Instruct: Given a question, retrieve passages that can help answer the question.
Query: What is a magnetic field?
A magnetic field is a vector field that describes the magnetic influence of electrical currents and magnetized materials. In everyday life, the effects of magnetic fields are often seen in permanent magnets, which pull on magnetic materials (such as iron) and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges (electric currents) such as those used in electromagnets. Magnetic fields exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field varies with location. As such, it is an example of a vector field.
On the Sun, magnetic reconnection may happen on solar arcades—a series of closely occurring loops of magnetic lines of force. These lines of force quickly reconnect into a low arcade of loops, leaving a helix of magnetic field unconnected to the rest of the arcade. The sudden release of energy during this process causes the solar flare and ejects the CME. The helical magnetic field and the material that it contains may violently expand outwards forming a CME. This also explains why CMEs and solar flares typically erupt from what are known as the active regions on the Sun where magnetic fields are much stronger on average.
The magnetostatic energy is the energy stored in the field generated by a material's magnetic moments. The magnet's field reaches its maximum intensity if all the magnetic moments orient in one direction; this is what occurs in a hard magnet. In order to prevent building up the magnetic field, sometimes magnetic moments tend to form loops. That way, the energy stored in the magnetic field can be constrained; this is what occurs in a soft magnet. What determines whether a magnet is hard or soft is the dominant term of its magnetic energy. For hard magnets, the anisotropy constant is relatively large, making the magnetic moments align with easy axis. The opposite case applies to soft magnets, in which the magnetostatic energy is dominant.
A material is paramagnetic only above its Curie temperature. Paramagnetic materials are non-magnetic when a magnetic field is absent and magnetic when a magnetic field is applied. When a magnetic field is absent, the material has disordered magnetic moments; that is, the atoms are asymmetrical and not aligned. When a magnetic field is present, the magnetic moments are temporarily realigned parallel to the applied field; the atoms are symmetrical and aligned. The magnetic moments being aligned in the same direction are what causes an induced magnetic field.
The magnetic interaction is described in terms of a vector field, where each point in space (and time) is associated with a vector that determines what force a moving charge would experience at that point (see Lorentz force). Since a vector field is quite difficult to visualize at first, in elementary physics one may instead visualize this field with field lines. The magnetic flux through some surface, in this simplified picture, is proportional to the number of field lines passing through that surface (in some contexts, the flux may be defined to be precisely the number of field lines passing through that surface; although technically misleading, this distinction is not important). Note that the magnetic flux is the "net" number of field lines passing through that surface; that is, the number passing through in one direction minus the number passing through in the other direction (see below for deciding in which direction the field lines carry a positive sign and in which they carry a negative sign).
In more advanced physics, the field line analogy is dropped and the magnetic flux is properly defined as the surface integral of the normal component of the magnetic field passing through a surface. If the magnetic field is constant, the magnetic flux passing through a surface of vector area S is
where "B" is the magnitude of the magnetic field (the magnetic flux density) having the unit of Wb/m (tesla), "S" is the area of the surface, and "θ" is the angle between the magnetic field lines and the normal (perpendicular) to S. For a varying magnetic field, we first consider the magnetic flux through an infinitesimal area element dS, where we may consider the field to be constant: 
A generic surface, S, can then be broken into infinitesimal elements and the total magnetic flux through the surface is then the surface integral
From the definition of the magnetic vector potential A and the fundamental theorem of the curl the magnetic flux may also be defined as:
where the line integral is taken over the boundary of the surface "S", which is denoted ∂"S".
Electromagnetic propulsion (EMP), is the principle of accelerating an object by the utilization of a flowing electrical current and magnetic fields. The electrical current is used to either create an opposing magnetic field, or to charge a field, which can then be repelled. When a current flows through a conductor in a magnetic field, an electromagnetic force known as a Lorentz force, pushes the conductor in a direction perpendicular to the conductor and the magnetic field. This repulsing force is what causes propulsion in a system designed to take advantage of the phenomenon. The term electromagnetic propulsion (EMP) can be described by its individual components: electromagneticusing electricity to create a magnetic field, and propulsionthe process of propelling something. When a fluid (liquid or gas) is employed as the moving conductor, the propulsion may be termed magnetohydrodynamic drive. One key difference between EMP and propulsion achieved by electric motors is that the electrical energy used for EMP is not used to produce rotational energy for motion; though both use magnetic fields and a flowing electrical current.
The sequence of turning a particular coil on or off dictates what direction the effective electromagnetic fields are pointed. By turning on and off coils in sequence a rotating magnetic field can be created. These rotating magnetic fields interact with the magnetic fields of the magnets (permanent or electromagnets) in the stationary part of the motor (stator) to create a torque on the armature which causes it to rotate. In some DC motor designs the stator fields use electromagnets to create their magnetic fields which allow greater control over the motor. 
This is magnetization of one particle, the total magnetization of the solid is given by
formula_17
where "n" is the number density of magnetic moments. The formula above is known as the Langevin paramagnetic equation.
Pierre Curie found an approximation to this law which applies to the relatively high temperatures and low magnetic fields used in his experiments. Let's see what happens to the magnetization as we specialize it to large formula_4 and small formula_19. As temperature increases and magnetic field decreases, the argument of hyperbolic tangent decreases. Another way to say this is
No specific details of the workings of the claimed technology were made public. McCarthy stated in a 2006 RTÉ radio interview, "What we have developed is a way to construct magnetic fields so that when you travel round the magnetic fields, starting and stopping at the same position, you have gained energy". In 2011, Steorn's website was updated to suggest that the Orbo is based on magnetic fields which vary over time. Barry Williams of the Australian Skeptics has pointed out that Steorn is "not the first company to claim they have suddenly discovered the miraculous property of magnetism that allows you to get free energy" while Martin Fleischmann says that it is not credible that positioning of magnetic fields could create energy.
A magnet both produces its own magnetic field and responds to magnetic fields. The strength of the magnetic field it produces is at any given point proportional to the magnitude of its magnetic moment. In addition, when the magnet is put into an external magnetic field, produced by a different source, it is subject to a torque tending to orient the magnetic moment parallel to the field.[10] The amount of this torque is proportional both to the magnetic moment and the external field. A magnet may also be subject to a force driving it in one direction or another, according to the positions and orientations of the magnet and source. If the field is uniform in space, the magnet is subject to no net force, although it is subject to a torque.[11]
Principle: Magnetic Resonance Imaging (MRI) exploits the nuclear magnetic alignments of different atoms inside a magnetic field to generate images. MRI machines consist of large magnets that generate magnetic fields around the target of analysis. These magnetic fields cause paramagnetic atoms such as hydrogen, gadolinium, and manganese to align themselves in a magnetic dipole along the magnetic fields, created by the radiofrequency (RF) coils inside the MRI machine. What the machine captures from the subject is the relaxation of the atoms as they return to their normal alignment when the RF pulse is temporarily ceased. With this data, a computer will generate an image of the subject based on the resonance characteristics of different tissue types.
The demagnetizing field, also called the stray field (outside the magnet), is the magnetic field (H-field) generated by the magnetization in a magnet. The total magnetic field in a region containing magnets is the sum of the demagnetizing fields of the magnets and the magnetic field due to any free currents or displacement currents. The term "demagnetizing field" reflects its tendency to act on the magnetization so as to reduce the total magnetic moment. It gives rise to "shape anisotropy" in ferromagnets with a single magnetic domain and to magnetic domains in larger ferromagnets.
All observations on electromagnetism apply to what might be considered to be primarily magnetism, e.g. perturbations in the magnetic field are necessarily accompanied by a nonzero electric field, and propagate at the speed of light.
In a vacuum,
where is the vacuum permeability.
The solar magnetic field extends well beyond the Sun itself. The electrically conducting solar wind plasma carries the Sun's magnetic field into space, forming what is called the interplanetary magnetic field. In an approximation known as ideal magnetohydrodynamics, plasma particles only move along the magnetic field lines. As a result, the outward-flowing solar wind stretches the interplanetary magnetic field outward, forcing it into a roughly radial structure. For a simple dipolar solar magnetic field, with opposite hemispherical polarities on either side of the solar magnetic equator, a thin current sheet is formed in the solar wind. At great distances, the rotation of the Sun twists the dipolar magnetic field and corresponding current sheet into an Archimedean spiral structure called the Parker spiral. The interplanetary magnetic field is much stronger than the dipole component of the solar magnetic field. The Sun's dipole magnetic field of 50–400 μT (at the photosphere) reduces with the inverse-cube of the distance to about 0.1 nT at the distance of Earth. However, according to spacecraft observations the interplanetary field at Earth's location is around 5 nT, about a hundred times greater. The difference is due to magnetic fields generated by electrical currents in the plasma surrounding the Sun.
Scientific opinion is divided on what causes geomagnetic excursions. The dominant theory is that they are an inherent aspect of the dynamo processes that maintain the Earth's magnetic field. In computer simulations, it is observed that magnetic field lines can sometimes become tangled and disorganized through the chaotic motions of liquid metal in the Earth's core. In such cases, this spontaneous disorganization can cause decreases in the magnetic field as perceived at the Earth's surface. In truth, under this scenario, the Earth's magnetic field intensity does not significantly change in the core itself, but rather energy is transferred from a dipole configuration to higher order multipole moments which decay more rapidly with the distance from the Earth's core, so that the expression of such a magnetic field at the surface of the Earth would be considerably less, even without significant changes in the strength of the deep field. This scenario is supported by observed tangling and spontaneous disorganizations in the solar magnetic field. However, this process in the sun invariably leads to a reversal of the solar magnetic field (see: solar cycle), and has never been observed such that the field would recover without large scale changes in field orientation.
IEEE 1902.1 RuBee uses magnetic waves also often called inductive communication. James Clerk Maxwell presented his now famous set of equations (Maxwell's Equations) to the Royal Society in 1864. These equations describe what happens when an electron travels along a conductive wire. Two fields are created, the Electric Field, labeled E, and the Magnetic Field, labeled H. These electric and magnetic fields travel through the aether, (i.e. outer space or the far field), at the speed of light with an assumed impedance of 377 Ω. E, the electric field, may be given in newtons per coulomb or volts per meter, and H, the magnetic field, may be given in gauss or amperes per meter. The two fields are tied together with the aether to form simple electric circuit capable of transferring power. However, when these two fields are measured in what is called the near field (much less than the wavelength of the signal) very strange things happen. (Also see Capps “Near Field or Far Field"). E and H are no longer connected in a simple predictable manner. The value of "c" (speed of light) and the resistance of the aether are altered and it is possible to produce large H values with low E values. It is as if the aether impedance has been reduced to only a few ohms.
Note that v does not represent the velocity that magnetic fields lines travel through the conductor. The magnetic field pattern observed depends on the frame of reference. They have no velocity on their own. To illustrate, imagine that one were to take a magnet and flip it 180 degrees. The result of assuming that these field lines actually have velocity of their own would be that magnetic field lines far away would swing to the other side, potentially faster than the speed of light, however, that is not what happens.
A horseshoe magnet (A-1) has a north and south pole. If a piece of carbon steel contacts both poles, a magnetic circuit is created. In an electromagnetic coupling, the north and south pole is created by a coil shell and a wound coil.
In a clutch, (B1) when power is applied, a magnetic field is created in the coil (A2 blue). This field (flux) overcomes an air gap between the clutch rotor (A2 yellow) and the armature (A2 red). This magnetic attraction, pulls the armature in contact with the rotor face. The frictional contact, which is being controlled by the strength of the magnetic field, is what causes the rotational motion to start.
Instead, what happens is that rotating a magnet causes subatomic particles in the magnet to acquire a change in velocity. However, in the rotated magnet, the velocities of electrons would vary ahead or behind those of the other particles, due to their lower mass compared to nuclei. There is length contraction of fields propagating from moving charges, and the length contraction of the electric fields E of the electrons would be greater or lesser than the contraction of the E fields of the positive nuclei depending on whether the rotation of the magnet was aligned to, or opposed to, the electron spins which give rise to the magnetism.
Flux pinning is the phenomenon where a superconductor is pinned in space above a magnet. The superconductor must be a type-II superconductor because type-I superconductors cannot be penetrated by magnetic fields. The act of magnetic penetration is what makes flux pinning possible. At higher magnetic fields (above Hc1 and below Hc2) the superconductor allows magnetic flux to enter in quantized packets surrounded by a superconducting current vortex (see Quantum vortex). These sites of penetration are known as flux tubes. The number of flux tubes per unit area is proportional to the magnetic field with a constant of proportionality equal to the magnetic flux quantum. On a simple 76 millimeter diameter, 1-micrometer thick disk, next to a magnetic field of 28 kA/m, there are approximately 100 billion flux tubes that hold 70,000 times the superconductor's weight. At lower temperatures the flux tubes are pinned in place and cannot move. This pinning is what holds the superconductor in place thereby allowing it to levitate. This phenomenon is closely related to the Meissner effect, though with one crucial difference — the Meissner effect shields the superconductor from all magnetic fields causing repulsion, unlike the pinned state of the superconductor disk which pins flux, and the superconductor in place.
Magnetic current imaging uses the magnetic fields produced by currents in electronic devices to obtain images of those currents. This is accomplished though the fundamental physics relationship between magnetic fields and current, the Biot-Savart Law:
As a result, the current can be directly calculated from the magnetic field knowing only the separation between the current and the magnetic field sensor. The details of this mathematical calculation can be found elsewhere, but what is important to know here is that this is a direct calculation that is not influenced by other materials or effects, and that through the use of Fast Fourier Transforms these calculations can be performed very quickly. A magnetic field image can be converted to a current density image in about 1 or 2 seconds.
An azimuthal magnetic field is one that runs east–west. A meridional magnetic field is one that runs north–south. In the solar dynamo model of the Sun, differential rotation of the solar plasma causes the meridional magnetic field to stretch into an azimuthal magnetic field, a process called the omega-effect. The reverse process is called the alpha-effect.[47] A dipole magnetic field is one seen around a bar magnet or around a charged elementary particle with nonzero spin. A quadrupole magnetic field is one seen, for example, between the poles of four bar magnets. The field strength grows linearly with the radial distance from its longitudinal axis. A solenoidal magnetic field is similar to a dipole magnetic field, except that a solid bar magnet is replaced by a hollow electromagnetic coil magnet. A toroidal magnetic field occurs in a doughnut-shaped coil, the electric current spiraling around the tube-like surface, and is found, for example, in a tokamak. A poloidal magnetic field is generated by a current flowing in a ring, and is found, for example, in a tokamak. A radial magnetic field is one in which field lines are directed from the center outwards, similar to the spokes in a bicycle wheel. An example can be found in a loudspeaker transducers (driver).[48] A helical magnetic field is corkscrew-shaped, and sometimes seen in space plasmas such as the Orion Molecular Cloud.[49]
The behaviour of light striking the interface is solved by considering the electric and magnetic fields that constitute an electromagnetic wave, and the laws of electromagnetism as shown below. The ratio of waves' electric field (or magnetic field) amplitudes are supplied, but in practice one is more often interested in formulae which determine "power" coefficients, since power (or irradiance) is what can be directly measured at optical frequencies. The power of a wave is generally proportional to the square of the electric (or magnetic) field amplitude.
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 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
However, the domains can also exist in other configurations in which their magnetization mostly points in the same direction, creating an external magnetic field. Although these are not minimum energy configurations, due to a phenomenon where the domain walls become "pinned" to defects in the crystal lattice they can be "local" minimums of the energy, and therefore can be very stable. Applying an external magnetic field to the material can make the domain walls move, causing the domains aligned with the field to grow, and the opposing domains to shrink. When the external field is removed, the domain walls remain pinned in their new orientation and the aligned domains produce a magnetic field. This is what happens when a piece of ferromagnetic material is "magnetized" and becomes a permanent magnet.