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Encyclopedia > Magnetic field
Electromagnetism
Electricity · Magnetism
Magnetostatics
Ampère's law · Electric current
Magnetic field · Magnetic flux
Biot-Savart law
Magnetic dipole moment
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Magnetic field lines shown by iron filings. The high permeability of individual iron filings causes the magnetic field to be larger at the ends of the filings. This causes individual filings to attract each other, forming elongated clusters that trace out the appearance of lines. It would not be expected that these "lines" be precisely accurate field lines for this magnet; rather, the magnetization of the iron itself would be expected to alter the field somewhat.

When placed in a magnetic field, magnetic dipoles tend to align their axes to be parallel with the magnetic field, as can be seen when iron filings are in the presence of a magnet (see picture at right). Magnetic fields also have their own energy, with an energy density proportional to the square of the field intensity. The magnetic field (B) is typically measured in either teslas (SI units) or gauss (cgs units), while the magnetic field intensity (H) is measured in Amperes/metre (SI units) or oersted (cgs units). For other uses, see Magnet (disambiguation). ... SI unit. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... The gauss, abbreviated as G, is the cgs unit of magnetic flux density (B), named after the German mathematician and physicist Carl Friedrich Gauss. ... This article or section is in need of attention from an expert on the subject. ... In physics, the ampere (symbol: A, often informally abbreviated to amp) is the SI base unit used to measure electrical currents. ... This article is about the unit of length. ... The oersted is old CGS unit of magnetic field strength (or magnetic induction). ...

There are some notable specific incarnations of the magnetic field. For the physics of magnetic materials, see magnetism and magnet, and more specifically ferromagnetism, paramagnetism, and diamagnetism. For constant magnetic fields, such as are generated by stationary dipoles and steady currents, see magnetostatics. For magnetic fields created by changing electric fields, see electromagnetism. For other senses of this word, see magnetism (disambiguation). ... For other uses, see Magnet (disambiguation). ... Ferromagnetism is the phenomenon by which materials, such as iron, in an external magnetic field become magnetized and remain magnetized for a period after the material is no longer in the field. ... Simple Illustration of a paramagnetic probe made up from miniature magnets. ... Levitating pyrolytic carbon Diamagnetism is a form of magnetism that is only exhibited by a substance in the presence of an externally applied magnetic field. ... Look up current in Wiktionary, the free dictionary. ... Magnetostatics is the study of static magnetic fields. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ...

The electric field and the magnetic field are tightly interlinked, in two senses. First, changes in either of these fields can cause ("induce") changes in the other, according to Maxwell's equations. Second according to Einstein's theory of special relativity, a magnetic force in one inertial frame of reference may be an electric force in another, or vice-versa (see relativistic electromagnetism for examples). Together, these two fields make up the electromagnetic field, which is best known for underlying light and other electromagnetic waves. In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... For thermodynamic relations, see Maxwell relations. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... An inertial frame of reference, or inertial reference frame, is one in which Newtons first and second laws of motion are valid. ... Relativistic electromagnetism is the idea of explaining electromagnetism based on relativistic (Albert Einstein 1905) arguments. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... For other uses, see Light (disambiguation). ... Electromagnetic radiation is a propagating wave in space with electric and magnetic components. ...

In classical physics,the magnetic field $mathbf{B}$ is a vector field (that is, some vector at every point of space and time), with SI units of teslas (one tesla is one newton-second per coulomb-metre) and cgs units of gauss. It has the property of being a solenoidal vector field. Vector field given by vectors of the form (âˆ’y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a (locally) Euclidean space. ... Look up si, Si, SI in Wiktionary, the free dictionary. ... For other uses, see Newton (disambiguation). ... This article is about the unit of time. ... The coulomb (symbol: C) is the SI unit of electric charge. ... This article is about the unit of length. ... This article or section is in need of attention from an expert on the subject. ... The gauss, abbreviated as G, is the cgs unit of magnetic flux density (B), named after the German mathematician and physicist Carl Friedrich Gauss. ... This article is in need of attention. ...

The field $mathbf{B}$ can be both defined and measured by means of a small magnetic dipole (i.e., bar magnet). The magnetic field exerts a torque on magnetic dipoles that tends to make them point in the same direction as the magnetic field (as in a compass), and moreover the magnitude of that torque is proportional to the magnitude of the magnetic field. Therefore, in order to measure the magnetic field at a particular point in space, you can put a small freely-rotating bar magnet (such as a compass) there: the direction it winds up pointing is the direction of $mathbf{B}$; and the ratio of the maximum magnitude of the torque to the dipole moment of the bar magnet is the magnitude $|mathbf{B}|$. For other uses, see Magnet (disambiguation). ... For other senses of this word, see torque (disambiguation). ... This article is about the navigational instrument. ... Dipole moment refers to the quality of a system to behave like a dipole. ...

(There are, in addition, several other different but physically equivalent ways to define the magnetic field, for example via the Lorentz force law (see below), or as the solution to Maxwell's equations.) Lorentz force. ... For thermodynamic relations, see Maxwell relations. ...

It follows from any of these definitions that the magnetic field vector (being a vector product) is a pseudovector (also called an axial vector). In mathematics, the cross product is a binary operation on vectors in three dimensions. ... In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but gains an additional sign flip under an improper rotation (a transformation that can be expressed as an inversion followed by a proper rotation). ... In physics and mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation, but gains an additional sign flip under an improper rotation (a transformation that can be expressed as an inversion followed by a proper rotation). ...

In a bar magnet, for example, the direction of the magnetic field is as follows: In the interior of the magnet, it points roughly towards the magnet's north pole; and outside the magnet, it points roughly towards the magnet's south pole.[1]

### B and H

There are two quantities that physicists may refer to as the magnetic field, notated $mathbf{H}$ and $mathbf{B}$. The vector field $mathbf{H}$ is known among electrical engineers as the magnetic field intensity or magnetic field strength also known as auxiliary magnetic field or magnetizing field. The vector field $mathbf{B}$ is known as magnetic flux density or magnetic induction or simply magnetic field, as used by physicists, and has the SI units of teslas (T), equivalent to webers (Wb) per square metre or volt seconds per square metre. Magnetic flux has the SI units of webers so the $mathbf{B}$ field is that of its areal density. [1][2][3][4][2] The vector field $mathbf{H}$ has the SI units of amperes per metre and is something of the magnetic analog to the electric displacement field represented by $mathbf{D}$, with the SI units of the latter being ampere-seconds per square metre. Although the term "magnetic field" was historically reserved for $mathbf{H}$, with $mathbf{B}$ being termed the "magnetic induction", $mathbf{B}$ is now understood to be the more fundamental entity, and most modern writers refer to $mathbf{B}$ as the magnetic field, except when context fails to make it clear whether the quantity being discussed is $mathbf{H}$ or $mathbf{B}$. See: [3] An engineers degree is an academic degree which is intermediate in rank between a masters degree and a doctorate; it is occasionally to be encountered in the United States in technical fields. ... In physics, the weber (symbol: Wb) is the SI unit of magnetic flux. ... Josephson junction array chip developed by NIST as a standard volt. ... Magnetic flux, represented by the Greek letter Î¦ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. ... For other uses, see Ampere (disambiguation). ... In physics, the electric displacement field or electric flux density or electric induction is a vector field that appears in Maxwells equations. ...

The difference between the $mathbf{B}$ and the $mathbf{H}$ vectors can be traced back to Maxwell's 1855 paper entitled On Faraday's Lines of Force. It is later clarified in his concept of a sea of molecular vortices that appears in his 1861 paper On Physical Lines of Force - 1861. Within that context, $mathbf{H}$ represented pure vorticity (spin), whereas $mathbf{B}$ was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability µ to be a measure of the density of the vortex sea. Hence the relationship, This article is in need of attention. ...

(1) Magnetic induction current causes a magnetic current density

$mathbf{B} = mu mathbf{H}$

was essentially a rotational analogy to the linear electric current relationship,

(2) Electric convection current

$mathbf{J} = rho mathbf{v}$

where ρ is electric charge density. $mathbf{B}$ was seen as a kind of magnetic current of vortices aligned in their axial planes, with $mathbf{H}$ being the circumferential velocity of the vortices. With µ representing vortex density, we can now see how the product of µ with vorticity $mathbf{H}$ leads to the term magnetic flux density which we denote as $mathbf{B}$. Current flowing through a wire produces a magnetic field (B, labeled M here) around the wire. ...

The electric current equation can be viewed as a convective current of electric charge that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the $mathbf{B}$ vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force. This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ...

The extension of the above considerations confirms that where $mathbf{B}$ is to $mathbf{H}$, and where $mathbf{J}$ is to ρ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that $mathbf{E}$ is to $mathbf{D}$. Ie. $mathbf{B}$ parallels with $mathbf{E}$, whereas $mathbf{H}$ parallels with $mathbf{D}$.

In SI units, $mathbf{B}$ and $mathbf{H}$ are measured in teslas (T) and amperes per metre (A/m), respectively; or, in cgs units, in gauss (G) and oersteds (Oe), respectively. Two parallel wires carrying an electric current in the same direction will generate a magnetic field that will cause a force of attraction between them. This fact is used to define the value of an ampere of electric current. See Ampere's force law and ampere. The oersted is old CGS unit of magnetic field strength (or magnetic induction). ... For other uses, see Ampere (disambiguation). ...

The fields $mathbf{B}$ and $mathbf{H}$ are also related by the equation

$mathbf{B}=mu_0(mathbf{H}+mathbf{M})$ (SI units)
$mathbf{B}=mathbf{H}+4pimathbf{M}$ (cgs units),

where $mathbf{M}$ is magnetization. Look up si, Si, SI in Wiktionary, the free dictionary. ... This article or section is in need of attention from an expert on the subject. ... Magnetization is a property of some materials (e. ...

## Force due to a magnetic field

Main article: Lorentz force

Lorentz force. ...

### Force on a charged particle

Charged particle drifts in a homogenous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (eg. gravity) (D) In an inhomgeneous magnetic field, grad H
$mathbf{F} = q (mathbf{v} times mathbf{B}),$

where Image File history File links Charged-particle-drifts. ... Image File history File links Charged-particle-drifts. ... Charged particle drifts in a homegenous magnetic field. ...

F is the force (in newtons)
q is the electric charge of the particle (in coulombs)
v is the instantaneous velocity of the particle (in metres per second)
B is the magnetic field (in teslas)
and × is the cross product.

For other uses, see Force (disambiguation). ... For other uses, see Newton (disambiguation). ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... This article is about velocity in physics. ... For the cross product in algebraic topology, see KÃ¼nneth theorem. ...

### Force on current-carrying wire

A straight, stationary wire carrying an electric current, when placed in an external magnetic field, feels a force. This force is the result of the Lorentz force (see above) acting on each electron (or any other charge carrier) moving in the wire. The formula for the total force is as follows: A wire is a single, usually cylindrical, elongated strand of drawn metal. ... This box:      Electric current is the flow (movement) of electric charge. ... Lorentz force. ...

$mathbf{F} = I mathbf{L} times mathbf{B} ,$

where

F = Force, measured in newtons
I = current in wire, measured in amperes
B = magnetic field vector, measured in teslas
$times$ = vector cross product
L = a vector, whose magnitude is the length of wire (measured in metres), and whose direction is along the wire, aligned with the direction of conventional current flow.

Alternatively, some authors write In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ...

$mathbf{F} = L mathbf{I} times mathbf{B}$

where the vector direction is now associated with the current variable, instead of the length variable. The two forms are equivalent.

If the wire is not straight but curved, the force on it can be computed by applying this formula to each infinitesimal segment of wire, then adding up all these forces via integration. Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. ... This article is about the concept of integrals in calculus. ...

The Lorentz force on a macroscopic current is often referred to as the Laplace force.

### Direction of force

The direction of force is determined by the above equations, in particular using the right-hand rule to evaluate the cross product. Equivalently, one can use Fleming's left hand rule for motion, current and polarity to determine the direction of any one of those from the other two, as seen in the example. It can also be remembered in the following way. The digits from the thumb to second finger indicate 'Force', 'B-field', and 'I(Current)' respectively, or F-B-I in short. Another similar trick is the right hand grip rule. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... Flemings left hand rule (for motors) shows the direction of the thrust on a conductor carrying a current in a magnetic field. ... The left-handed orientation is shown on the left, and the right-handed on the right. ... Flemings left hand rule (for motors) shows the direction of the thrust on a conductor carrying a current in a magnetic field. ... Prediction of direction of field (B), given that the current I flows in the direction of the thumb. ...

## Magnetic field of a steady current

Main article: Biot-Savart law
Current (I) through a wire produces a magnetic field ($mathbf{B}$) around the wire. The field is oriented according to the right hand grip rule.

The magnetic field generated by a steady current (a continual flow of charges, for example through a wire, which is constant in time and in which charge is neither building up nor depleting at any point), is described by the Biot-Savart law: The Biot-Savart law is a physical law with applications in both electromagnetics and fluid dynamics. ... Illustration of a magnetic field around a wire through which current is flowing. ... Illustration of a magnetic field around a wire through which current is flowing. ... Prediction of direction of field (B), given that the current I flows in the direction of the thumb. ... This box:      Electric current is the flow (movement) of electric charge. ... This box:      Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interaction. ... The Biot-Savart law is a physical law with applications in both electromagnetics and fluid dynamics. ...

$dmathbf{B} = frac{mu_0}{4pi} frac{I dmathbf{l} times mathbf{hat r}}{r^2}$

(in SI units), where Look up si, Si, SI in Wiktionary, the free dictionary. ...

I is the current,
$dmathbf{l}$ is a vector, whose magnitude is the length of the differential element of the wire, and whose direction is the direction of conventional current,
$dmathbf{B}$ is the differential contribution to the magnetic field resulting from this differential element of wire,
μ0 is the magnetic constant,
$mathbf{hat r}$ is the unit displacement vector from the wire element to the point at which the field is being computed, and
r is the distance from the wire element to the point at which the field is being computed.

This is a consequence of Ampere's law, one of the four Maxwell's equations. Alternatively, it can be thought of as a true, empirical law in its own right, which contributes to the derivation of Maxwell's equations. From a practical point of view, though, the law is true and useful regardless of its philosophical origin. Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. ... In electricity, current is the rate of flow of charges, usually through a metal wire or some other electrical conductor. ... The magnetic constant () is the permeability of vacuum. ... In physics, Ampères law is the magnetic equivalent of Gausss law, discovered by André-Marie Ampère. ... For thermodynamic relations, see Maxwell relations. ...

## Properties

### Magnetic field lines

Like any vector field, the magnetic field can be depicted with field lines -- a set of lines through space whose direction at any point is the direction of the local magnetic field vector, and whose density is proportional to the magnitude of the local magnetic field vector. Note that the choice of which field lines to draw in such a depiction is arbitrary, apart from the requirement that they be spaced out so that their density approximates the magnitude of the local field. The level of detail at which the magnetic field is depicted can be increased by increasing the number of lines. Vector field given by vectors of the form (âˆ’y, x) In mathematics a vector field is a construction in vector calculus which associates a vector to every point in a (locally) Euclidean space. ... Equipotential surfaces are surfaces of constant scalar potential. ...

Although any vector field can be depicted with field lines, this visualization is particularly helpful for the magnetic field (in three-dimensional space), as it makes certain aspects of it more transparent. For example, "Gauss's law for magnetism" states that the magnetic field is solenoidal (has zero divergence). This is equivalent to the simple statement that, in any field-line depiction of a magnetic field, the field lines cannot have starting or ending points; they must form a closed loop, or else extend to infinity on both ends. For thermodynamic relations, see Maxwell relations. ... In vector calculus a solenoidal vector field is a vector field v with divergence zero: This condition is clearly satisfied whenever v has a vector potential, because if then The converse holds: for any solenoidal v there exists a vector potential A such that . ... In vector calculus, the divergence is an operator that measures a vector fields tendency to originate from or converge upon a given point. ... In mathematics, a closed manifold, or compact manifold, is a manifold that is compact as a topological space. ...

Various physical phenomena have the effect of displaying field lines. For example, iron filings placed in a magnetic field will line up in such a way as to visually show magnetic field lines (see figure at top); although a close inspection will reveal that the "lines" are not quite continuous. Another place where magnetic field lines are visually displayed is in the polar auroras, in which visible streaks of light line up with the local direction of Earth's magnetic field (due to plasma particle dipole interactions). The Aurora Borealis, or Northern Lights, shines above Bear Lake Aurora Borealis as seen over Canada at 11,000m (36,000 feet) Red and green Aurora in Fairbanks, Alaska Aurora Borealis redirects here. ...

Note that when a magnetic field is depicted with field lines, it is not meant to imply that the field is only nonzero along the drawn-in field lines. The field is typically smooth and continuous everywhere, and can be estimated at any point (whether on a field line or not) by looking at the direction and density of the field lines nearby. The use of iron filings to display a field presents something of an exception to this picture: the magnetic field is in fact much larger along the "lines" of iron, due to the large permeability of iron relative to air. This article is in need of attention. ...

The direction of the magnetic field corresponds to the direction that a magnetic dipole (such as a small magnet) will orient itself in that magnetic field (see definition above). Therefore, a cluster of small particles of ferromagnetic material, such as iron filings, placed in the magnetic field will line up in such a way as to visually show the magnetic field lines (see figure at top). Another place where magnetic field lines are visually displayed is the polar auroras, in which visible streaks of light line up with the local direction of Earth's magnetic field. This article is about the electromagnetic phenomenon. ... Ferromagnetism is a phenomenon by which a material can exhibit a spontaneous magnetization, and is one of the strongest forms of magnetism. ... The Aurora Borealis, or Northern Lights, shines above Bear Lake Aurora Borealis as seen over Canada at 11,000m (36,000 feet) Red and green Aurora in Fairbanks, Alaska Aurora Borealis redirects here. ...

### Pole labelling confusions

See also North Magnetic Pole and South Magnetic Pole. Part of the Carta Marina of 1539 by Olaus Magnus, depicting the location of magnetic north vaguely conceived as Insula Magnetu[m] (Latin for Magnetic Island) off modern day Murmansk. ... The Earths South Magnetic Pole is the wandering point on the Earths surface where the geomagnetic field lines are directed vertically upwards. ...

The "north" and "south" poles of a magnet or a magnetic dipole are labelled similarly to north and south poles of a compass needle. Near the north pole of a bar or a cylinder magnet, the magnetic field vector is directed out of the magnet; near the south pole, into the magnet. This magnetic field continues inside the magnet (so there are no actual "poles" anywhere inside or outside of a magnet where the field stops or starts). Breaking a magnet in half does not separate the poles but produces two magnets with two poles each.

Earth's magnetic field is probably produced by electric currents in its liquid core. The magnetosphere shields the surface of the Earth from the charged particles of the solar wind. ... This box:      Electric current is the flow (movement) of electric charge. ...

## Rotating magnetic fields

Main article: Alternator

The rotating magnetic field is a key principle in the operation of alternating-current motors. A permanent magnet in such a field will rotate so as to maintain its alignment with the external field. This effect was conceptualized by Nikola Tesla, and later utilised in his, and others, early AC (alternating-current) electric motors. 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, in order 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 will 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. Early 20th century Alternator made in Budapest, Hungary, in the power generating hall of a hydroelectric station. ... For other kinds of motors, see motor. ... Nikola Tesla (1856-1943)[1] was a world-renowned Serbian inventor, physicist, mechanical engineer and electrical engineer. ...

Because magnets degrade with time, synchronous motors 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. A synchronous electric motor is distinguished by its rotor spinning at the same rate as the oscillating field which drives it. ... Induction Motor (IM) is one kind of AC motor where power is supplied to the rotating device by induction. ... The rotor is the non-stationary part of a rotary electric motor or alternator, which rotates because the wires and magnetic field of the motor are arranged so that a torque is developed about the rotors axis. ... The stator is the fixed part of a rotating machine. ... As the circular plate moves down through a small region of constant magnetic field directed into the page, eddy currents are induced in the plate. ...

In 1882, Nikola Tesla identified the concept of the rotating magnetic field. In 1885, Galileo Ferraris independently researched the concept. In 1888, Tesla gained U.S. Patent 381,968  for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin. Year 1882 (MDCCCLXXXII) was a common year starting on Sunday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Friday of the 12-day slower Julian calendar). ... 1885 (MDCCCLXXXV) is a common year starting on Thursday of the Gregorian calendar (or a common year starting on Saturday of the 12-day slower Julian calendar). ... Galileo Ferraris (October 30, 1847 - February 7, 1897) was an Italian physicist and electrical engineer, noted mostly for his studies on alternating current. ... For the toll-free telephone number see Toll-free telephone number Year 1888 (MDCCCLXXXVIII) was a leap year starting on Sunday (click on link for calendar) of the Gregorian calendar (or a leap year starting on Friday of the 12-day slower Julian calendar). ... For other uses, see Turin (disambiguation). ...

## Hall effect

Main article: Hall effect

Because the Lorentz force is charge-sign-dependent (see above), it results in charge separation when a conductor with current is placed in a transverse magnetic field, with a buildup of opposite charges on two opposite sides of conductor in the direction normal to the magnetic field, and the potential difference between these sides can be measured. Hall effect diagram, showing electron flow (rather than conventional current). ... Lorentz force. ...

The Hall effect is often used to measure the magnitude of a magnetic field as well as to find the sign of the dominant charge carriers in semiconductors (negative electrons or positive holes). Hall effect diagram, showing electron flow (rather than conventional current). ...

## Special relativity and electromagnetism

Main article: Relativistic electromagnetism

According to special relativity, electric and magnetic forces are part of a single physical phenomenon, electromagnetism; an electric force perceived by one observer will be perceived by another observer in a different frame of reference as a mixture of electric and magnetic forces. A magnetic force can be considered as simply the relativistic part of an electric force when the latter is seen by a moving observer. Relativistic electromagnetism is the idea of explaining electromagnetism based on relativistic (Albert Einstein 1905) arguments. ... For a less technical and generally accessible introduction to the topic, see Introduction to special relativity. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field. ...

More specifically, rather than treating the electric and magnetic fields as separate fields, special relativity shows that they naturally mix together into a rank-2 tensor, called the electromagnetic tensor. This is analogous to the way that special relativity "mixes" space and time into spacetime, and mass, momentum and energy into four-momentum. In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... For other uses of this term, see Spacetime (disambiguation). ... It has been suggested that this article or section be merged with Momentum#Momentum_in_relativistic_mechanics. ...

## Magnetic field shape descriptions

Schematic quadrupole magnet("four-pole") magnetic field. There are four steel pole tips, two opposing magnetic north poles and two opposing magnetic south poles.
• 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.[4]
• A dipole magnetic field is one seen around a bar magnet or around a 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.

General

Mathematics In physics, the space surrounding an electric charge or in the presence of a time-varying magnetic field has a property called an electric field. ... The electromagnetic field is a physical field that is produced by electrically charged objects and which affects the behaviour of charged objects in the vicinity of the field. ... Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles. ... For other senses of this word, see magnetism (disambiguation). ... Magnetohydrodynamics (MHD) (magnetofluiddynamics or hydromagnetics) is the academic discipline which studies the dynamics of electrically conducting fluids. ... Magnetic flux, represented by the Greek letter Î¦ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field. ... In physics, a magnetic monopole is a hypothetical particle that may be loosely described as a magnet with only one pole (see electromagnetic theory for more on magnetic poles). ... Magnetic reconnection is the process whereby magnetic field lines from different magnetic domains are spliced to one another, changing the overall topology of a magnetic field. ... In physics, the magnetic potential is a method of representing the magnetic field by using a potential value instead of the actual vector field. ... ...

• Ampère's law — magnetic equivalent of Gauss's law.
• Biot-Savart law — the magnetic field set up by a steadily flowing line current.
• Magnetic helicity — extent to which a magnetic field "wraps around itself".
• Maxwell's equations — four equations describing the behavior of the electric and magnetic fields, and their interaction with matter.

Applications An electric current produces a magnetic field. ... The Biot-Savart law is a physical law with applications in both electromagnetics and fluid dynamics. ... this page is about helicity in magnetic fields. ... For thermodynamic relations, see Maxwell relations. ...

• Helmholtz coil — a device for producing a region of nearly uniform magnetic field.
• Maxwell coil — a device for producing a large volume of almost constant magnetic field.
• Earth's magnetic field — a discussion of the magnetic field of the Earth.
• Dynamo theory — a proposed mechanism for the creation of the Earth's magnetic field.
• Electric motor — AC motors used magnetic fields.
• Rapid-decay theory - a creationist theory.
• Stellar magnetic field — a discussion of the magnetic field of stars.
• Teltron Tube

A Helmholtz coil The term Helmholtz coils refers to a device for producing a region of nearly uniform magnetic field. ... Maxwell coil layout in cylindrical coordinates. ... The magnetosphere shields the surface of the Earth from the charged particles of the solar wind. ... The Dynamo theory proposes a mechanism by which a celestial body such as the Earth generates a magnetic field. ... For other kinds of motors, see motor. ... The rapid-decay theory proposes a mechanism by which a celestial body, such as the Earth, generates a magnetic field and leads to the conclusion that the Earth is no older than 10,000 years. ... The magnetic field of the Sun is driving this massive ejection of plasma. ... This article is a stub Overview A teltron tube is used to fire electrons. ...

## References

Web

Books Year 2006 (MMVI) was a common year starting on Sunday of the Gregorian calendar. ... is the 306th day of the year (307th in leap years) in the Gregorian calendar. ...

• Durney, Carl H. and Johnson, Curtis C. (1969). Introduction to modern electromagnetics. McGraw-Hill. ISBN 0-07-018388-0.
• Rao, Nannapaneni N. (1994). Elements of engineering electromagnetics (4th ed.). Prentice Hall. ISBN 0-13-948746-8.
• Griffiths, David J. (1999). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X.
• Jackson, John D. (1999). Classical Electrodynamics (3rd ed.). Wiley. ISBN 0-471-30932-X.
• Tipler, Paul (2004). Physics for Scientists and Engineers: Electricity, Magnetism, Light, and Elementary Modern Physics (5th ed.). W. H. Freeman. ISBN 0-7167-0810-8.
• Furlani, Edward P. (2001). Permanent Magnet and Electromechanical Devices: Materials, Analysis and Applications. Academic Press Series in Electromagnetism. ISBN 0-12-269951-3.

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## Notes

1. ^ http://en.allexperts.com/q/Physics-1358/magnetic-field-lines-depicted.htm
2. ^ Magnetic Field Strength is also sometimes called Magnetic Field Intensity. For more information reference the sources Durney and Johnson, and also Rao.
3. ^ The standard graduate textbook by Jackson follows this usage. Edward Purcell, in Electricity and Magnetism, McGraw-Hill, 1963, writes, Even some modern writers who treat B as the primary field feel obliged to call it the magnetic induction because the name magnetic field was historically preempted by H. This seems clumsy and pedantic. If you go into the laboratory and ask a physicist what causes the pion trajectories in his bubble chamber to curve, he'll probably answer "magnetic field," not "magnetic induction." You will seldom hear a geophysicist refer to the earth's magnetic induction, or an astrophysicist talk about the magnetic induction of the galaxy. We propose to keep on calling B the magnetic field. As for H, although other names have been invented for it, we shall call it "the field H" or even "the magnetic field H".
4. ^ The Solar Dynamo, retrieved Sep 15, 2007.

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