Magnetic field

For the indie-pop band, see The Magnetic Fields. The Magnetic Fields is a band led by New York City singer-songwriter Stephin Merritt.

Electromagnetism

Electricity · Magnetism

Magnetostatics
· Ampère’s law · Electric current · Magnetic field · Magnetic flux · Biot–Savart law · Magnetic dipole moment · Gauss’s law for magnetism ·

This box: view • talk • edit

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.

Magnetic field lines shown by iron filings. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Magnetostatics is the study of static Magnetic fields In Electrostatics the charges are stationary whereas here the currents are stationary or dc(direct In Classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère, relates the integrated Magnetic field around a closed Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic The Biot–Savart Law is an equation in electromagnetism that describes the Magnetic field B generated by an Electric current. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current A field line is a Locus that is defined by a Vector field and a starting location within the field Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 The high permeability of individual iron filings causes the magnetic field to be larger at the ends of the filings. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. 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. Magnetization is defined as the quantity of Magnetic moment per unit volume

In physics, a magnetic field is a field that permeates space and which can exert a magnetic force on moving electric charges and on magnetic dipoles (such as permanent magnets). Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a 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). A magnet (from Greek grc μαγνήτης λίθος " Magnesian stone" is a material or object that produces a Magnetic field. In addition, a changing magnetic field can induce an electric field. 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 (that can Magnetic fields surround and are created by electric currents, magnetic dipoles, and changing electric fields. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. 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 (that can Magnetic fields also have their own energy, with an energy density proportional to the square of the field intensity. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός

There are some notable specific instances of the magnetic field. For the physics of magnetic materials, see magnetism and magnet, and more specifically ferromagnetism, paramagnetism, and diamagnetism. In Physics, magnetism is one of the Phenomena by which Materials exert attractive or repulsive Forces on other Materials. A magnet (from Greek grc μαγνήτης λίθος " Magnesian stone" is a material or object that produces a Magnetic field. Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it Paramagnetism is a form of magnetism which occurs only in the presence of an externally applied magnetic field Diamagnetism is the property of an object which causes it to create a magnetic field in opposition of an externally applied Magnetic field, thus causing a repulsive effect For constant magnetic fields, such as are generated by stationary dipoles and steady currents, see magnetostatics. Magnetostatics is the study of static Magnetic fields In Electrostatics the charges are stationary whereas here the currents are stationary or dc(direct For magnetic fields created by changing electric fields, see electromagnetism. Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of

The electric field and the magnetic field are tightly interlinked, in two senses. 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 (that can First, changes in either of these fields can cause ("induce") changes in the other, according to Maxwell's equations. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric 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). Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial In Physics, an inertial frame of reference is a Frame of reference which belongs to a set of frames in which Physical laws hold in the same and simplest Relativistic electromagnetism is the idea of explaining Electromagnetism based on relativistic ( Albert Einstein 1905 arguments Together, these two fields make up the electromagnetic field, which is best known for underlying light and other electromagnetic waves. The electromagnetic field is a physical field produced by electrically charged objects. Light, or visible light, is Electromagnetic radiation of a Wavelength that is visible to the Human eye (about 400–700 Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter.

1 B and H
- 1.1 Alternative Names for B and H
- 1.2 Units
2 Permanent magnets and magnetic poles
3 Visualizing the Magnetic Field
- 3.1 Magnetic B field lines
- 3.2 Pole labeling confusions
4 Definition of B
5 Effects of the Magnetic Field, B
6 Sources of Magnetic Fields
7 The H Field
8 Rotating magnetic fields
9 Hall effect
10 Special relativity and electromagnetism
11 Magnetic field shape descriptions
12 See also
13 References
14 Notes
15 External links

B and H

There are two quantities that physicists may refer to as the magnetic field, notated $\mathbf{H}$ and $\mathbf{B}$ . 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. Most modern writers refer to $\mathbf{B}$ as the magnetic field. See: ^[1] This article will follow that convention and will discuss the more fundamental $\mathbf{B}$ magnetic field, before treating the $\mathbf{H}$ field.

See History of B and H below for further discussion.

Alternative Names for B and H

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. Electrical engineering, sometimes referred to as electrical and electronic engineering, is a field of Engineering that deals with the study and application of The vector field $\mathbf{B}$ is known as magnetic flux density or magnetic induction or simply magnetic field, as used by physicists.

Units

Main articles: Tesla (unit), Gauss (unit), and Oersted

The magnetic field $\mathbf{B}$ has the SI units of teslas (T), equivalent to webers (Wb) per square meter or volt seconds per square meter. The tesla (symbol T) is the SI derived unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic The gauss, abbreviated as G is the Cgs unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic Oersted (abbreviated as Oe) is the unit of magnetizing field (also known as magnetic field strength or intensity in the CGS system of units The tesla (symbol T) is the SI derived unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic In Physics, the weber (symbol Wb ˈveɪbɚ ˈwiːbɚ is the SI unit of Magnetic flux. The volt (symbol V) is the SI derived unit of electric Potential difference or Electromotive force. (Since magnetic flux has the SI units of webers, and the $\mathbf{B}$ field is the areal density of magnetic flux, it makes sense that the unit of $\mathbf{B}$ should be equivalent to webers per square meter. Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic )^[2]^[3]^[4] In cgs units, $\mathbf{B}$ has units of gauss. The centimetre-gram-second system ( CGS) is a system of physical units. The gauss, abbreviated as G is the Cgs unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic

The vector field $\mathbf{H}$ is measured in Amperes/meter (SI units) or oersted (cgs units). The ampere, in practice often shortened to amp, (symbol A is a unit of Electric current, or amount of Electric charge per second The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International Oersted (abbreviated as Oe) is the unit of magnetizing field (also known as magnetic field strength or intensity in the CGS system of units

Permanent magnets and magnetic poles

The direction of the magnetic field near the poles of a magnet is revealed by placing compasses nearby. A compass, magnetic compass or mariner's compass is a navigational instrument for determining direction relative to the earth's Magnetic poles It consists As seen here, the magnetic field points towards a magnet's south pole and away from its north pole.

Main article: Magnet

Permanent magnets are objects that produce their own persistent magnetic fields. A magnet (from Greek grc μαγνήτης λίθος " Magnesian stone" is a material or object that produces a Magnetic field. A magnet (from Greek grc μαγνήτης λίθος " Magnesian stone" is a material or object that produces a Magnetic field. All permanent magnets have both a north and a south pole. (Magnetic poles always come in north-south pairs. ) Like poles repel and opposite poles attract. (See Force on a magnetic dipole due to a non-uniform B below. ) The magnetism in a permanent magnet arises from properties of the atoms (in particular the electrons) that compose it; in particular, it turns out that each atom is a little individual magnet, and when these magnets line up, they combine to create a macroscopic magnetic effect. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J For more details about what happens both microscopically and macroscopically, see the article ferromagnetism. Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it

If allowed to twist freely, a magnet will turn to point in the direction of the magnetic field at its location. (See Torque on a magnetic dipole below. ) A compass is a small magnet that uses this effect to point in the direction the local magnetic field. A compass, magnetic compass or mariner's compass is a navigational instrument for determining direction relative to the earth's Magnetic poles It consists By definition, the direction of the magnetic field at a point is the direction that the north pole of a magnet would want to point.

If a compass is placed near the north pole of a magnet then it will point away from that pole---like poles repel. In other words, the magnetic field points away from a magnet near its north pole. The opposite occurs if we place the compass near a magnet's south pole; the magnetic field points towards the magnet near its south pole. Not all magnetic fields are describable in terms of poles, though. A straight current-carrying wire, for instance, produces a magnetic field that points neither towards nor away from the wire, but encircles it instead. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. A wire is a single usually cylindrical, elongated string of drawn Metal.

Visualizing the Magnetic Field

The strength and direction of the magnetic field due to an object varies from position to position. If one wanted to map out a magnetic field, they could in principle measure the strength and direction of the magnetic field at a large number of points. They could then mark each location with an arrow (called [[vector (spatial)|vector]s whose direction points in the direction of the magnetic field and whose length is proportional to the strength of the magnetic field. This is a valid and useful way of marking out and visualizing the magnetic field of an object. It has the unfortunate consequence, though, of cluttering up a graph even when using a small number of points. An alternative method of visualizing the magnetic field is to use magnetic field lines.

Magnetic B field lines

Various physical phenomena have the effect of displaying magnetic field line. For example, iron filings placed in a magnetic field will line up in such a way as to visually show the orientation of the magnetic field (see figure at top). Another place where magnetic fields 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). In these phenomena, the direction of the magnetic field is revealed by the direction that a magnetic dipole (such as a small magnet) will orient itself in that magnetic field (see definition below). In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a

These field lines provide us with a way to depict or draw the magnetic field (or any other vector field). A field line is a Locus that is defined by a Vector field and a starting location within the field In Mathematics a vector field is a construction in Vector calculus which associates a vector to every point in a (locally Euclidean space. Technically, field lines are a set of lines through space whose direction at any point is the direction of the local magnetic field, and whose density is proportional to the magnitude of the local magnetic field. 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. ^[5] 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 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.

This visualization is particularly helpful for the magnetic field, as it makes certain aspects of it more transparent. For example, consider the field lines around the magnet in the above figure. Notice that all the magnetic field lines start at one end of the magnet and end at the other. If we were able to trace out the entire field lines we would note that they extend through the magnet to form a complete loop. Examining the magnetic field around a current carrying wire we notice magnetic field lines the formed complete loops around the wire. In fact, this is a general rule about magnetic fields; they either make a complete circle or extend out to infinity. Magnetic field lines cannot have starting or ending points. This is mathematically equivalent to Gauss's law for magnetism which states that the magnetic field is solenoidal (has zero divergence). In Vector calculus a solenoidal vector field (also known as an incompressible vector field) is a Vector field v with Divergence zero In Vector calculus, the divergence is an Operator that measures the magnitude of a Vector field &rsquos source or sink at a given point the Further when we examine the magnetic field loops we will see that within the loops there is always some source that is creating the magnetic field. This source could be a current, a dipole or magnet, or a changing electric field but it is always within the loops of magnetic field they create.

Since magnetic field lines always come in loops, magnetic poles always come in N and S pairs. If a magnetic field line enters a magnet somewhere it has to leave the magnet somewhere else, since it is not allowed to end. For this reason as well, cutting a magnet in half will result in two separate magnets each with both a north and a south pole.

Pole labeling confusions

A sketch of Earth's magnetic field representing the source of Earth's magnetic field as a magnet. Notice that the south pole of that magnet is deep in Earth's interior below Earth's North Magnetic Pole. The Earth's North Magnetic Pole is the wandering point on the Earth's surface at which the Earth's magnetic field points vertically downwards (i Earth's magnetic field is produced in the outer liquid part of its core due to a dynamo that produce electrical currents there. A dynamo, originally another name for an Electrical generator, now means a generator that produces Direct current with the use of a commutator.

Main article: Earth's magnetic field

See also North Magnetic Pole and South Magnetic Pole. Earth 's magnetic field (and the surface magnetic field) is approximately a Magnetic dipole, with one pole near the North pole (see The Earth's North Magnetic Pole is the wandering point on the Earth's surface at which the Earth's magnetic field points vertically downwards (i The Earth 's South Magnetic Pole is the wandering point on the Earth's surface where the geomagnetic field lines are directed vertically upwards

Placed anywhere on Earth the north pole of a compass will point roughly North toward Earth's North Magnetic Pole. The Earth's North Magnetic Pole is the wandering point on the Earth's surface at which the Earth's magnetic field points vertically downwards (i This may be considered the definition of the north pole of a magnet. The fact that the compass turn in this manner is proof that Earth has a magnetic field deep in its interior. This definition of the north pole of a magnet is unfortunate since the north pole of a compass points in a direction that leads to the 'south pole of a magnet. (Opposites attract. ) Earth's magnetic field is such that its south pole is directly beneath the north magnetic pole deep in its interior. The north magnetic pole is so named not because of the polarity of the field there but because of its geological location.

The figure to the right is a sketch of Earth's magnetic field. The direction of Earth's magnetic field is represented by the field lines. Notice that the magnetic field at any given point does not point straight toward (or away) from the poles but has a significant up/down component. (In addition, there is an East/West component as Earth's magnetic poles do not coincide exactly with Earth's geological pole. ) Notice that the magnetic field is actually produced by a 'magnet' that is deep in Earth's interior.

The Earth's magnetic field is probably due to a dynamo that produces electric currents in the outer liquid part of its core. Earth 's magnetic field (and the surface magnetic field) is approximately a Magnetic dipole, with one pole near the North pole (see A dynamo, originally another name for an Electrical generator, now means a generator that produces Direct current with the use of a commutator. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. Earth's magnetic field is not constant. Its strength and the location of its poles vary. The poles even periodically reverse direction. A geomagnetic reversal is a change in the orientation of Earth's magnetic field such that the positions of magnetic north and magnetic south become interchanged The Earth's magnetic field is currently getting weaker and maybe about to start this reversal process.

Definition of B

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-meter) and cgs units of gauss. In Mathematics a vector field is a construction in Vector calculus which associates a vector to every point in a (locally Euclidean space. The newton (symbol N) is the SI derived unit of Force, named after Isaac Newton in recognition of his work on Classical The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units The coulomb (symbol C) is the SI unit of Electric charge. It is named after Charles-Augustin de Coulomb. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International The centimetre-gram-second system ( CGS) is a system of physical units. The gauss, abbreviated as G is the Cgs unit of Magnetic field B (which is also known as "magnetic flux density" and "magnetic It has the property of being a solenoidal vector field. In Vector calculus a solenoidal vector field (also known as an incompressible vector field) is a Vector field v with Divergence zero (The term solenoidal means that the field lines always formed closed loops, as described above. )

The field $\mathbf{B}$ can be both defined and measured by means of a small magnetic dipole (i. e. , bar magnet). A magnet (from Greek grc μαγνήτης λίθος " Magnesian stone" is a material or object that produces a Magnetic field. 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. A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about A compass, magnetic compass or mariner's compass is a navigational instrument for determining direction relative to the earth's Magnetic poles It consists 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 $|\mathbf{B}|$ .

(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. In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric )

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 two vectors in a three-dimensional Euclidean space that results in another vector which In Physics and Mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation but gains an In Physics and Mathematics, a pseudovector (or axial vector) is a quantity that transforms like a vector under a proper rotation but gains an

Effects of the Magnetic Field, B

The magnetic field at a point can reveal itself in 4 different ways.

Sideways force on a moving charge or current
Torque on a magnetic dipole
Force on a magnetic dipole due to a non-uniform B
force due to a changing B

Charged particle drifts in a homogenous magnetic field. (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (e.g. gravity) (D) In an inhomogeneous magnetic field, grad H

Charged particle drifts in a homogenous magnetic field. In many cases of practical interest the motion in a Magnetic field of an electrically charged particle (such as an Electron or Ion in a plasma (A) No disturbing force (B) With an electric field, E (C) With an independent force, F (e. g. gravity) (D) In an inhomogeneous magnetic field, grad H

Force due to a magnetic field on a moving charge

Main article: Lorentz force

Force on a charged particle

A charged particle moving in a magnetic field will feel 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. In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation This force is known as the Lorentz Force. In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation The force is always perpendicular to both the velocity of the particle and the magnetic field that created it. Neither a stationary particle nor one moving in the direction of the magnetic field line $\mathbf{B}$ will experience a force. For that reason, charged particles move in a helix along magnetic field lines. (The continuous sideways force due to the magnetic field will cause it to change direction continuously but not speed up nor slow down. ) Because the magnetic field is always perpendicular to the motion magnetic fields can do no work on a moving charge. Therefore magnetic fields cannot change the energy of a simple charged particle. It can, however, change the direction of a particle, so that a force applied in one direction will cause the particle to drift in a perpendicular direction. (See above figure. )

Force on current-carrying wire

The force on a current carrying wire is similar to that of a moving charge as expected since a charge carrying wire is a collection of moving charges. A current carrying wire will feel a sideways force in the presence of a magnetic field. The Lorentz force on a macroscopic current is often referred to as the Laplace force. In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation

The right-hand rule: For a positive current or moving positive charge in the direction of the thumb of the right hand and the magnetic field along the direction of the fingers (pointing away from palm) the force on the current will be in a direction out of the palm. The direction of the force is reversed for a negative charge or current.

Direction of force

The direction of force on a positive charge or a current is determined by the right-hand rule. For the related yet different principle relating to electromagnetic coils see Right hand grip rule. See the figure on the right. Using the right hand and pointing the thumb in direction of the moving positive charge or positive current and the fingers in the direction of the magnetic field the resulting force on the charge will point outwards from the palm. The force on a negative 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 (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 will produce the same current. ) A magnetic field combined with an electric field can distinguish between current made of positive charge and that made of negative charge, but only by measuring the sign of the (sideways to the current) charge build up. (See the above figure part B, where the direction of the electric field corresponds to the direction of a moving current. ) This phenomenon is known as the Hall effect. Another similar trick to the right hand rule is the right hand grip rule. For the related yet different principle relating to electromagnetic coils see Right-hand rule.

Torque on a magnetic dipole

A magnet placed in a magnetic field will feel a torque that will try to align the magnet with the magnetic field. A torque (τ in Physics, also called a moment (of force is a pseudo- vector that measures the tendency of a force to rotate an object about The torque on a magnet due to an external magnetic field is easy to observe by placing two magnets near each other while allowing one to rotate. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current This magnetic torque is the basis for how compasses work. A compass, magnetic compass or mariner's compass is a navigational instrument for determining direction relative to the earth's Magnetic poles It consists It is used to define the direction of the magnetic field (see above).

The magnetic torque also provides the driving torque for simple electric motors. An electric motor uses Electrical energy to produce Mechanical energy. By attaching a magnet to a shaft we can cause the magnet to rotate by placing an external magnetic field that causes it to twist. The simplest way to do this is to place the north pole of an external magnet near the north pole of the rotating magnet (called the rotor) and a south pole of the external magnet near the south pole of the rotor. ROTOR was a huge and elaborate air defence Radar system built by the British Government in the early 1950s to counter possible attack by Soviet Bombers If we use an electromagnet we can continually flip the poles of the external stationary magnet (called the stator) causing the rotor to turn as long as the poles of the stator are being flipped. An electromagnet is a type of Magnet in which the Magnetic field is produced by the flow of an electric current. The stator is the stationary part of an Electric generator or Electric motor.

See Rotating magnetic fields below for an example using this effect with electromagnets.

Force on a magnetic dipole due to a non-uniform B

The most commonly experienced effect of the magnetic field is the force between two magnets. Like poles repel and opposites attract. One, in principle, could express this force in terms of the poles having a positive (north pole) or negative (south pole) charge. This model is called the Gilbert model and produces the correct $\mathbf{B}$ field outside of the magnet. Unfortunately, this model predicts the wrong magnetic field inside a magnet. (Due to its relative simplicity the Gilbert model is still useful as long as nothing depends on the magnetic $\mathbf{B}$ field inside a magnet. )

Expressing the same force between two magnets using the magnetic $\mathbf{B}$ field is more complicated. For example, a uniform magnetic field will not cause a force on an external magnet. The south pole of a magnet is attracted to the north pole of the magnet because the field is stronger closer to the magnet. ^[6] The force on a magnetic dipole depends not on the strength nor direction of the magnetic $\mathbf{B}$ field but how it varies with location. A magnet will move to maximize the magnetic field in the direction of its magnetic moment. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current

Care should be taken to distinguish the magnetic force on a magnetic dipole from the magnetic force on a moving charge. The magnetic force on a charge only occurs when the charge is moving and is in a sideways direction. It is felt for uniform and non-uniform magnetic fields. The magnetic force on a dipole, on the other hand, is present only in non-uniform (in space) fields and is in the direction that increases magnetic field strength in the same direction as the magnetic moment of the magnet. In Physics, Astronomy, Chemistry, and Electrical engineering, the term magnetic moment of a system (such as a loop of Electric current . Neither does the force on a magnetic dipole depend on its speed.

Electric force due to a changing B

Main article: Faraday's law of induction

If the magnetic field in an area is varying with time it generates an electric field that forms closed loops around that area. Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of A conducting wire that forms a closed loop around the area will have an induced voltage generated by this changing magnetic field. This effect is represented mathematically as Faraday's Law and forms the basis of generators. Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of In Electricity generation, an electrical generator is a device that converts Mechanical energy to Electrical energy, generally using Electromagnetic Indeed, Faraday's Law forms the basis of modern civilization in that it allows the conversion of mechanical energy to electrical energy. Care must be taken to understand that the changing magnetic field is a source for an extended electric field. The changing magnetic field does not only create an electric field at that location; rather it generates an electric field that forms closed loops around the location where the magnetic field is changing.

Mathematically, Faraday's law is most often represented in terms of the change of magnetic flux with time. The magnetic flux is the property of a closed loop (say of a coil of wire) and is the product of the area times the magnetic field that is normal to that area. Engineers and physicists often use magnetic flux as a convenient physical property of a loop(s). They then express the magnetic $\mathbf{B}$ field as the magnetic flux per unit area. It is for this reason that the $\mathbf{B}$ field is often referred to as the magnetic flux density. This approach has the benefit of making certain calculations easier such as in magnetic circuits. A magnetic circuit is a closed path containing a Magnetic flux. It is typically not used outside of electrical circuits, though, because the magnetic $\mathbf{B}$ field truly is the more 'fundamental' quantity in that it directly connects all of electrodynamics in the simplest manner.

Sources of Magnetic Fields

Magnetic $\mathbf{B}$ fields, essentially, are generated by currents of electrical charge. We say that currents are sources for magnetic fields. Altogether there are 4 sources for magnetic fields—the last is only hypothetical:

Electrical currents (moving charges)
Magnetic dipoles
Changing electric field
Magnetic monopole (hypothetical)

Electrical currents (moving charges)

All moving charges produce a magnetic field. ^[7] The magnetic field of a moving charge is very complicated but is well known. (See Jefimenko's equations. Jefimenko's equations describe the behavior of the electric and Magnetic fields in terms of the sources at Retarded times Combined with the Continuity ) It forms closed loops around a line that is pointing in the direction the charge is moving. The magnetic field of a current on the other hand is much easier to calculate.

Magnetic field of a steady current

Main article: Biot-Savart law

Current (I) through a wire produces a magnetic field () around the wire. The field is oriented according to the right hand grip rule.

Current (I) through a wire produces a magnetic field ( $\mathbf{B}$ ) around the wire. The Biot–Savart Law is an equation in electromagnetism that describes the Magnetic field B generated by an Electric current. The field is oriented according to the right hand grip rule. For the related yet different principle relating to electromagnetic coils see Right-hand 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. Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. The Biot–Savart Law is an equation in electromagnetism that describes the Magnetic field B generated by an Electric current. ^[8] This is a consequence of Ampere's law, one of the four Maxwell's equations that describe electricity and magnetism. In Classical electromagnetism, Maxwell's equations are a set of four Partial differential equations that describe the properties of the electric The magnetic field lines generated by a current carrying wire form concentric circles around the wire. The direction of the magnetic field of the loops is determined by the right hand grip rule. For the related yet different principle relating to electromagnetic coils see Right-hand rule. (See figure to the right. ) The strength of the magnetic field decreases with distance from the wire.

A current carrying wire can be bent in a loop such that the field is concentrated (and in the same direction) inside of the loop. The field will be weaker outside of the loop. Stacking many such loops to form a solenoid (or long coil) can greatly increase the magnetic field in the center and decrease the magnetic field outside of the solenoid. Such devices are called electromagnets and are extremely important in generating strong and well controlled magnetic fields. An electromagnet is a type of Magnet in which the Magnetic field is produced by the flow of an electric current. An infinitely long solenoid will have a uniform magnetic field inside of the loops and no magnetic field outside. A finite length electromagnet will produce essentially the same magnetic field as a uniform permanent magnet of the same shape and size. An electromagnet has the advantage, though, that you can easily vary the strength (even creating a field in the opposite direction) simply by controlling the input current. One important use is to continually switch the polarity of a stationary electromagnet to force a rotating permanent magnet to continually rotate using the fact that opposite poles attract and like poles repel. This can be used to create an important type of electrical motor.

Magnetic dipoles

Main article: Magnetic dipole

Magnetic field lines around a ”magnetostatic dipole” the magnetic dipole itself is in the center and is seen from the side. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a

The magnetic field due to a permanent magnet is well known. (See the first figure of article. ) But, what causes the magnetic field of a permanent magnet? The answer again is that the magnetic field is essentially created due to currents. But this time it is due to the cumulative effect of many small 'currents' of electrons 'orbiting' the nuclei of the magnetic material. Alternatively it is due to the structure of the electron itself which, in some sense, we can think of as forming a tiny loop of current. (The true nature of the electron's magnetic field is relativistic in nature, but this model often works. Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial ) Both of these tiny loops are modeled in terms of what we call the magnetic dipole. We can define the dipole moment of that dipole as the current times the area of the loop, then derive an equation for the magnetic field due to that magnetic dipole. (See the above image for what that magnetic field looks like. ) By adding up the magnetic fields of many magnetic dipoles we can calculate the magnetic field of a larger magnet.

Changing electric field

Main article: Ampere's Law

The final known source of magnetic fields is a changing electric field. In Classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère, relates the integrated Magnetic field around a closed Just as a changing magnetic field generates an electric field so does a changing electric field generate a magnetic field. (Together these two effects bootstrap together to form and electromagnetic wave, light. ) Similar to the way magnetic field lines formed close loops around current and to the way that electric field lines form closed loops around areas where the magnetic $\mathbf{B}$ field is changing, a changing (with time) electric field generates a magnetic field that forms closed loops around the region where the electric field is changing. Since the changing electric field causes the same indistinguishable magnetic field as a current in that region (and because of the prevailing yet incorrect ether model of electrodynamics at that time) this source of magnetic $\mathbf{B}$ field is known as 'displacement current'. See also the disambiguation page for Aether. Alchemy, Natural philosophy, and early modern Physics proposed the existence ^[9] The fact that a changing electric field creates a magnetic field is known as Maxwell's correction to Ampere's Law. In Classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère, relates the integrated Magnetic field around a closed

Magnetic monopole (hypothetical)

The magnetic monopole is a hypothetical particle that has not been found and may or may not exist. A magnetic monopole has, as it name suggests, only one pole. It is essentially a magnetic charge. It would either be a magnetic north pole corresponding to a positive magnetic charge or a magnetic south pole corresponding to a negative magnetic charge. To date, no one has found an isolated magnetic pole despite effort to discover it. Magnetic poles always come in pairs due to currents of electrical charge. The reason for the search is that if just one magnetic monopole was found then it would provide a reason due to quantum mechanics for the quantization of electrical charge. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons

The H Field

See also: Magnetization

The term 'magnetic field' can also be used to describe the magnetic $\mathbf{H}$ field. Magnetization is defined as the quantity of Magnetic moment per unit volume The magnetic $\mathbf{H}$ field is a vector field similar to the magnetic $\mathbf{B}$ field except with different units and is completely different than the magnetic $\mathbf{B}$ field in the interior of a magnetic material. In SI units, $\mathbf{B}$ and $\mathbf{H}$ are measured in teslas (T) and amperes per meter (A/m), respectively; or, in cgs units, in gauss (G) and oersteds (Oe), respectively. Oersted (abbreviated as Oe) is the unit of magnetizing field (also known as magnetic field strength or intensity in the CGS system of units The fields $\mathbf{B}$ and $\mathbf{H}$ are related by the equation

$\mathbf{B}=\mu_0(\mathbf{H}+\mathbf{M})$ (SI units)

$\mathbf{B}=\mathbf{H}+4\pi\mathbf{M}$ (cgs units),

where $\mathbf{M}$ is magnetization of any magnetic material. The centimetre-gram-second system ( CGS) is a system of physical units. Magnetization is defined as the quantity of Magnetic moment per unit volume Since magnetization exists only where there is magnetic material the form of $\mathbf{H}$ varies from $\mathbf{B}$ only inside a magnetic material. Outside of magnetic material $\mathbf{B}$ and $\mathbf{H}$ differ only by a multiplicative constant.

Physical Interpretation of the H field

It is often important to distinguish between two different types of currents: free current and bound current. Magnetization is defined as the quantity of Magnetic moment per unit volume Magnetization is defined as the quantity of Magnetic moment per unit volume Free currents are currents that can be directly controlled and easily measured, for instance by changing the voltage applied to the wire. Bound currents are, as their name implies, bound to magnetic materials. As an example of bound current consider a uniform permanent bar magnet. A bar magnet is formed by many tiny magnets called magnetic dipoles each of which is essentially a tiny loop of current. By lining up a huge number of these dipoles we can create a large magnetic field. If we add up the currents of all these tiny loops we will find that the currents cancel in the interior of the bar magnet but add up along the outside edge of the bar magnet. (This current loops around the sides and not at the poles. ) No one charge makes the complete trip around the magnet (each charge is bound to their tiny loop) but the net effect is a real current that flows on the outside of the magnet. (If the magnetization is not uniform then a bound current will flow through the bulk of the magnetic material as well. )

The magnetic $\mathbf{H}$ is useful because it treats these two types of currents differently. The free currents it treats in the normal fashion and therefore has the same form as the magnetic $\mathbf{B}$ field it would generate. The magnetic $\mathbf{H}$ fields treats the field inside of a magnetic material (due to that magnetic material) in a manner similar to the Gilbert model. (By subtracting the magnetization from the B field we are essentially converting the bound current sources to Gilbert-like magnetic charges at the poles. ) Unlike the magnetic $\mathbf{B}$ which always forms closed loops the field due to the magnetic charges flow outward (or inward depending on the sign of the magnetic charge) in both directions from the poles. And while the magnetic field is exactly the same on the outside of the magnetic material for both models the magnetic fields inside are quite different.

Putting both sources together we see that the magnetic $\mathbf{H}$ field is the same as the magnetic $\mathbf{B}$ field to a multiplicative constant outside of magnetic materials, but is completely different from the magnetic $\mathbf{B}$ field inside a magnetic material. The advantage of this hybrid $\mathbf{H}$ field is that these sources are treated so differently that we can often pick out one source from the other. For example a line integral of the magnetic $\mathbf{H}$ field in a closed loop will yield the total free current in the loop (and not the bound current). This is unlike the magnetic $\mathbf{B}$ field where a similar integral will yield the sum of both the free and the bound current. If one wants to isolate the contribution due to the bound currents then a surface integral of $\mathbf{H}$ over any closed surface will pick out the 'magnetic charges' at the poles.

Sources of the H field

Unlike the magnetic $\mathbf{B}$ field that only has a current source such that the magnetic $\mathbf{B}$ field loops around currents, the magnetic $\mathbf{H}$ field has two types of sources. The first source of magnetic $\mathbf{H}$ field are the free currents for which $\mathbf{H}$ loop around similar to the way $\mathbf{B}$ field loops around the total current. The second source of the magnetic $\mathbf{H}$ field are 'magnetic charges' near the poles of the magnetic material. More precisely, these 'magnetic charges' are calculated as $-\mathbf{\nabla}\cdot\mathbf{M}$ .

Uses of the H field

Energy Stored in Magnetic Fields

In order to create a magnetic field we need to do work to establish a free current. If we are to ask how much energy does it take to create a specific magnetic field using a particular free current then we need to distinguish between the free and the bound currents. It is the free current that we are 'pushing' on. The bound currents are freeloaders. They create a magnetic field that the free current has to work against without doing any of the work. If we are to calculate the energy of creating a magnetic field $\mathbf{B}$ we need to have a way of separating out the free current. The magnetic $\mathbf{B}$ cannot be used to determine this free current since $\mathbf{B}$ does not distinguish between bound and free current.

The magnetic $\mathbf{H}$ field does treat the two sources differently. Therefore it is useful in calculating the energy needed to create a magnetic field with a free current in the presence of magnetic materials. In this case the energy density needed, assuming a linear relationship between $\mathbf{H}$ and $\mathbf{B}$ , has the form of:

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

If there are no magnetic materials around then we can replace $\mathbf{H}$ with $\frac{\mathbf{B}}{\mu_o}$ .

Magnetic Circuits

Main article: magnetic circuits

The second main use for $\mathbf{H}$ is in magnetic circuits where inside a linear material $\mathbf{B} = \mu \mathbf{H}$ . A magnetic circuit is a closed path containing a Magnetic flux. Here, $μ$ is the permeability of the material. This is similar in form to Ohm's Law $\mathbf{J} = \sigma \mathbf{E}$ , where $\mathbf{J}$ is the current density, $σ$ is the conductance and $\mathbf{E}$ is the Electric field. Ohm's law applies to Electrical circuits it states that the current through a conductor between two points is directly proportional to the Extending this analogy we derive the counterpoint to the macroscopic Ohm's law ( $I = \frac{V}{R}$ ) as:

$\Phi = \frac F R_m,$

where $\Phi = \int \mathbf{B}\cdot d\mathbf{A}$ is the magnetic flux in the circuit, $F = \int \mathbf{H}\cdot d\mathbf{l}$ is the magnetomotive force applied to the circuit, and $R m$ is the reluctance of the circuit. Magnetomotive force is any physical cause that produces Magnetic flux, i Magnetic reluctance or "magnetic resistance" is analogous to resistance in an Electrical Circuit (although it does not dissipate magnetic Here the reluctance is defined as:

$R_m = \frac{l}{\mu A},$

where $A$ is the area, $μ$ is the permeability of the material, and $l$ is the length. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field.

Using this analogy it is straight-forward to easily calculate the magnetic flux of complicated magnetic field geometries, by using all the available techniques of circuit theory. Circuit theory is the theory of accomplishing work by means of routing matter through a loop.

History of B and H

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. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. Hence the relationship,

(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 $\mathbf{B}$ . In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges

The electric current equation can be viewed as a convective current of electric charge that involves linear motion. Electric charge is a fundamental conserved property of some Subatomic particles which determines their Electromagnetic interaction. 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.

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 $\mathbf{D}$ .

Rotating magnetic fields

Main article: Alternator

The rotating magnetic field is a key principle in the operation of alternating-current motors. alternator is an electromechanical device that converts mechanical energy to Alternating current electrical energy An electric motor uses Electrical energy to produce Mechanical energy. 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. There have already been discussions about Tesla's ethnicity on the talk page 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.

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. A synchronous electric motor is an AC motor distinguished by a rotor spinning with coils passing magnets at the same rate as the Alternating current An induction motor (IM is a type of asynchronous AC motor where power is supplied to the rotating device by means of electromagnetic 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 The stator is the stationary part of an Electric generator or Electric motor. 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. An eddy current (also known as Foucault current) is an electrical phenomenon discovered by French physicist Léon Foucault in

In 1882, Nikola Tesla identified the concept of the rotating magnetic field. Year 1882 ( MDCCCLXXXII) was a Common year starting on Sunday (link will display the full calendar of the Gregorian calendar (or a Common In 1885, Galileo Ferraris independently researched the concept. Year 1885 ( MDCCCLXXXV) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Common Galileo Ferraris ( October 30, 1847 – February 7, 1897) was an Italian Physicist and Electrical engineer, noted mostly In 1888, Tesla gained U.S. Patent 381,968 for his work. Year 1888 ( MDCCCLXXXVIII) was a Leap year starting on Sunday (click on link for calendar of the Gregorian calendar (or a Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.

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. The Hall effect refers to the Potential difference ( Hall voltage) on the opposite sides of an Electrical conductor through which there is an Electric In Physics, the Lorentz force is the Force on a Point charge due to Electromagnetic fields It is given by the following equation

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). The Hall effect refers to the Potential difference ( Hall voltage) on the opposite sides of an Electrical conductor through which there is an Electric

Special relativity and electromagnetism

Main articles: Classical electromagnetism and special relativity and Relativistic electromagnetism

See also: Moving magnet and conductor problem

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. The theory of Special relativity plays an important role in the modern theory of Classical electromagnetism. Relativistic electromagnetism is the idea of explaining Electromagnetism based on relativistic ( Albert Einstein 1905 arguments The moving magnet and conductor problem is a famous Thought experiment, originating in the 19th century concerning the intersection of Classical electromagnetism and Special relativity (SR (also known as the special theory of relativity or STR) is the Physical theory of Measurement in Inertial Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of A magnetic force can be considered as simply the relativistic part of an electric force when the latter is seen by a moving observer. 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 (that can

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. History The word tensor was introduced in 1846 by William Rowan Hamilton to describe the norm operation in a certain type of algebraic system (eventually The electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is This is analogous to the way that special relativity "mixes" space and time into spacetime, and mass, momentum and energy into four-momentum. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS In Special relativity, four-momentum is the generalization of the classical three-dimensional Momentum to four-dimensional Spacetime.

Magnetic field shape descriptions

Schematic quadrupole magnet("four-pole") magnetic field. Quadrupole magnets consist of groups of four Magnets laid out so that in the Multipole expansion of the field the dipole terms cancel and where the lowest significant 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 solar dynamo is the physical process that generates the Sun 's Magnetic field. The reverse process is called the alpha-effect. ^[10]

A dipole magnetic field is one seen around a bar magnet or around a particle with nonzero spin. In physics there are two kinds of dipoles ( Hellènic: di(s- = two- and pòla = pivot hinge An electric dipole is a In Quantum mechanics, spin is a fundamental property of atomic nuclei, Hadrons and Elementary particles For particles with non-zero spin

A quadrupole magnetic field is one seen, for example, between the poles of four bar magnets. Quadrupole magnets consist of groups of four Magnets laid out so that in the Multipole expansion of the field the dipole terms cancel and where the lowest significant 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 tokamak is a machine producing a toroidal Magnetic field for confining a plasma.

A poloidal magnetic field is generated by a current flowing in a ring, and is found, for example, in a tokamak. A tokamak is a machine producing a toroidal Magnetic field for confining a plasma.

References

Web

Nave, R. A teltron tube (named for Teltron Inc which originally manufactured it before being bought by 3B Scientific Ltd , Magnetic Field Strength H, <http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfield.html>. Retrieved on 4 June 2007

Oppelt, Arnulf (2006-11-02), magnetic field strength, <http://searchsmb.techtarget.com/sDefinition/0,290660,sid44_gci763586,00.html>. Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 1570 - A Tidal wave in the North Sea devastates the coast from Holland to Jutland, killing more than 1000 Retrieved on 4 June 2007

magnetic field strength converter, <http://www.unitconversion.org/unit_converter/magnetic-field-strength.html>. Retrieved on 4 June 2007

Books

Durney, Carl H. and Johnson, Curtis C. (1969). Introduction to modern electromagnetics. McGraw-Hill. The McGraw-Hill Companies Inc, ( is a Publicly traded corporation headquartered in Rockefeller Center in New York City. ISBN 0-07-018388-0.

Rao, Nannapaneni N. (1994). Elements of engineering electromagnetics (4th ed. ). Prentice Hall. Prentice Hall is a leading educational publisher It is an Imprint of Pearson Education Inc ISBN 0-13-948746-8.

Griffiths, David J. (1999). Introduction to Electrodynamics (3rd ed. ). Prentice Hall. Prentice Hall is a leading educational publisher It is an Imprint of Pearson Education Inc 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.

Notes

^ 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 $\mathbf{B}$ 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 $\mathbf{B}$ the magnetic field. As for $\mathbf{H}$ , although other names have been invented for it, we shall call it "the field $\mathbf{H}$ " or even "the magnetic field $\mathbf{H}$ ".
^ Magnetic Field Strength H
^ What is magnetic field strength?
^ Magnetic Field Strength Converter
^ 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. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field.
^ The Gilbert, model also produces the same result if you remember to include the force on both poles. In fact this model works very well as long as you do not examine the field inside of a magnet and you remember that poles always come in pairs. Nor does this model say anything about how electricity interacts with magnetism.
^ In special relativity this means that the electrical field and the magnetic field must be two parts of the same phenomenon. For a moving single charge or charges moving together we can always shift to a reference system in which they are not moving. In that reference system there is no magnetic field. Yet, the physics has to be the same in all reference systems. It turns out the electric field changes as well which produces the same force in the original reference frame. It is probably a mistake, though, to say that the electric field causes the magnetic field when relativity is accounted for, since relativity favors no particular reference frame. (One could just as easily say that the magnetic field caused an electric field). More importantly it is not always possible to move into a coordinate system in which all of the charges are stationary. See classical electromagnetism and special relativity for more information. The theory of Special relativity plays an important role in the modern theory of Classical electromagnetism.
^ In practice the Biot-Savart law and other laws of magnetostatics can often be used even when the charge is changing in time as long as it is not changing too quickly. This situation is known as being quasistatic.
^ In the ether model the displacement current is a real current that occurs because the electric field 'displaces' positive charge in one direction and negative charge in the opposite direction in the ether. A change in the electric field will then shift these charges around causing a current in the ether. This model can still be useful even though it is incorrect in that it helps to give a better understanding of the displacement field.
^ The Solar Dynamo, retrieved Sep 15, 2007.

External links

Information

Crowell, B. , "Electromagnetism".

Nave, R. , "Magnetic Field". HyperPhysics.

"Magnetism", The Magnetic Field. theory. uwinnipeg. ca.

Hoadley, Rick, "What do magnetic fields look like?" 17 July 2005. Events 180 - Twelve inhabitants of Scillium in North Africa are executed for being Christians Year 2005 ( MMV) was a Common year starting on Saturday (link displays full calendar of the Gregorian calendar.

Field density

Jiles, David (1994). Introduction to Electronic Properties of Materials (1st ed. ). Springer. ISBN 0-412-49580-5.

Rotating magnetic fields

"Rotating magnetic fields". Integrated Publishing.

"Introduction to Generators and Motors", rotating magnetic field. Integrated Publishing.

"Induction Motor-Rotating Fields".

Diagrams

McCulloch, Malcolm,"A2: Electrical Power and Machines", Rotating magnetic field. eng. ox. ac. uk.

"AC Motor Theory" Figure 2 Rotating Magnetic Field. Integrated Publishing.

Journal Articles

Yaakov Kraftmakher, "Two experiments with rotating magnetic field". 2001 Eur. J. Phys. 22 477-482.

Bogdan Mielnik and David J. Fernández C. , "An electron trapped in a rotating magnetic field". Journal of Mathematical Physics, February 1989, Volume 30, Issue 2, pp. 537-549.

Sonia Melle, Miguel A. Rubio and Gerald G. Fuller "Structure and dynamics of magnetorheological fluids in rotating magnetic fields". Phys. Rev. E 61, 4111 – 4117 (2000).

Dictionary

-noun

(physics) a condition in the space around a magnet or electric current in which there is a detectable magnetic force and two magnetic poles are present

© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
network: | |

Contents