the stationary magnet creates a magnetic torque on the magnet that is free to rotate. This magnetic torque $m$ tends to align a magnet's poles with the magnetic field lines. A compass, therefore, turns to align itself with Earth's magnetic field.

In terms of the pole model, two equal and opposite magnetic charges experiencing the same $B$ also experience equal and opposite forces. Since these equal and opposite forces are in different locations, this produces a torque proportional to the distance (perpendicular to the force) between them. With the definition of $∇$ as the pole strength times the distance between the poles, this leads to $m · B$, where $m · B$ is a constant called the vacuum permeability, measuring $4$ V·s/(A·m) and $θ$ is the angle between $m · B = mBcos(θ)$ and $m$.

Mathematically, the torque $B$ on a small magnet is proportional both to the applied magnetic field and to the magnetic moment $m$ of the magnet:

$$\boldsymbol{\tau}=\mathbf{m}\times\mathbf{B} = \mu_0\mathbf{m}\times\mathbf{H}, \,$$

where × represents the vector cross product. This equation includes all of the qualitative information included above. There is no torque on a magnet if $B$ is in the same direction as the magnetic field, since the cross product is zero for two vectors that are in the same direction. Further, all other orientations feel a torque that twists them toward the direction of magnetic field.

Interactions with electric currents
Currents of electric charges both generate a magnetic field and feel a force due to magnetic B-fields.

Magnetic field due to moving charges and electric currents

All moving charged particles produce magnetic fields. Moving point charges, such as electrons, produce complicated but well known magnetic fields that depend on the charge, velocity, and acceleration of the particles.

Magnetic field lines form in concentric circles around a cylindrical current-carrying conductor, such as a length of wire. The direction of such a magnetic field can be determined by using the "right-hand grip rule" (see figure at right). The strength of the magnetic field decreases with distance from the wire. (For an infinite length wire the strength is inversely proportional to the distance.)

Bending a current-carrying wire into a loop concentrates the magnetic field inside the loop while weakening it outside. Bending a wire into multiple closely spaced loops to form a coil or "solenoid" enhances this effect. A device so formed around an iron core may act as an electromagnet, generating a strong, well-controlled magnetic field. An infinitely long cylindrical electromagnet has a uniform magnetic field inside, and no magnetic field outside. A finite length electromagnet produces a magnetic field that looks similar to that produced by a uniform permanent magnet, with its strength and polarity determined by the current flowing through the coil.

The magnetic field generated by a steady current $θ$ (a constant flow of electric charges, in which charge neither accumulates nor is depleted at any point) is described by the Biot–Savart law: $$ \mathbf{B} = \frac{\mu_0I}{4\pi}\int_{\mathrm{wire}}\frac{\mathrm{d}\boldsymbol{\ell} \times \mathbf{\hat r}}{r^2},$$ where the integral sums over the wire length where vector $m$ is the vector line element with direction in the same sense as the current $B$, $B$ is the magnetic constant, $m · B$ is the distance between the location of $m$ and the location where the magnetic field is calculated, and $τ$ is a unit vector in the direction of $H$. For example, in the case of a sufficiently long, straight wire, this becomes: $$ |\mathbf{B}| = \frac{\mu_0}{2\pi r}I$$ where $+q$. The direction is tangent to a circle perpendicular to the wire according to the right hand rule.

A slightly more general way of relating the current $$I$$ to the $−q$-field is through Ampère's law: $$\oint \mathbf{B} \cdot \mathrm{d}\boldsymbol{\ell} = \mu_0 I_{\mathrm{enc}},$$ where the line integral is over any arbitrary loop and $$I_\text{enc}$$ is the current enclosed by that loop. Ampère's law is always valid for steady currents and can be used to calculate the $B$-field for certain highly symmetric situations such as an infinite wire or an infinite solenoid.

In a modified form that accounts for time varying electric fields, Ampère's law is one of four Maxwell's equations that describe electricity and magnetism.

Force on a charged particle
A charged particle moving in a $H$-field experiences a sideways force that is proportional to the strength of the magnetic field, the component of the velocity that is perpendicular to the magnetic field and the charge of the particle. This force is known as the Lorentz force, and is given by $$\mathbf{F} = q\mathbf{E} + q \mathbf{v} \times \mathbf{B},$$ where $m$ is the force, $τ = μ_{0} m H sin θ$ is the electric charge of the particle, $μ_{0}$ is the instantaneous velocity of the particle, and $H$ is the magnetic field (in teslas).

The Lorentz force is always perpendicular to both the velocity of the particle and the magnetic field that created it. When a charged particle moves in a static magnetic field, it traces a helical path in which the helix axis is parallel to the magnetic field, and in which the speed of the particle remains constant. Because the magnetic force is always perpendicular to the motion, the magnetic field can do no work on an isolated charge. It can only do work indirectly, via the electric field generated by a changing magnetic field. It is often claimed that the magnetic force can do work to a non-elementary magnetic dipole, or to charged particles whose motion is constrained by other forces, but this is incorrect because the work in those cases is performed by the electric forces of the charges deflected by the magnetic field.

Force on current-carrying wire
The force on a current carrying wire is similar to that of a moving charge as expected since a current carrying wire is a collection of moving charges. A current-carrying wire feels a force in the presence of a magnetic field. The Lorentz force on a macroscopic current is often referred to as the Laplace force. Consider a conductor of length $m$, cross section $τ$, and charge $m$ due to electric current $m$. If this conductor is placed in a magnetic field of magnitude $I$ that makes an angle $dℓ$ with the velocity of charges in the conductor, the force exerted on a single charge $I$ is $$F = qvB \sin\theta,$$ so, for $μ_{0}$ charges where $$N = n \ell A ,$$ the force exerted on the conductor is $$f = F N = q v B n\ell A \sin\theta = Bi\ell \sin\theta, $$ where $r$.

Relation between H and B
The formulas derived for the magnetic field above are correct when dealing with the entire current. A magnetic material placed inside a magnetic field, though, generates its own bound current, which can be a challenge to calculate. (This bound current is due to the sum of atomic sized current loops and the spin of the subatomic particles such as electrons that make up the material.) The $dℓ$-field as defined above helps factor out this bound current; but to see how, it helps to introduce the concept of magnetization first.

Magnetization
The magnetization vector field $r̂$ represents how strongly a region of material is magnetized. It is defined as the net magnetic dipole moment per unit volume of that region. The magnetization of a uniform magnet is therefore a material constant, equal to the magnetic moment $r$ of the magnet divided by its volume. Since the SI unit of magnetic moment is A⋅m2, the SI unit of magnetization $r = |r|$ is ampere per meter, identical to that of the $B$-field.

The magnetization $B$ field of a region points in the direction of the average magnetic dipole moment in that region. Magnetization field lines, therefore, begin near the magnetic south pole and ends near the magnetic north pole. (Magnetization does not exist outside the magnet.)

In the Amperian loop model, the magnetization is due to combining many tiny Amperian loops to form a resultant current called bound current. This bound current, then, is the source of the magnetic $B$ field due to the magnet. Given the definition of the magnetic dipole, the magnetization field follows a similar law to that of Ampere's law: $$\oint \mathbf{M} \cdot \mathrm{d}\boldsymbol{\ell} = I_\mathrm{b},$$ where the integral is a line integral over any closed loop and $B$ is the bound current enclosed by that closed loop.

In the magnetic pole model, magnetization begins at and ends at magnetic poles. If a given region, therefore, has a net positive "magnetic pole strength" (corresponding to a north pole) then it has more magnetization field lines entering it than leaving it. Mathematically this is equivalent to: $$\oint_S \mu_0 \mathbf{M} \cdot \mathrm{d}\mathbf{A} = - q_\mathrm{M},$$ where the integral is a closed surface integral over the closed surface $F$ and $q$ is the "magnetic charge" (in units of magnetic flux) enclosed by $v$. (A closed surface completely surrounds a region with no holes to let any field lines escape.) The negative sign occurs because the magnetization field moves from south to north.

H-field and magnetic materials

In SI units, the H-field is related to the B-field by $$\mathbf{H}\ \equiv \ \frac{\mathbf{B}}{\mu_0} - \mathbf{M}.$$

In terms of the H-field, Ampere's law is $$\oint \mathbf{H} \cdot \mathrm{d}\boldsymbol{\ell} = \oint \left(\frac{\mathbf{B}}{\mu_0} - \mathbf{M}\right) \cdot \mathrm{d}\boldsymbol{\ell} = I_\mathrm{tot} - I_\mathrm{b} = I_\mathrm{f},$$ where $B$ represents the 'free current' enclosed by the loop so that the line integral of $ℓ$ does not depend at all on the bound currents.

For the differential equivalent of this equation see Maxwell's equations. Ampere's law leads to the boundary condition $$\left(\mathbf{H_1^\parallel} - \mathbf{H_2^\parallel}\right) = \mathbf{K}_\mathrm{f} \times \hat{\mathbf{n}},$$ where $A$ is the surface free current density and the unit normal $$\hat{\mathbf{n}}$$ points in the direction from medium 2 to medium 1.

Similarly, a surface integral of $q$ over any closed surface is independent of the free currents and picks out the "magnetic charges" within that closed surface: $$\oint_S \mu_0 \mathbf{H} \cdot \mathrm{d}\mathbf{A} = \oint_S (\mathbf{B} - \mu_0 \mathbf{M}) \cdot \mathrm{d}\mathbf{A} = 0 - (-q_\mathrm{M}) = q_\mathrm{M},$$

which does not depend on the free currents.

The $i$-field, therefore, can be separated into two independent parts: $$\mathbf{H} = \mathbf{H}_0 + \mathbf{H}_\mathrm{d}, $$

where $B$ is the applied magnetic field due only to the free currents and $θ$ is the demagnetizing field due only to the bound currents.

The magnetic $q$-field, therefore, re-factors the bound current in terms of "magnetic charges". The $N$ field lines loop only around "free current" and, unlike the magnetic $i = nqvA$ field, begins and ends near magnetic poles as well.

Magnetism
Most materials respond to an applied $H$-field by producing their own magnetization $M$ and therefore their own $m$-fields. Typically, the response is weak and exists only when the magnetic field is applied. The term magnetism describes how materials respond on the microscopic level to an applied magnetic field and is used to categorize the magnetic phase of a material. Materials are divided into groups based upon their magnetic behavior:
 * Diamagnetic materials produce a magnetization that opposes the magnetic field.
 * Paramagnetic materials produce a magnetization in the same direction as the applied magnetic field.
 * Ferromagnetic materials and the closely related ferrimagnetic materials and antiferromagnetic materials can have a magnetization independent of an applied B-field with a complex relationship between the two fields.
 * Superconductors (and ferromagnetic superconductors) are materials that are characterized by perfect conductivity below a critical temperature and magnetic field. They also are highly magnetic and can be perfect diamagnets below a lower critical magnetic field. Superconductors often have a broad range of temperatures and magnetic fields (the so-named mixed state) under which they exhibit a complex hysteretic dependence of $M$ on $H$.

In the case of paramagnetism and diamagnetism, the magnetization $M$ is often proportional to the applied magnetic field such that: $$\mathbf{B} = \mu \mathbf{H},$$ where $B$ is a material dependent parameter called the permeability. In some cases the permeability may be a second rank tensor so that $I_{b}$ may not point in the same direction as $S$. These relations between $q_{M}$ and $S$ are examples of constitutive equations. However, superconductors and ferromagnets have a more complex $B$-to-$H$ relation; see magnetic hysteresis.

Stored energy
Energy is needed to generate a magnetic field both to work against the electric field that a changing magnetic field creates and to change the magnetization of any material within the magnetic field. For non-dispersive materials, this same energy is released when the magnetic field is destroyed so that the energy can be modeled as being stored in the magnetic field.

For linear, non-dispersive, materials (such that $M$ where $I_{f}$ is frequency-independent), the energy density is:

$$ u = \frac{\mathbf{B} \cdot \mathbf{H}}{2}= \frac{\mathbf{B} \cdot \mathbf{B}}{2\mu} = \frac{\mu\mathbf{H} \cdot \mathbf{H}}{2}.$$

If there are no magnetic materials around then $H$ can be replaced by $K_{f}$. The above equation cannot be used for nonlinear materials, though; a more general expression given below must be used.

In general, the incremental amount of work per unit volume $H$ needed to cause a small change of magnetic field $H$ is:

$$\delta W = \mathbf{H}\cdot\delta\mathbf{B}.$$

Once the relationship between $H_{0}$ and $H_{d}$ is known this equation is used to determine the work needed to reach a given magnetic state. For hysteretic materials such as ferromagnets and superconductors, the work needed also depends on how the magnetic field is created. For linear non-dispersive materials, though, the general equation leads directly to the simpler energy density equation given above.

Appearance in Maxwell's equations
Like all vector fields, a magnetic field has two important mathematical properties that relates it to its sources. (For $H$ the sources are currents and changing electric fields.) These two properties, along with the two corresponding properties of the electric field, make up Maxwell's Equations. Maxwell's Equations together with the Lorentz force law form a complete description of classical electrodynamics including both electricity and magnetism.

The first property is the divergence of a vector field $H$, $B$, which represents how $B$ "flows" outward from a given point. As discussed above, a $M$-field line never starts or ends at a point but instead forms a complete loop. This is mathematically equivalent to saying that the divergence of $B$ is zero. (Such vector fields are called solenoidal vector fields.) This property is called Gauss's law for magnetism and is equivalent to the statement that there are no isolated magnetic poles or magnetic monopoles.

The second mathematical property is called the curl, such that $M$ represents how $B$ curls or "circulates" around a given point. The result of the curl is called a "circulation source". The equations for the curl of $M$ and of $μ$ are called the Ampère–Maxwell equation and Faraday's law respectively.

Gauss' law for magnetism
One important property of the $H$-field produced this way is that magnetic $B$-field lines neither start nor end (mathematically, $B$ is a solenoidal vector field); a field line may only extend to infinity, or wrap around to form a closed curve, or follow a never-ending (possibly chaotic) path. Magnetic field lines exit a magnet near its north pole and enter near its south pole, but inside the magnet $H$-field lines continue through the magnet from the south pole back to the north. If a $B$-field line enters a magnet somewhere it has to leave somewhere else; it is not allowed to have an end point.

More formally, since all the magnetic field lines that enter any given region must also leave that region, subtracting the "number" of field lines that enter the region from the number that exit gives identically zero. Mathematically this is equivalent to Gauss's law for magnetism: $$\oint_S \mathbf{B} \cdot \mathrm{d}\mathbf{A} = 0$$ where the integral is a surface integral over the closed surface $H$ (a closed surface is one that completely surrounds a region with no holes to let any field lines escape). Since $B = μH$ points outward, the dot product in the integral is positive for $μ$-field pointing out and negative for $μ$-field pointing in.

Faraday's Law
A changing magnetic field, such as a magnet moving through a conducting coil, generates an electric field (and therefore tends to drive a current in such a coil). This is known as Faraday's law and forms the basis of many electrical generators and electric motors. Mathematically, Faraday's law is: $$\mathcal{E} = - \frac{\mathrm{d}\Phi}{\mathrm{d}t}$$

where $$\mathcal{E}$$ is the electromotive force (or EMF, the voltage generated around a closed loop) and $μ_{0}$ is the magnetic flux—the product of the area times the magnetic field normal to that area. (This definition of magnetic flux is why $δW$ is often referred to as magnetic flux density.) The negative sign represents the fact that any current generated by a changing magnetic field in a coil produces a magnetic field that opposes the change in the magnetic field that induced it. This phenomenon is known as Lenz's law. This integral formulation of Faraday's law can be converted into a differential form, which applies under slightly different conditions.

$$ \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}} {\partial t} $$

Ampère's Law and Maxwell's correction
Similar to the way that a changing magnetic field generates an electric field, a changing electric field generates a magnetic field. This fact is known as Maxwell's correction to Ampère's law and is applied as an additive term to Ampere's law as given above. This additional term is proportional to the time rate of change of the electric flux and is similar to Faraday's law above but with a different and positive constant out front. (The electric flux through an area is proportional to the area times the perpendicular part of the electric field.)

The full law including the correction term is known as the Maxwell–Ampère equation. It is not commonly given in integral form because the effect is so small that it can typically be ignored in most cases where the integral form is used.

The Maxwell term is critically important in the creation and propagation of electromagnetic waves. Maxwell's correction to Ampère's Law together with Faraday's law of induction describes how mutually changing electric and magnetic fields interact to sustain each other and thus to form electromagnetic waves, such as light: a changing electric field generates a changing magnetic field, which generates a changing electric field again. These, though, are usually described using the differential form of this equation given below.

$$ \nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}} {\partial t} $$

where $δB$ is the complete microscopic current density, and $ε0$ is the vacuum permittivity.

As discussed above, materials respond to an applied electric $H$ field and an applied magnetic $B$ field by producing their own internal "bound" charge and current distributions that contribute to $B$ and $A$ but are difficult to calculate. To circumvent this problem, $∇ · A$ and $A$ fields are used to re-factor Maxwell's equations in terms of the free current density $B$:

$$\nabla \times \mathbf{H} = \mathbf{J}_\mathrm{f} + \frac{\partial \mathbf{D}} {\partial t}$$

These equations are not any more general than the original equations (if the "bound" charges and currents in the material are known). They also must be supplemented by the relationship between $B$ and $∇ × A$ as well as that between $A$ and $B$. On the other hand, for simple relationships between these quantities this form of Maxwell's equations can circumvent the need to calculate the bound charges and currents.

As different aspects of the same phenomenon
According to the special theory of relativity, the partition of the electromagnetic force into separate electric and magnetic components is not fundamental, but varies with the observational frame of reference: An electric force perceived by one observer may be perceived by another (in a different frame of reference) as a magnetic force, or a mixture of electric and magnetic forces.

The magnetic field existing as electric field in other frames can be shown by consistency of equations obtained from Lorentz transformation of four force from Coulomb's Law in particle's rest frame with Maxwell's laws considering definition of fields from Lorentz force and for non accelerating condition. The form of magnetic field hence obtained by Lorentz transformation of four-force from the form of Coulomb's law in source's initial frame is given by: $$\mathbf{B} = \frac q {4 \pi \varepsilon_0 r^3}  \frac {1- \beta^2} {(1- \beta^2 \sin^2 \theta)^{3/2}} \frac{\mathbf{v} \times \mathbf{r}}{c^2} = \frac{\mathbf{v} \times \mathbf{E}}{c^2}$$where $$q$$ is the charge of the point source, $$\varepsilon_0$$ is the vacuum permittivity, $$\mathbf{r}$$ is the position vector from the point source to the point in space, $$\mathbf{v}$$ is the velocity vector of the charged particle, $$\beta$$ is the ratio of speed of the charged particle divided by the speed of light and $$\theta$$ is the angle between $$\mathbf{r}$$ and $$\mathbf{v}$$. This form of magnetic field can be shown to satisfy maxwell's laws within the constraint of particle being non accelerating. The above reduces to Biot-Savart law for non relativistic stream of current ($$\beta\ll 1$$).

Formally, special relativity combines the electric and magnetic fields into a rank-2 tensor, called the electromagnetic tensor. Changing reference frames mixes these components. This is analogous to the way that special relativity mixes space and time into spacetime, and mass, momentum, and energy into four-momentum. Similarly, the energy stored in a magnetic field is mixed with the energy stored in an electric field in the electromagnetic stress–energy tensor.

Magnetic vector potential
In advanced topics such as quantum mechanics and relativity it is often easier to work with a potential formulation of electrodynamics rather than in terms of the electric and magnetic fields. In this representation, the magnetic vector potential $E$, and the electric scalar potential $B$, are defined using gauge fixing such that: $$\begin{align} \mathbf{B} &= \nabla \times \mathbf{A}, \\ \mathbf{E} &= -\nabla \varphi - \frac{ \partial \mathbf{A} }{ \partial t }. \end{align}$$

The vector potential, $B$ given by this form may be interpreted as a generalized potential momentum per unit charge just as $B$ is interpreted as a generalized potential energy per unit charge. There are multiple choices one can make for the potential fields that satisfy the above condition. However, the choice of potentials is represented by its respective gauge condition.

Maxwell's equations when expressed in terms of the potentials in Lorenz gauge can be cast into a form that agrees with special relativity. In relativity, $B$ together with $B$ forms a four-potential regardless of the gauge condition, analogous to the four-momentum that combines the momentum and energy of a particle. Using the four potential instead of the electromagnetic tensor has the advantage of being much simpler—and it can be easily modified to work with quantum mechanics.

Propagation of Electric and Magnetic fields
Special theory of relativity imposes the condition for events related by cause and effect to be time-like separated, that is that causal efficacy propagates no faster than light. Maxwell's equations for electromagnetism are found to be in favor of this as electric and magnetic disturbances are found to travel at the speed of light in space. Electric and magnetic fields from classical electrodynamics obey the principle of locality in physics and are expressed in terms of retarded time or the time at which the cause of a measured field originated given that the influence of field travelled at speed of light. The retarded time for a point particle is given as solution of:

$$t_r=\mathbf{t}-\frac{|\mathbf{r} - \mathbf{r}_s(t_r)|}{c}$$

where ${t_r}$ is retarded time or the time at which the source's contribution of the field originated, ${r}_s(t)$  is the position vector of the particle as function of time, $\mathbf{r}$  is the point in space, $\mathbf{t}$  is the time at which fields are measured and $c$  is the speed of light. The equation subtracts the time taken for light to travel from particle to the point in space from the time of measurement to find time of origin of the fields. The uniqueness of solution for ${t_r}$ for given $$\mathbf{t}$$, $$\mathbf{r}$$ and $$r_s(t)$$ is valid for charged particles moving slower than speed of light.

Magnetic field of arbitrary moving point charge
The solution of maxwell's equations for electric and magnetic field of a point charge is expressed in terms of retarded time or the time at which the particle in the past causes the field at the point, given that the influence travels across space at the speed of light.

Any arbitrary motion of point charge causes electric and magnetic fields found by solving maxwell's equations using green's function for retarded potentials and hence finding the fields to be as follows:

$$\mathbf{A}(\mathbf{r},\mathbf{t}) = \frac{\mu_0c}{4 \pi} \left(\frac{q \boldsymbol{\beta}_s}{(1 - \mathbf{n}_s \cdot \boldsymbol{\beta}_s)|\mathbf{r} - \mathbf{r}_s|} \right)_{t=t_r} = \frac{\boldsymbol{\beta}_s(t_r)}{c} \varphi(\mathbf{r}, \mathbf{t})$$

$$\mathbf{B}(\mathbf{r}, \mathbf{t}) = \frac{\mu_0}{4 \pi} \left(\frac{q c(\boldsymbol{\beta}_s \times \mathbf{n}_s)}{\gamma^2 (1-\mathbf{n}_s \cdot \boldsymbol{\beta}_s)^3 |\mathbf{r} - \mathbf{r}_s|^2} + \frac{q \mathbf{n}_s \times \Big(\mathbf{n}_s \times \big((\mathbf{n}_s - \boldsymbol{\beta}_s) \times \dot{\boldsymbol{\beta}_s}\big) \Big)}{(1 - \mathbf{n}_s \cdot \boldsymbol{\beta}_s)^3 |\mathbf{r} - \mathbf{r}_s|} \right)_{t=t_r} = \frac{\mathbf{n}_s(t_r)}{c} \times \mathbf{E}(\mathbf{r}, \mathbf{t})$$

where $\varphi(\mathbf{r}, \mathbf{t})$ and $\mathbf{A}(\mathbf{r},\mathbf{t})$ are electric scalar potential and magnetic vector potential in Lorentz gauge, $$q$$ is the charge of the point source, ${n}_s(\mathbf{r},t)$  is a unit vector pointing from charged particle to the point in space, $ \boldsymbol{\beta}_s(t)$  is the velocity of the particle divided by the speed of light and $\gamma (t)$  is the corresponding Lorentz factor. Hence by the principle of superposition, the fields of a system of charges also obey principle of locality.

Quantum electrodynamics
The classical electromagnetic field incorporated into quantum mechanics forms what is known as the semi-classical theory of radiation. However, it is not able to make experimentally observed predictions such as spontaneous emission process or Lamb shift implying the need for quantization of fields. In modern physics, the electromagnetic field is understood to be not a classical field, but rather a quantum field; it is represented not as a vector of three numbers at each point, but as a vector of three quantum operators at each point. The most accurate modern description of the electromagnetic interaction (and much else) is quantum electrodynamics (QED), which is incorporated into a more complete theory known as the Standard Model of particle physics.

In QED, the magnitude of the electromagnetic interactions between charged particles (and their antiparticles) is computed using perturbation theory. These rather complex formulas produce a remarkable pictorial representation as Feynman diagrams in which virtual photons are exchanged.

Predictions of QED agree with experiments to an extremely high degree of accuracy: currently about 10−12 (and limited by experimental errors); for details see precision tests of QED. This makes QED one of the most accurate physical theories constructed thus far.

All equations in this article are in the classical approximation, which is less accurate than the quantum description mentioned here. However, under most everyday circumstances, the difference between the two theories is negligible.

Earth's magnetic field

The Earth's magnetic field is produced by convection of a liquid iron alloy in the outer core. In a dynamo process, the movements drive a feedback process in which electric currents create electric and magnetic fields that in turn act on the currents.

The field at the surface of the Earth is approximately the same as if a giant bar magnet were positioned at the center of the Earth and tilted at an angle of about 11° off the rotational axis of the Earth (see the figure). The north pole of a magnetic compass needle points roughly north, toward the North Magnetic Pole. However, because a magnetic pole is attracted to its opposite, the North Magnetic Pole is actually the south pole of the geomagnetic field. This confusion in terminology arises because the pole of a magnet is defined by the geographical direction it points.

Earth's magnetic field is not constant—the strength of the field and the location of its poles vary. Moreover, the poles periodically reverse their orientation in a process called geomagnetic reversal. The most recent reversal occurred 780,000 years ago.

Rotating magnetic fields
The rotating magnetic field is a key principle in the operation of alternating-current motors. A permanent magnet in such a field rotates so as to maintain its alignment with the external field.

Magnetic torque is used to drive electric motors. In one simple motor design, a magnet is fixed to a freely rotating shaft and subjected to a magnetic field from an array of electromagnets. By continuously switching the electric current through each of the electromagnets, thereby flipping the polarity of their magnetic fields, like poles are kept next to the rotor; the resultant torque is transferred to the shaft.

A rotating magnetic field can be constructed using two orthogonal coils with 90 degrees phase difference in their AC currents. However, in practice such a system would be supplied through a three-wire arrangement with unequal currents.

This inequality would cause serious problems in standardization of the conductor size and so, to overcome it, three-phase systems are used where the three currents are equal in magnitude and have 120 degrees phase difference. Three similar coils having mutual geometrical angles of 120 degrees create the rotating magnetic field in this case. The ability of the three-phase system to create a rotating field, utilized in electric motors, is one of the main reasons why three-phase systems dominate the world's electrical power supply systems.

Synchronous motors use DC-voltage-fed rotor windings, which lets the excitation of the machine be controlled—and induction motors use short-circuited rotors (instead of a magnet) following the rotating magnetic field of a multicoiled stator. The short-circuited turns of the rotor develop eddy currents in the rotating field of the stator, and these currents in turn move the rotor by the Lorentz force.

The Italian physicist Galileo Ferraris and the Serbian-American electrical engineer Nikola Tesla independently researched the use of rotating magnetic fields in electric motors. In 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin and Tesla gained for his work.

Hall effect
The charge carriers of a current-carrying conductor placed in a transverse magnetic field experience a sideways Lorentz force; this results in a charge separation in a direction perpendicular to the current and to the magnetic field. The resultant voltage in that direction is proportional to the applied magnetic field. This is known as the Hall effect.

The Hall effect is often used to measure the magnitude of a magnetic field. It is used as well to find the sign of the dominant charge carriers in materials such as semiconductors (negative electrons or positive holes).

Magnetic circuits
An important use of $S$ is in magnetic circuits where $dA$ inside a linear material. Here, $B$ is the magnetic permeability of the material. This result is similar in form to Ohm's law $B$, where $Φ$ is the current density, $B$ is the conductance and $E$ is the electric field. Extending this analogy, the counterpart to the macroscopic Ohm's law ($∂Σ(t)$) is:

$$\Phi = \frac F R_\mathrm{m},$$

where $\Phi = \int \mathbf{B}\cdot \mathrm{d}\mathbf{A}$ is the magnetic flux in the circuit, $F = \int \mathbf{H}\cdot \mathrm{d}\boldsymbol{\ell}$  is the magnetomotive force applied to the circuit, and $Σ(t)$ is the reluctance of the circuit. Here the reluctance $dA$ is a quantity similar in nature to resistance for the flux. Using this analogy it is straightforward to calculate the magnetic flux of complicated magnetic field geometries, by using all the available techniques of circuit theory.

Largest magnetic fields
, the largest magnetic field produced over a macroscopic volume outside a lab setting is 2.8 kT (VNIIEF in Sarov, Russia, 1998). As of October 2018, the largest magnetic field produced in a laboratory over a macroscopic volume was 1.2 kT by researchers at the University of Tokyo in 2018. The largest magnetic fields produced in a laboratory occur in particle accelerators, such as RHIC, inside the collisions of heavy ions, where microscopic fields reach 1014 T. Magnetars have the strongest known magnetic fields of any naturally occurring object, ranging from 0.1 to 100 GT (108 to 1011 T).

Common formulæ
Additional magnetic field values can be found through the magnetic field of a finite beam, for example, that the magnetic field of an arc of angle $$\theta$$ and radius $$R$$ at the center is $$B=\frac{\mu_o\theta I}{4\pi R}$$, or that the magnetic field at the center of a N-sided regular polygon of side $$a$$ is $$B=\frac{\mu_0NI}{\pi a}\sin\left(\frac \pi N\right)\tan\left(\frac \pi N\right)$$, both outside of the plane with proper directions as inferred by right hand thumb rule.

Early developments
While magnets and some properties of magnetism were known to ancient societies, the research of magnetic fields began in 1269 when French scholar Petrus Peregrinus de Maricourt mapped out the magnetic field on the surface of a spherical magnet using iron needles. Noting the resulting field lines crossed at two points he named those points "poles" in analogy to Earth's poles. He also articulated the principle that magnets always have both a north and south pole, no matter how finely one slices them.

Almost three centuries later, William Gilbert of Colchester replicated Petrus Peregrinus' work and was the first to state explicitly that Earth is a magnet. Published in 1600, Gilbert's work, De Magnete, helped to establish magnetism as a science.

Mathematical development

In 1750, John Michell stated that magnetic poles attract and repel in accordance with an inverse square law Charles-Augustin de Coulomb experimentally verified this in 1785 and stated explicitly that north and south poles cannot be separated. Building on this force between poles, Siméon Denis Poisson (1781–1840) created the first successful model of the magnetic field, which he presented in 1824. In this model, a magnetic $Σ(t)$-field is produced by magnetic poles and magnetism is due to small pairs of north–south magnetic poles.

Three discoveries in 1820 challenged this foundation of magnetism. Hans Christian Ørsted demonstrated that a current-carrying wire is surrounded by a circular magnetic field. Then André-Marie Ampère showed that parallel wires with currents attract one another if the currents are in the same direction and repel if they are in opposite directions. Finally, Jean-Baptiste Biot and Félix Savart announced empirical results about the forces that a current-carrying long, straight wire exerted on a small magnet, determining the forces were inversely proportional to the perpendicular distance from the wire to the magnet. Laplace later deduced a law of force based on the differential action of a differential section of the wire, which became known as the Biot–Savart law, as Laplace did not publish his findings.

Extending these experiments, Ampère published his own successful model of magnetism in 1825. In it, he showed the equivalence of electrical currents to magnets and proposed that magnetism is due to perpetually flowing loops of current instead of the dipoles of magnetic charge in Poisson's model. Further, Ampère derived both Ampère's force law describing the force between two currents and Ampère's law, which, like the Biot–Savart law, correctly described the magnetic field generated by a steady current. Also in this work, Ampère introduced the term electrodynamics to describe the relationship between electricity and magnetism.

In 1831, Michael Faraday discovered electromagnetic induction when he found that a changing magnetic field generates an encircling electric field, formulating what is now known as Faraday's law of induction. Later, Franz Ernst Neumann proved that, for a moving conductor in a magnetic field, induction is a consequence of Ampère's force law. In the process, he introduced the magnetic vector potential, which was later shown to be equivalent to the underlying mechanism proposed by Faraday.

In 1850, Lord Kelvin, then known as William Thomson, distinguished between two magnetic fields now denoted $dℓ$ and $J$. The former applied to Poisson's model and the latter to Ampère's model and induction. Further, he derived how $E$ and $B$ relate to each other and coined the term permeability.

Between 1861 and 1865, James Clerk Maxwell developed and published Maxwell's equations, which explained and united all of classical electricity and magnetism. The first set of these equations was published in a paper entitled On Physical Lines of Force in 1861. These equations were valid but incomplete. Maxwell completed his set of equations in his later 1865 paper A Dynamical Theory of the Electromagnetic Field and demonstrated the fact that light is an electromagnetic wave. Heinrich Hertz published papers in 1887 and 1888 experimentally confirming this fact.

Modern developments
In 1887, Tesla developed an induction motor that ran on alternating current. The motor used polyphase current, which generated a rotating magnetic field to turn the motor (a principle that Tesla claimed to have conceived in 1882). Tesla received a patent for his electric motor in May 1888. In 1885, Galileo Ferraris independently researched rotating magnetic fields and subsequently published his research in a paper to the Royal Academy of Sciences in Turin, just two months before Tesla was awarded his patent, in March 1888.

The twentieth century showed that classical electrodynamics is already consistent with special relativity, and extended classical electrodynamics to work with quantum mechanics. Albert Einstein, in his paper of 1905 that established relativity, showed that both the electric and magnetic fields are part of the same phenomena viewed from different reference frames. Finally, the emergent field of quantum mechanics was merged with electrodynamics to form quantum electrodynamics, which first formalized the notion that electromagnetic field energy is quantized in the form of photons.

General

 * Magnetohydrodynamics – the study of the dynamics of electrically conducting fluids
 * Magnetic hysteresis – application to ferromagnetism
 * Magnetic nanoparticles – extremely small magnetic particles that are tens of atoms wide
 * Magnetic reconnection – an effect that causes solar flares and auroras
 * Magnetic scalar potential
 * SI electromagnetism units – common units used in electromagnetism
 * Orders of magnitude (magnetic field) – list of magnetic field sources and measurement devices from smallest magnetic fields to largest detected
 * Upward continuation
 * Moses Effect

Mathematics

 * Magnetic helicity – extent to which a magnetic field wraps around itself

Applications

 * Dynamo theory – a proposed mechanism for the creation of the Earth's magnetic field
 * Helmholtz coil – a device for producing a region of nearly uniform magnetic field
 * Magnetic field viewing film – Film used to view the magnetic field of an area
 * Magnetic pistol – a device on torpedoes or naval mines that detect the magnetic field of their target
 * Maxwell coil – a device for producing a large volume of an almost constant magnetic field
 * Stellar magnetic field – a discussion of the magnetic field of stars
 * Teltron tube – device used to display an electron beam and demonstrates effect of electric and magnetic fields on moving charges

title: Magnetic field


text:
Nansen passport

Nansen passports, originally and officially stateless persons passports, were internationally recognized refugee travel documents from 1922 to 1938, first issued by the League of Nations's Office of the High Commissioner for Refugees to stateless refugees. They quickly became known as "Nansen passports" for their promoter, the Norwegian statesman and polar explorer Fridtjof Nansen.

History
The end of World War I saw significant turmoil, leading to a refugee crisis. Numerous governments were toppled, and national borders were redrawn, often along generally ethnic lines. Civil war broke out in some countries. Many people left their homes because of war or persecution or fear thereof. The upheaval resulted in many people being without passports, or even nations to issue them, which prevented much international travel, often trapping refugees.

The precipitating event for the Nansen passport was the 1921 announcement by the new government of the Soviet Union revoking the citizenship of Russians living abroad, including some 800,000 refugees from the Russian Civil War. The first Nansen passports were issued following an international agreement reached at the Intergovernmental Conference on Identity Certificates for Russian Refugees, convened by Fridtjof Nansen in Geneva from July 3, 1922, to July 5, 1922, in his role as High Commissioner for Refugees for the League of Nations. By 1942, they were honoured by governments in 52 countries.

In 1924, the Nansen arrangement was broadened to also include Armenian, and in 1928 to Assyrian, Assyro-Chaldean, Bulgarian and Turkish refugees. Approximately 450,000 Nansen passports were provided to stateless people and refugees who needed travel documents, but could not obtain one from a national authority.

Following Nansen's death in 1930, the passport was handled by the Nansen International Office for Refugees within the League of Nations. At that point the passport no longer included a reference to the 1922 conference, but were issued in the name of the League. The office was closed in 1938; passports were thereafter issued by a new agency, the Office of the High Commissioner for Refugees under the Protection of the League of Nations in London.

Legacy
The Nansen International Office for Refugees was awarded the 1938 Nobel Peace Prize for its efforts to establish the Nansen passports.

While Nansen passports are no longer issued, existing national and supranational authorities, including the United Nations, issue travel documents for stateless people and refugees, including certificates of identity (or "alien's passports") and refugee travel documents.

In a 2024 essay, the famous chess grandmaster and Russian dissident Garry Kasparov called for the international community to establish a "Free Russia passport". In his words, this passport should be issued to Russian emigrants provided they sign a declaration "which sets out the key principles for a Ukrainian victory and a Russia without Putin". In the essay, he compared his idea to the legacy of the Nansen passport, although he stressed the comparison is imperfect.

Notable bearers

 * Robert Capa
 * Sergiu Celibidache
 * Princess Vera Constantinovna of Russia
 * Marc Chagall
 * Françoise Frenkel
 * Alexander Galich
 * Zuzanna Ginczanka
 * Alexander Grothendieck
 * G. I. Gurdjieff
 * Anatol Heintz
 * Ze'ev Jabotinsky
 * Vladimir Nabokov
 * Aristotle Onassis
 * Krikor Pambuccian
 * Anna Pavlova
 * Grand Duchess Maria Pavlovna of Russia (1890–1958)
 * St. Grigol Peradze
 * Jadwiga Piłsudska
 * Sergey Rakhmaninov
 * Dimitri Riabouchinsky
 * Rabbi Menachem Mendel Schneerson
 * Otto Skorzeny
 * Victor Starffin
 * Igor Stravinsky
 * Dries Riphagen
 * King Alfonso XIII of Spain

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Nansen passport


text:
Nuraghe

The nuraghe, or nurhag, is the main type of ancient megalithic edifice found in Sardinia, Italy, developed during the Nuragic Age between 1900 and 730 BC. Today it has come to be the symbol of Sardinia and its distinctive culture known as the Nuragic civilization. More than 7,000 nuraghes have been found, though archeologists believe that originally there were more than 10,000.

Etymology
Natively, the structure is called a nurhage (, ; plural: Logudorese Sardinian nuraghes, Campidanese Sardinian nuraxis, Italian nuraghi). According to the Oxford English Dictionary the etymology is "uncertain and disputed": "The word is perhaps related to the Sardinian place names Nurra, Nurri, Nurru, and to Sardinian nurra 'heap of stones, cavity in earth' (although these senses are difficult to reconcile). A connection with the Semitic base of Arabic nūr 'light, fire, etc.' is now generally rejected." The Latin word murus ('wall') may be related to it, being a result of the derivation: murus–*muraghe–nuraghe. However, such theories are debated.

An etymological theory suggests a Proto-Basque origin by the term *nur (stone) with the common -ak plural ending; the Paleo-Sardinian suffix -ake is also found in some Indo-European languages such as Latin and Greek. Another possible explanation is that the term nuraghe came from the name of the Iberian mythological hero Norax, and the root *nur would be an adaptation of the Indo-European root *nor.

General layout
The typical nuraghe is situated in areas where previous prehistoric Sardinian cultures had been distributed, that, is not far from alluvial plains (though few nuraghes appear in plains currently as they were destroyed by human activities such as agriculture, dams and road building) and has the outer shape of a truncated conical tower, thus resembling a medieval tower, with a tholos-like vault inside.

The structure's walls consist of three components: an outer layer (tilted inwards and made of many layers of stones whose size diminishes with increasing height: mostly, lower layers consist of rubble masonry, while upper layers tend to be of ashlar masonry); an inner layer, made of smaller stones (to form a corbelled dome of the bullet-shaped tholos type, and where ashlar masonry is used more frequently); and an intermediate layer of very small pieces and dirt, which makes the whole construction very sturdy: it stands only by virtue of the weight of its stones, which may each amount to several tons. Some nuraghes are about 20 meters (60 ft) in height, the tallest one known, Nuraghe Arrubiu, reached a height of 25–30 meters.

The entrance leads into a corridor, on whose sides are often open niches, that lead to the round chamber. A spiral stone stair, leading to upper floors (if present) and/or to a terrace, was built within the thick walls and it was illuminated by embrasures. The Nuragic towers might have as much as three corbel chambers one on top of the other. In complex nuraghes corridors were often present, sometimes corbelled, such as at Santu Antine, in which the corbelled arch corridors were superimposed on two levels, and reached a length of 27 meters.

Today fewer than 7,000 nuraghes remain standing; their number was originally larger. Nuraghes are most prevalent in the northwest and south-central parts of the island.

Function
There is no consensus on the function of the nuraghes: they could have been rulers' residences, military strongholds, meeting halls, religious temples, ordinary dwellings or a combination of any of these things. Some of the nuraghes are, however, located in strategic places – such as hills – from which important passages could be easily controlled. They might have been something between a "status symbol" and a "passive defence" building, meant to be a deterrent for possible enemies.

Nuraghes could also have been the "national" symbol of the Nuragic peoples. Small-scale models of nuraghe have often been excavated at religious sites (e.g. in the "maze" temple at the Su Romanzesu site near Bitti in central Sardinia). Nuraghes may have just connoted wealth or power, or they may have been an indication that a site had its owners. Recent unconfirmed theories tend to suggest that Sardinian towns were independent entities (such as the city-states, although in a geographical sense they were not cities) that formed federations and that the building of these monuments might have depended on agreed-on distributions of territory among federated unities.

They were not tombs of princes and their families, as was mistakenly believed by taking as an argument the discovery of human remains there, but of strata of a later age than the Nuragic, that is, Carthaginian and Roman. Neither were they monumental temples, which today are known to be of different shapes and types, even for prehistoric island times, likewise burials (domus de janas or "fairy houses"; tumbas de sos gigantes or "tombs of the giants").

In 2002, Juan Belmonte and Mauro Zedda measured the entrance orientations (declinations and azimuths) of 272 simple nuraghes and of the central towers of 180 complex ones. The data revealed clear peaks corresponding to orientations pointing to the sunrise at winter solstice and to the Moon at its southernmost rising position. These alignments remained constant throughout the history of nuraghe. The most common declinations revealed were of around −43° for the earlier nuraghes, shifting to just −45½° for the later. Zedda has suggested that the target is likely a star, quite possibly Alpha Centauri.

Protonuraghe
Protonuraghes are considered to be the most archaic type; they differ somewhat from the "classical" (tholos-vaulted) nuraghes in their stockier look. Protonuraghes generally follow an irregular plan and lack the large circular room present in presumed later forms; instead, they are laid out along one or more corridors or long rooms. Although lacking the central circular room, they are sometimes similar in size to later nuraghes.

Mixed nuraghe
This type is distinguished by the restorations made in later times, supposedly because of a change to the protonuraghes design, or for other needs.

Single-tower nuraghe
This is considered to be the predominant type of nuraghe, and it represents the most diffused typology. The single tower, of a truncated conical shape, contains one or more superimposed chambers, covered by a tholos-shaped chamber. The access, generally located at the ground level, leads into a passageway that leads, in the front, into the central chamber and in one side (usually the left) in the helical staircase, built inside the wall mass, that lead to the terrace or to the upper-floor chamber.

In addition to the usual circular rooms, in their inside can be found other smaller environments such as niches.

A "tancadu" nuraghe
A "tancadu" nuraghe (Sardinian term for courtyard) represents the evolution of the single-tower nuraghe; another circular building was later added to the main tower, with two enclosing curtain walls connecting the two. A courtyard was present within the structure, sometimes provided with a well.

Polylobed nuraghe
Also called Nuragic royal palaces, the polylobed nuraghes are the least frequent typology. Very elaborate and often designed in a unified manner, they look like veritable fortresses with several towers linked by high ramparts, whose function was to offer more useful space and perhaps to reinforce the central tower. These "Megalithic castles" were surrounded by additional walls, sometimes also provided with towers (the so-called bulwark).

Notable nuraghes
Nuraghes are inscribed on the UNESCO World Heritage Site list. Su Nuraxi di Barumini, in the south of the island, has been chosen to represent all the nuragic patrimony, but one of the highest and most complex nuraghes is the Nuraghe Santu Antine near the village of Torralba, in northern Sardinia. Other famous nuraghes are near Alghero (Nuraghe Palmavera), Macomer, Abbasanta (see Losa), Orroli (Nuraghe Arrubiu), Gonnesa (Nuraghe Seruci) and Villanovaforru (Nuraghe Genna Maria).

Date and cultural significance
The nuraghes were built between the middle of the Bronze Age (18th–15th centuries BCE) and the Late Bronze Age. The claim that the El-Ahwat structures from Israel might be related has been contested; those are dated to either the 12th or the 11th century BCE. The only buildings widely accepted as being related to nuraghes are the torri (plural of torre) from southern Corsica and the talaiots from Menorca and Majorca.

According to Massimo Pallottino, an Italian archaeologist specialized in Etruscology, the architecture produced by the Nuragic civilization was the most advanced of any in the western Mediterranean during this epoch, including those in the regions of Magna Graecia. Of the 7,000 extant nuraghes, only a few have been scientifically excavated.

title: Nuraghe


text:
List of archaeological and artistic sites of Sardinia

This is a list of archaeological and artistic sites of Sardinia, Italy:
 * Acquafredda near Siliqua, castle, 13th century
 * Aiodda near Nurallao-Nuragus, Giants' Tomb
 * Albucciu near Olbia-Arzachena, nuraghe
 * Alghero
 * Anghelu Ruju near Alghero Ozieri, necropolis
 * Antas near Fluminimaggiore, temple
 * Ardara, Romanesque church of Santa Maria del Regno
 * Argentiera carbon mines, ghost villages, industrial architecture
 * Asoru near Muravera, nuraghe
 * Arrubiu
 * Assemini Catalan Gothic church, 16th century, Byzantine oratorio, 10th century
 * Barumini nuragic palace and village (*Su Nuraxi), Catalan church 15th century, Catalan Gothic villa
 * Benetutti church, 15th century, paintings
 * Biristeddi Giants Tomb
 * Bisarcio Romanesque church
 * Bonarcado church 11th century
 * Bonorva nuragic temple, nuragic tombs, Carthaginian fort, medieval village, church 16th century
 * Bonu Ighinu, cave
 * Borore
 * Bosa
 * Brodu
 * Bulzi
 * Burghidu, nuraghe
 * Cabu Abbas
 * Cagliari
 * Cala Domestica
 * Campu Luntanu
 * Carbonia
 * Castelsardo
 * Coddu Vecchiu, Giants Tomb
 * Cornus
 * Dolianova
 * Domu de Orgia
 * Domu s Orku
 * Friarosu
 * Fonte e Mola
 * Funtana Cuverta
 * Genna Maria
 * Genna Salixi
 * Genoni
 * Gergei
 * Gesturi
 * Golgo
 * Gonnostramatza
 * Iglesias
 * Is Concias
 * Is Paras, nuraghe
 * Izzana, nuraghe
 * Kukkuru Nuraxi
 * Laconi
 * Li Muri
 * Losa, nuraghe
 * Lugherras, nuraghe
 * Macomer
 * Madau
 * Mandra Antine
 * Massama
 * Milis
 * Molafa
 * Monte Arci
 * Monte d'Accoddi
 * Monte Sirai A fortified hilltop town founded in the 8th century BC
 * Montessu
 * Montevecchio
 * Moseddu
 * Nora
 * Nugoro
 * Nuxis
 * Olbia, church of San Simplicio (Olbia)
 * Oliena
 * Olmedo
 * Olzai
 * Oristano
 * Orolo, nuraghe
 * Ossi
 * Ottana
 * Ozieri
 * Palmavera
 * Pani Loriga
 * Perfugas
 * Ploaghe
 * Porto Torres
 * Pranu Mutteddu
 * Quirra
 * Roccia dell Elefante
 * Saccargia
 * Sa Coveccada, dolmen
 * San Cosimo
 * San Giovanni di Sinis
 * San Mauro
 * San Platano
 * San Salvatore
 * Sant Antioco
 * Santa Cristina di Paulilatino
 * Santa Giusta, ex-Cathedral of Santa Giusta
 * Santa Vittoria
 * Santu Antine Nuraghe
 * Sa Punta e su Nurake
 * Sardara
 * Sas Concas
 * Sassari
 * Sa Testa
 * Seneghe
 * Serra Orrios
 * Seruci
 * Sibiola
 * Silanus
 * Sorradile
 * Sorres
 * Sos Furrighesos
 * Suelli
 * Sulci, Phoenician city, Carthaginian necropolis, Roman ruins
 * Su Mulinu
 * Su Pranu
 * Su Tempiesu
 * Tamuli
 * Tergu, church of Nostra Signora di Tergu
 * Tharros
 * Thiesi
 * Thomes
 * Tiscali
 * Tratalias
 * Trullas
 * Tuili
 * Tuvixeddu necropolis Carthaginian and later Roman necropolis
 * Uta
 * Villamar
 * Zuri


text:
User:Loffe

I mostly do cleanups, fixes links, spellings and remove vandalism, add recent info to current events. Especially try to get spelling with å, ä, ö and apostrophes correct.

I live in Sweden.

I'm an optimist.

title: User:Loffe


text:
User:Berek

I live in Lanark, Scotland. Some time ago I returned to the site, having spent a lot of time at everything2.

My main interests include Scotland and Scottish history, other historical pieces, planetary science and the Solar System, and articles on countries and places.

I often patrol Uncategorized pages or, adding categories, stub tags, and wikiproject tags, and as such, consider myself a WikiGnome. I am also now a new pages and pending changes reviewer.
 * User:Berek/edit history

NPP Award for 2022[edit] The New Page Reviewer's Iron Award For over 360 article reviews during 2022. Thank you for patrolling new pages and helping us out with the backlog! -MPGuy2824 (talk) 03:16, 2 January 2023 (UTC)[reply]

Personal links:
 * Help:Contents/Fun stuff
 * Portal:India
 * User:Berek/India
 * List of Game of Thrones episodes
 * World War II
 * List_of_Wikipedians_by_number_of_edits
 * KIC 8462852
 * User talk:Berek/Archive 1
 * Turboencabulator
 * Category:Stubs
 * Help: Wikipedia: The Missing Manual
 * Editor's index to Wikipedia
 * Special:ListUsers
 * User:Berek/Game of Thrones
 * User:Berek/List of birds of Scotland
 * Routes to Work South
 * Uncategorized pages
 * Department of Fun
 * User:Berek/World War II
 * edit count
 * Articles with too few wikilinks
 * Wiki Library
 * Wow signal
 * Humorous userboxes
 * History of Scotland
 * Special:NewPagesFeed
 * User:Berek/Sandbox
 * 20th century
 * Duke of Waltham
 * User:Neddyseagoon
 * WikiGnome/Kudos
 * WP |class=start|importance=low
 * WikiProject
 * April Fools/April Fools' Day 2021
 * User:DisillusionedBitterAndKnackered

I agree to multi-license all my contributions, with the exception of my user pages, as described below:

title: User:Berek


text:
User:Edgar~enwiki

Intro

At the moment I am focused on Spanish Wikipedia, which I guess needs me more than the English one.

My link to my personal and record pages (in Spanish) is:

I will be working soon in the English Wikipedia.☺

title: User:Edgar~enwiki


text:
User:Tarquin

Current Wikipedia status
2006 Checking watchlist a few times a week. Doing the odd bit of article polishing, link fixing, and that sort of stuff.

personal appeal?

 * I’m doing this for the child in Africa who is going to use free textbooks and reference works produced by our community and find a solution to the crushing poverty that surrounds him.

Could our Glorious Leader keep his libertarian notions of self-empowerment to himself? Poverty in Africa is caused in large part by the lack of fair trade and crushing debt. I fully support the production of free textbooks for the developing world, but this is just too much.

I still fully support Wikipedia, but I doubt its founder's motives, and I find his political opinions abhorrent.

---

 * Is Wiki for everybody, even for those who dokkn't care to educate themselves as to how it works? -- BlackHat on http://c2.com/cgi/wiki?WikiSquatting

 * Father Christmas and the Tooth Fairy are part of the charm of childhood. So is God. Some of us grow out of all three. -- Richard Dawkins

 * La seule chose vraie, c'est la guerre psychologique! -- Savancosinus, La Zizanie, Goscinny & Uderzo

 * The vote went nowhere and became such a confusing mess and joke that people on nearly all sides of the argument were able to logically argue that their choice was the actual winner.  -- no, it's not the "election" of Dubya. It's Wikipedia talk:Manual of Style (dates and numbers).

 * The creationists have no scientific evidence to support their case, so instead they constantly repeat long-refuted pseudoscientific arguments. This has no place in the classroom. If a religion is incompatible with scientific thought, then so much worse for that religion. To argue that it is unconstitutional to only present scientific arguments on a subject that has nothing to do with religion is preposterous -- by the same logic you could argue that the theory of gravity should be balanced with "alternative views" because these guys think they can fly in the air if they concentrate hard enough. -- User:Eloquence, writing on Talk:Creationism.

---

The state of this page tells you an awful lot about me: I tend to accumulate clutter, I hardly ever delete anything, and my mind tends to wander.

runs through shouting "Wikipedia is more popular than Jesus! Wikipedia is more popular than Jesus!"

need to know

 * GFDL images All photos I have taken and diagrams I have made for Wikipedia are GFDL. They may not be marked with the tag as they predate its existence. Feel free to add the GFDL tag to any images whose description page states I took the photograph or drew the diagram. You can also move them to Commons if you like, but please let me know if you do.
 * slight wikipediholic tendencies (well, more than slight, I'm apparently 10th in the most active rankings. eek.)
 * administrator, so feel free to ask me stuff on my talk page
 * generally of a crabby disposition, but it's all a front for rampant idealism (or perhaps the other way round. I forget)
 * tendency to ramble, see below.

subpages, attic space, out back

 * User:Tarquin/Utility
 * Collection of links to pages in need of User:Tarquin/metrication
 * List of stuff User:Tarquin/to do
 * Image markup gallery

Memorable mailing list posts:
 * Jimbo on crackpots (thanks for the link, User:Angela)
 * some more on the same:

the following will self-destruct in ...
I was back briefly after an absence of a few months. But then things like this happen and sap my strength. I don't have the inclination to engage in edit wars.

... but look at the TeX equations! the soft curves of the integral sign! the variables leaping from tree to tree, as they float down the mighty rivers of British Columbia. ! The Giant Redwood. The Larch. The Fir! The mighty Scots Pine! ... Sing! Sing! [singing] I'ma lumberjack, and I'm okay. ... (men in white coats enter and carry Tarquin offstage)

(In short: I like the new TeX markup.)

Vague rambling biog
Hullo. I'm Tarquin, for long and complicated reasons. Okay, they're not complicated at all. It's just an in-joke in my family. I may get round to explaining it one day, but it's really not that interesting.

There's a family rumour that we're descended from René Descartes. My great-great-grandfather's family was from La Haye, Descartes' birthplace, and his father was mayor. It's completely unsubstantiated.

Meanwhile, I'm British. With, as well as the French ancestry, a few touches of other European countries thrown in.

Contrary to rumours, I am not an AI somewhere in northern Canada. I'm an AI in England. ;-)

I fall under the "hey, I ordered a cheeseburger" personality type. Not that I'd be seen dead doing such a thing. I'm reliably informed on a semi-regular basis that I'm cantakerous.

Interesting life skills: I have both perfect pitch and relative pitch. I've never been able to pin down just what the term "photographic memory" is supposed to mean, but I do have a good one. Stuff just tends to drop in of its own accord. It's very handy for building up the Wiki Web, as I tend to click if I've already seen a page on a given subject. It also means I regard pages like Mnemonic with complete bemusement: remembering "Roy G. Biv" or "HOMES" seems to me to be an extra burden on the memory, not a lightening. There's the mnemonic, plus what it actually is supposed to represent. "Richard Of York Gave Battle In Vain" was drilled into me at school, but decoding that to get the order of colours is slower than just visualizing a colour wheel.

I'm a very sloppy typist. I have the unfortunate tendency of saving articles with one or two atrocious typos. On the other hand, I'm an excellent proofreader when it's someone else's work. So karmically it balances out... ;-) I probably fix two typos for each one I leave.

I run a wiki on the Unreal engine here: http://wiki.beyondunreal.com/

Are you wikipediholic test score: 20 (increased now I'm on wikipedia-L)

 * Feb 2003 revision: 41. I note with interest this question: Do you make edits while drunk or under the influence of other intoxicating substances and find that nobody reverts your changes? ... ... ... some of my finest work is made under the influence of single malt :-)

An end to all edit wars
Troubled with edit wars? NPOV going down the drain? Tearing your hair out over the latest edit conflict? Fear not. Here's the simple solution:

 * 1) First determine who is resolutely refusing to budge & making things difficult. Let's call them X.
 * 2) Identify their nationality
 * 3) Find the page "list of famous {nationality}"
 * 4) Add contentious entries. Remove some. Invent some names. Ideally, a pop band whom no-one has ever heard of. Give them a kooky name like "The Wet Fredericks" or "Tiger With Bagels".
 * 5) Bump this page on RC a few times next time X is around
 * 6) Reel them into a long and protracted edit was on the list page. Get them deeply riled about how famous or not their fellow nationals are. Imply that no-one cares.
 * 7) This will completely distract them from their earlier crusade. And let's face it, "list of X" pages are pointless anyway.

Points will be awarded for the best "Talk:list of famous {nationality}" pages. And what do points mean?

Finding stuff
Arg. I just went looking for the conventions on names of saints. Simple, eh? You'd think so. Well, I had to go through this list of pages:
 * 1) Policies and guidelines
 * 2) Naming conventions (good start)
 * 3) Naming conventions (names and titles) (seems reasonable to expect it here... but no. It says "see the talk page. So I move on...)
 * 4) Wikipedia talk:Naming conventions (use browser's search function to find something in the morass... nope, not here either. Link to another talk page)
 * 5) and finally Talk:List of saints

... only to find it's not decided yet. Four pages, wandering with no visible signs of organization. This is not a good way to organize things.

Stub Tennis
We should hold Olympics. Pgdudda mentions "WikiRoulette". I hereby coin the name "Stub Tennis". (I can be fairly sure I've made the name up, a search draws a blank both here and on WardsWiki.) To play stub tennis, do this:
 * Find a stub
 * add something to it, either
 * some vague factoid you remember
 * do a search on the topic or some of the names in it & create two-way links (LinksAreContent...)
 * for stub tennis to work, someone else has to react to its being bumped on Recent Changes.
 * the article is batted to and fro between two or more wikipedians.

Thoughts on Wikipedia
I wonder sometimes... at what point will Larry Sanger's holographic image step out of the vault and tell us what our real purpose is?

How I ended up here
For those who really wish to know, I landed on Wikipedia quite by accident in January 2002: I was idly reading an article on operating systems for the next generation of mobile phones (I am not sure why...), which was detailing Micro$oft's foray into this field. The article went on to say that many cool things would be possible with the colour screens that we'd be seeing on advanced models; but that given minimal memory and ways of addressing the screen all aimed at minimizing power consumption, programmers who worked on games on 1980s computers such as the Commodore 64 and the ZX Spectrum would find their skills at squeezing the maximum effiencency out of the minimum code once again in demand.

In particular (it said), the problem of "attribute clash" seen on the Spectrum was again rearing its ugly head. Intrigued by the term - it was implied that it related to colour on the screen - I Googled it, and the first link got me to Wikipedia...

I do of course try and tone done my style when writing Wikipedia entries: I do have a tendency to ramble. ;-)

Rant and Rave
the rant and rave section is currently closed while I think of something else to complain about

My (current) number one Wikipedia grouse is this: "Venice, Italy", "London, England" and so forth. That is how cities are indentified in the US; not in the rest of the world. A rout through UK train timetables for the few duplicate towns shows they use "Gillingham (Kent)", for example. The same form or "Gillingham in Kent" is usual in newspaper or reference articles if readers may not know which county a place is in. However, in the interests of consistency in page names, we're stuck with the stateside terminology. It's probably all irrational reactions to cultural imperialism. That or seeing that dratted comma always reminds me of Marilyn Monroe saying "Paris, France is in Europe?" in Gentlemen prefer blondes...

Second grouse: bad French. Most Anglophones are shovelled some sort of French at school, and are under the impression that they a) recall it and b) it was correct in the first place. I tidied French phrases used by English speakers, and just spotted Twinkle twinkle little star. Translation is a sticky art, but I wish people would at least ensure nouns and adjectives agree in gender and number.

Articles
My principal fields of interest are music and maths, but also a mixed bag of things.

(this list that follows hasn't been updated in ages. as a WikiWeeder, I end up editing the most bizarre articles. I'd never heard of the Holden car company, I have no interest in the Ford Escort, and the Killer poke was just a rumour I'd once heard)

lately, I've started: - Through the Looking-Glass - Arlo Guthrie - Oliver Heaviside - Pink Panther - Henry Mancini - Baron Haussmann - Oulipo - Life: A User's Manual - Joseph Heller - Penrose triangle - Raymond Smullyan (couldn't believe he wasn't already covered... ) - Disability: radical new start and moved older things to subpages. I somewhat see the sense in having the "disability etiquette" page, yet I can't help but think "how would people react to a page called 'how to address a black person'?". Were things like that written in the 1960s? - Fitts' law - Tower of Hanoi (the algorithm I linked to on KnowHowWiki is mine too...) - TGV - Axe historique - Periodic table/Wide Table - Pere Lachaise - Beryl Bainbridge - Companion planting - Spurn - Significant figure (feels like MONTHS since I've actually started a page; so much weeding to do!) - Jodrell Bank (a stub whose progress I look forward to seeing) - Unit vector - Strait-jacket - Laundry symbols -- who first devised these? - VAL - Blackcurrant - Penny-farthing - Babbling

Stuff I've added to lately: - The Simpsons (but, like, who hasn't?) - Goscinny - Paris Metro - French Revolutionary Calendar - Isambard Kingdom Brunel - T.H. White - SAMPA: seeing this bastardized ascii IPA bugged me to the point that I had to dig up the page on it... found it in need of work; made tables and added diphthongs ([faI@]...). I plan to upload recordings of phonemes soon. - Acronym: gave this a polish - Alexander Technique -- it's great. I recommend it. Hard work and most teachers are expensive but it really is worth it. - Mercator projection - Tube map: gave this a rewrite. I've been fascinated by the tube map (& the metro map) as far back as I can remember (Goodfellas voice-style ;) ) - Piano - Octave and Note

Stuff I intend to read up on:

 * Marcel Proust
 * Stendhal

To do:
 * keep an eye out for Ealing, Ealing Studios and Ealing Comedies -- all three links exist, with no page yet. Clean up links when one is created. Also musing which name is most appropriate.

 * rewrite harmonic

I'm vaguely collecting links to style guides found dotted around: User:Tarquin/Style Guides (this is probably obsolete by the way.)

-

http://c2.com/cgi/wiki?MyMyersBriggsTypeIs ENFP, apparently. Whoopee-do.

Test of IPA:

ca:Usuari:Tarquin da:Bruger:Tarquin de:Benutzer:Tarquin eo:Vikipediisto:Tarquin fr:Utilisateur:Tarquin nl:Gebruiker:Tarquin

title: User:Tarquin


text:
Wikipedia:PHP script new features

'''This is an incomplete list of the features the new wikipedia software has to offer. See also Bug reports for "features" that shouldn't be in the script.''' Some additional features, added in July 2002, are listed in Software Phase III.

 * User settings See your user settings page if you are logged in.
 * Side bar A bar on the left or right of the screen with useful system functions.
 * Skins Different ways to present the site. Check out the promising "Cologne Blue".
 * Minor edit presentation You can choose whether you want to see minor edits on the RecentChanges page.
 * Special Functions Accessible from the "Special Pages" link on every page, or from the side bar if that has been switched on.
 * File upload feature allows users to upload graphics or sound files, see special:Upload. Uploaded files are listed on RecentChanges and they are also logged on log:Uploads.
 * Watchlist Every page has a link "Watch this article for me". Use special:Watchlist to track changes on the articles you declared an interest in; watched articles are also bolded in the Recent changes list.
 * Various Lists of new pages, of "orphaned" pages which no other page links to, of pages which are linked to but don't yet exist, of long and short pages, of the pages with the highest number of page-views, of user pages, and other statistics.
 * Namespaces Separated from the page name with a colon. This very page is within the wikipedia namespace.
 * Normal namespaces Currently, there are the "blank" namespace (for normal articles), wikipedia (for articles about Wikipedia), user (for user pages), special (for system pages like RecentChanges). This keeps user pages from interfering with article content.
 * Talk namespaces All namespaces have their own Talk namespace ("Talk", "Wikipedia talk", "User talk"), to use instead of a /Talk page. A "discuss this page" link will appear in the sidebar and at the bottom of the screen on each page; "view this article" links take you back from the talk page to the main page.
 * Other stuff
 * Automatic signature Just type three times ~ when you edit, and on saving the page, it will be replaced with your user name and a link to your user page. If you use four tildes, the current date will be added as well. Mainly intended for Talk pages.
 * Word-extension linking If you include a link of the form wars, or wartime , the system will automatically display it as if you had typed wars or wartime , respectively, saving some typing.
 * Parenthetical hiding If you include a link of the form kernel (mathematics), the parenthetical portion will be hidden in the link: kernel. This is useful for disambiguating different meanings of a word without making linking too difficult or cluttering up the text of articles. This also works with cropping out namespaces when you want a cleaner-looking link: copyrights becomes copyrights
 * User contributions At the top of each user page, there is a link to display a list of all articles the user has worked on, according to the database.
 * Counter on every page (see bottom) for the number of times the page has been viewed.
 * Search Searches are now always based on the most current version of all articles. Boolean search ("and", "or", "not") is possible. By default, "and" is used, meaning that only articles matching all the search terms are returned. Search terms shorter than three letters always cause the search to fail and should be avoided. See Searching for details.
 * Interlanguage links: handy method for linking articles between the versions of Wikipedia in various languages.
 * Side-by-side diffs - the diffs are shown side-by-side, and changes portions of lines are highlighted, making it much easier to see what's what. Additionally, a diff is shown during an edit conflict so you can see exactly what you need to reintegrate.
 * No longer supported
 * Subpages A page with a slash (/) in its title is treated like any other page; there are no special subpage features anymore.
 * CamelCase By using a word with MixedCase, you don't automatically create a link anymore.

title: Wikipedia:PHP script new features


text:
User:Zundark

I’ve been editing the English Wikipedia since August 2001, though I’m not as active here as I used to be. Nowadays I can sometimes be found instead on Wikimedia Commons or Wikidata, or even on the English Wiktionary.

title: User:Zundark