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## PowerPedia:Magnetic field

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|} In Physics, a magnetic field is that part of the Electromagnetic field that exists when there is a changing or constant Electric field. A changing electric field can be caused by the movement of an electrically There was an error working with the wiki: Code[29]d object, as in an Electric current or a combination of the orbit of an Electron around an Atom and the spin of electrons themselves, as in a There was an error working with the wiki: Code[30].

#### Introduction

" Magnetic field is a radiation of Waves magnetic force (magnetic force waves).

Magnetism is produced by Waves of magnetic force (magnetic force waves) .

The atoms in the magnet add their magnetic fields and thus enhance overall is causing an exponential growth that produces a chain reaction and this releases energy in waves of magnetic force thus creating the magnetic field . Compression between Waves of magnetic force same polarity is magnetic repellency . Connection and Annexation Waves of magnetic force different polarity is magnetic attraction . (magnetic attraction is the unifying force of atomic magnetic fields ). quote by Author Juan Carlos Aviles Moran ".

Magnetic field is usually denoted by the symbol {B} \ . Historically, {B} \ was called the magnetic flux density or magnetic induction. A distinct quantity, {H}, was called the magnetic field (strength), and this terminology is still often used to distinguish the two in the context of magnetic materials (non-trivial There was an error working with the wiki: Code[8] ?). Otherwise, however, this distinction is often ignored, and both quantities are frequently referred to as "the magnetic field." (Some authors call H the auxiliary field, instead.) In linear materials, such as air or free space, the two quantities are linearly related:

: {B} = \mu {H} \

where

:\ \mu is the magnetic There was an error working with the wiki: Code[9] of the medium, measured in There was an error working with the wiki: Code[31] per Metre.

In There was an error working with the wiki: Code[10]s (T) and There was an error working with the wiki: Code[11] (G) and There was an error working with the wiki: Code[32]s (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. While like charges repel and unlike ones attract, the opposite holds for currents: if the current in one of the two parallel wires is reversed, the two will repel.

A magnetic field is conventionally viewed as the relativistic part of an electric field. When an electric charge is moving from the perspective of an observer, the electric field of this charge due to space contraction is no longer seen by the observer as spherically symmetric due to non-radial time dilation. One of the products of these qualitative changes is the part of the electric field which only acts on moving charges - which is conventionally call the "magnetic field". The quantum-mechanical motion of electrons in atoms produces the magnetic fields of permanent ferromagnets. Spinning charged particles also have magnetic moment. Some electrically neutral particles (like the neutron) with non-zero spin also have magnetic moment due to the charge distribution in their inner structure. Particles with zero spin never have magnetic moment. A magnetic field is a vector field: it associates with every point in space a (pseudo-)vector that may vary through time. The direction of the field is the equilibrium direction of a magnetic dipole (like a compass needle) placed in the field.

#### Properties

Maxwell did much to unify static electricity and magnetism, producing There was an error working with the wiki: Code[12] relating the two fields. However, under Maxwell's formulation, there were still two distinct fields describing different phenomena. It was There was an error working with the wiki: Code[33] who showed, using There was an error working with the wiki: Code[34], that electric and magnetic fields are two aspects of the same thing (a rank-2 There was an error working with the wiki: Code[35]), and that one observer may perceive a magnetic force where a moving observer perceives only an Electrostatic force. Thus, using special relativity, magnetic forces are a manifestation of electrostatic forces of charges in motion and may be predicted from knowledge of the electrostatic forces and the velocity of movement (relative to some observer) of the charges.

A changing magnetic field is mathematically the same as a moving magnetic field (see There was an error working with the wiki: Code[36] of motion). Thus, according to Einstein's field transformation equations (that is, the Lorentz transformation of the field from a There was an error working with the wiki: Code[37] reference frame to a non-moving reference frame), part of it is manifested as an electric field component. This is known as There was an error working with the wiki: Code[38] and is the principle behind There was an error working with the wiki: Code[39]s and Electric motors.

##### Magnetic field lines

The direction of the magnetic field vector follows from the definition above. It coincides with the direction of orientation of a There was an error working with the wiki: Code[40], such as a small magnet, a small loop of current in the magnetic field, or a cluster of small particles of There was an error working with the wiki: Code[41] material (see figure).

##### Pole labelling confusions

The end of a There was an error working with the wiki: Code[13] and align "head to tail" with each other, the magnetic pole located near the geographic There was an error working with the wiki: Code[42] is actually the "south" pole.

The "north" and "south" poles of a magnet or a There was an error working with the wiki: Code[43] 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 produced by Electric currents in its liquid core.

##### Field density

Magnetic field density, otherwise known as magnetic flux density, is essentially what the layman knows as a magnetic field &mdashakin to a There was an error working with the wiki: Code[14] or There was an error working with the wiki: Code[15]. 1 tesla = 1 There was an error working with the wiki: Code[16] per There was an error working with the wiki: Code[44]. It can be more easily explained if one works backwards from the equation:

:B=\frac {F} {I L} \,

where

:B is the magnitude of There was an error working with the wiki: Code[17]

:F is the Force experienced by a wire, measured in There was an error working with the wiki: Code[45]s

:I is the Electrical current, measured in Amperes

:L is the There was an error working with the wiki: Code[46] of the wire, measured in Metres

For a magnetic flux density to equal 1 tesla, a force of 1 There was an error working with the wiki: Code[18] There was an error working with the wiki: Code[47]s in the world have flux densities of 'only' 20 T. This is true obviously for both electromagnets and natural magnets, but a magnetic field can only act on moving charge&mdashhence the current, I, in the equation. The equation can be adjusted to incorporate moving single charges, ie protons, electrons, and so on via

:F = BQv \,

where

:Q is the charge in There was an error working with the wiki: Code[48]s, and

:v is the velocity of that charge in There was an error working with the wiki: Code[49].

.]]

There was an error working with the wiki: Code[19]'s left hand rule for motion, current and polarity can be used to determine the direction of any one of those from the other two, as seen in the example. It can also 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. For professional use, the There was an error working with the wiki: Code[20] of There was an error working with the wiki: Code[50]. Other units of magnetic flux density are

: 1 There was an error working with the wiki: Code[21] = 10-4 teslas = 100 microteslas (µT)

: 1 There was an error working with the wiki: Code[51] = 10-9 teslas = 1 nanotesla (nT)

#### Mathematics

The properties of the magnetic field can be computed using the Lorentz transformations. The Lorentz transformation of a spherically-symmetric proper electric field E of a moving electric charge (for example, the electric field of an electron moving in a conducting wire) from the charge's reference frame to the reference frame of a non-moving observer results in the following term which we can define or label as "magnetic field". The use of the symbol B for it and for the sake of mathematical simplicity (one symbol instead of seven). Intuitively B can be seen as a vector whose direction gives the axis of the possible directions of the force on a charged particle due to the magnetic field the possible directions being at right angles to the axis B, and the exact direction being at right angles to both the velocity of the particle and B. The magnitude of B is the amount of force per unit of charge multiplied by the speed of the particle.

:

{B} = {v}\times \frac{1}{c^2}{E}

where

: {v} \ is There was an error working with the wiki: Code[22]

: \times \ indicates a vector There was an error working with the wiki: Code[52]

:c is the There was an error working with the wiki: Code[53] measured in metres per second

:E is the electric field measured in There was an error working with the wiki: Code[54]s per There was an error working with the wiki: Code[55] or Volts per Metre

As seen from the definition, the unit of magnetic field is newton-second per coulomb-metre (or newton per ampere-metre) and is called the Tesla. Like the Electric field, the magnetic field exerts Force on electric charge&mdashbut unlike an electric field, only on moving charge:

:

{F} = q {v} \times {B}

where

:F is the force produced, measured in There was an error working with the wiki: Code[56]s

: q \ is Electric charge that the magnetic field is acting on, measured in There was an error working with the wiki: Code[57]s

: {v} \ is There was an error working with the wiki: Code[23]

Because magnetic field is the relativistic product of There was an error working with the wiki: Code[58]s, the force it produces is called the Lorentz force. The force due to the magnetic field is different in different frames&mdashmoving magnetic field transforms partially or fully back into electric fields under There was an error working with the wiki: Code[58]s. This results in There was an error working with the wiki: Code[60].

##### Charged particle flow magnetic field

Substituting into the definition of magnetic field

:

{B} = {v}\times \frac{1}{c^2}{E}

the proper Electric field of point-like charge (see There was an error working with the wiki: Code[61])

:{E} =

{ 1 \over 4 \pi \epsilon_0} {q \over {r}^2} \hatThere was an error working with the wiki: Code[1]=

{10^{-7}}{c^2} {q \over \ {r}^2} \hatThere was an error working with the wiki: Code[2]

results in the equation of magnetic field of moving charge, which is usually called the There was an error working with the wiki: Code[62]:

:

{B} = {v}\times \frac{\mu_0}{4 \pi}\frac{q}{r^2}{\hat r}

where

:q is Electric charge, whose motion creates the magnetic field, measured in coulombs

:v is Velocity of the Electric charge q that is generating B, measured in There was an error working with the wiki: Code[63]

:B is the magnetic field (measured in There was an error working with the wiki: Code[24]s)

##### Lorentz force on wire segment

Integrating the Lorentz force on an individual charged particle over a flow (current) of charged particles results in the Lorentz force on a stationary wire carrying electric current:

:F = I B l \,

where

:F = force, measured in newtons

:B = magnetic field, measured in tesla

:l = length of wire, measured in metre

:i = current in wire, measured in ampere

In the equation above, the current vector i is a vector with magnitude equal to the scalar current, i, and direction pointing along the wire in which the current is flowing. Alternatively, instead of current, the wire segment l can be considered a vector. The Lorentz force on a macroscopic current carrier is often referred to as the There was an error working with the wiki: Code[64].

##### Vector calculus

Separating the electric field of moving charge into stationary electric and magnetic components (as measured by a stationary observer)&mdashwhich are usually labeled as E and B&mdashreplaces complex Einstein relativistic field transformation equations by more compact and elegant mathematical statements known as There was an error working with the wiki: Code[65]. The two of them that describe the magnetic component are:

: \nabla \times {B} = \mu_0 {J} + \mu_0 \epsilon_0 \frac { \partial {E}} {\partial t}

: \nabla \cdot {B} = 0

where

:\nabla \times is the There was an error working with the wiki: Code[66] operator

:\nabla \cdot is the There was an error working with the wiki: Code[67] operator

: \mu_0 \ is the free-space There was an error working with the wiki: Code[25]

: {J} \ is There was an error working with the wiki: Code[68]

: \partial \ is the There was an error working with the wiki: Code[69]

:\epsilon_0 \ is the free-space There was an error working with the wiki: Code[70]

:{E} \ is the Electric field

: t \ is There was an error working with the wiki: Code[71]

The first equation is known as There was an error working with the wiki: Code[26]'s law with There was an error working with the wiki: Code[27]'s correction. The second term of this equation (Maxwell's correction) disappears in static (time-independent) systems. The second equation is a statement of the observed non-existence of There was an error working with the wiki: Code[72]s. These are two of the four There was an error working with the wiki: Code[73] written in the differential notation introduced by There was an error working with the wiki: Code[74].

#### Magnetic field energy

The energy of a long (or toroidal) solenoid is given by:

:{Energy} = L \frac{I^2} {2}

If we divide the energy by the volume of the solenoid, the density of the magnetic field energy can be obtained:

:u = \frac{B^2}{2 \mu}

For example, a magnetic field B of one tesla has an energy density about 398 kilojoules per cubic metre, and of 10 teslas, about 40 megajoules per cubic metre. This is the same as the pressure produced by magnetic field, since pressure and energy density are essentially the same physical quantities and thus have the same units. Thus, a magnetic field of 1 tesla produces a pressure of 398 kPa (about 4 atmospheres), and 10 T about 40 Mpa (~400 atm).

#### Rotating magnetic fields

The rotating magnetic field is a key principle in the operation of There was an error working with the wiki: Code[28]s. A permanent magnet in such a field will rotate so as to maintain its alignment with the external field. This effect was utilised in early 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.

Because magnets degrade with time, There was an error working with the wiki: Code[75]s and Induction motors use short-circuited There was an error working with the wiki: Code[76]s (instead of a magnet) following the rotating magnetic field of a multicoiled There was an error working with the wiki: Code[77]. The short-circuited turns of the rotor develop There was an error working with the wiki: Code[78]s in the rotating field of the stator, and these currents in turn move the rotor by the Lorentz force.

In There was an error working with the wiki: Code[79], Nikola Tesla identified the concept of the rotating magnetic field. In There was an error working with the wiki: Code[80], There was an error working with the wiki: Code[81] independently researched the concept. In There was an error working with the wiki: Code[82], Tesla gained There was an error working with the wiki: Code[3] for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in There was an error working with the wiki: Code[83].

#### Hall effect

The There was an error working with the wiki: Code[84] 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). Because the Lorentz force is charge dependent, 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 opposite sides of a thin sheet of conducting or semiconducting material in the form of a 'Hall bar' (or a van der Pauw element) through which an electric current is flowing, created by a magnetic field applied perpendicular to the Hall element. Edwin Hall discovered this effect in 1879. The ratio of the voltage created to the product of the amount of current and the magnetic field divided by the element thickness is known as the Hall coefficient and is a characteristic of the material of which the element is composed.

#### Magnetic field of celestial bodies

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A rotating body of conductive gas or liquid develops self-amplifying Electric currents, and thus a self-generated magnetic field, due to a combination of differential rotation (different angular velocity of different parts of body), There was an error working with the wiki: Code[85]s and induction. The distribution of currents can be quite complicated, with numerous open and closed loops, and thus the magnetic field of these currents in their immediate vicinity is also quite multitwisted. At large distances, however, the magnetic fields of currents flowing in opposite directions cancel out and only a net dipole field survives, slowly diminishing with distance. Because the major currents flow in the direction of conductive mass motion (equatorial currents), the major component of the generated magnetic field is the dipole field of the equatorial current loop, thus producing magnetic poles near the geographic poles of a rotating body. The magnetic fields of all celestial bodies are more or less aligned with the direction of rotation. Another feature of this There was an error working with the wiki: Code[86] is that the currents are AC rather than DC. Their direction, and thus the direction of the magnetic field they generate, alternates more or less periodically, changing amplitude and reversing direction, although still more or less aligned with the axis of rotation.

The Sun's major component of magnetic field reverses direction every 11 years (so the period is about 22 years), resulting in a diminished magnitude of magnetic field near reversal time. During this dormancy time, the There was an error working with the wiki: Code[87]s activity is maximized (because of the lack of There was an error working with the wiki: Code[88] on plasma) and, as a result, massive ejection of high energy plasma into the There was an error working with the wiki: Code[89] and interplanetary space takes place. Collisions of neighboring sunspots with oppositely directed magnetic fields result in the generation of strong electric fields near rapidly disappearing magnetic field regions. This electric field accelerates electrons and protons to high energies (kiloelectronvolts) which results in jets of extremely hot plasma leaving Sun's surface and heating coronal plasma to high temperatures (millions of K).

Compact and fast-rotating astronomical objects (There was an error working with the wiki: Code[90]s, There was an error working with the wiki: Code[91]s and There was an error working with the wiki: Code[92]s) have extremely strong magnetic fields. The magnetic field of a newly born fast-spinning neutron star is so strong (up to 108 teslas) that it electromagnetically radiates enough energy to quickly (in a matter of few million years) damp down the star rotation by 100 to 1000 times. Matter falling on a neutron star also has to follow the magnetic field lines, resulting in two hot spots on the surface where it can reach and collide with the star's surface. These spots are literally a few feet (about a metre) across but tremendously bright. Their periodic eclipsing during star rotation is believed to be the source of pulsating radiation (see There was an error working with the wiki: Code[93]s). Jets of relativistic plasma are often observed along the direction of the magnetic poles of active black holes in the centers of young galaxies. If the gas or liquid is very viscous (resulting in There was an error working with the wiki: Code[94] differential motion), the reversal of the magnetic field may not be very periodic. This is the case with the Earth's magnetic field, which is generated by turbulent currents in a viscous outer core.

#### Related concepts

General

Electric field - effect produced by an electric charge that exerts a force on charged objects in its vicinity.

Electromagnetic field - a field composed of two related vector fields, the electric field and the magnetic field.

Electromagnetism - the physics of the electromagnetic field: a field, encompassing all of space, composed of the electric field and the magnetic field.

Magnetism - phenomenon by which materials exert an attractive or repulsive force on other materials.

There was an error working with the wiki: Code[95] - the academic discipline which studies the dynamics of electrically conducting fluids.

There was an error working with the wiki: Code[96]

There was an error working with the wiki: Code[97]

Mathematics

There was an error working with the wiki: Code[98] - magnetic equivalent of Gauss's law.

There was an error working with the wiki: Code[99] - describes the magnetic field set up by a steadily flowing line current.

There was an error working with the wiki: Code[100] - extent to which a magnetic field "wraps around itself".

There was an error working with the wiki: Code[101] - four equations describing the behavior of the electric and magnetic fields, and their interaction with matter.

Applications

There was an error working with the wiki: Code[102] - a device for producing a region of nearly uniform magnetic field.

There was an error working with the wiki: Code[103] - a device for producing a large volume of almost constant magnetic field.

There was an error working with the wiki: Code[104] - a discussion of the magnetic field of the Earth.

There was an error working with the wiki: Code[105] - a proposed mechanism for the creation of the Earth's magnetic field.

Electric motor - AC motors used magnetic fields

#### References and external articles

There was an error working with the wiki: Code[4]

There was an error working with the wiki: Code[5]

There was an error working with the wiki: Code[6]

There was an error working with the wiki: Code[7]

Books

Griffiths, David J. (1998). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X.

Jackson, John D. (1998). 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.

Information

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

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

Hoadley, Rick, "What do magnetic fields look like?" There was an error working with the wiki: Code[106] There was an error working with the wiki: Code[107].

There was an error working with the wiki: Code[1], Wikipedia: The Free Encyclopedia. Wikimedia Foundation.

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.

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).