Magnetic field

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Electrostatics

Electromagnetism
Electricity · Magnetism
Electric charge
Coulomb's law
Electric field
Gauss's law
Electric potential
Electric dipole moment
Magnetostatics
Ampère's law
Magnetic field
Magnetic dipole moment
Electrodynamics
Electric current
Lorentz force law
Electromotive force
(EM) Electromagnetic induction
Faraday-Lenz law
Displacement current
Maxwell's equations
(EMF) Electromagnetic field
(EM) Electromagnetic radiation
Electrical Network
Electrical conduction
Electrical resistance
Capacitance
Inductance
Impedance
Resonant cavities
Waveguides
This box: view • talk • edit

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

Current (I) flowing through a wire produces a magnetic field ( $\mathbf{B}$ ) around the wire. The field is oriented according to the right-hand rule.

For other senses of this term, see magnetic field (disambiguation).

In physics, a magnetic field is that part of the electromagnetic field that exerts a force on a moving charge. A magnetic field can be caused either by another moving charge (i.e., by an electric current) or by a changing electric field. The magnetic field is a vector quantity, and has SI units of tesla, 1 T = 1 kg·s^-1·C^-1.

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, and most modern writers refer to $\mathbf{B}$ as the magnetic field, except when context fails to make it clear whether the quantity being discussed is $\mathbf{H}$ or $\mathbf{B}$ . See^[1]

[edit] Definition

The following term in Lorentz transformation of the electric field E of a charge moving with velocity v is called the magnetic field B:

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

where

$\mathbf{v} \$ is velocity of the electric charge, measured in metres per second

$\times \$ indicates a vector cross product

c is the speed of light in a vacuum measured in metres per second

$\mathbf{E}$ is the electric field measured in newtons per coulomb 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 — but unlike an electric field,it exerts a force only on a moving charge:

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

where

$\mathbf{F}$ is the force produced, measured in newtons

$q \$ is electric charge that the magnetic field is acting on, measured in coulombs

$\mathbf{v} \$ is velocity of the electric charge $q \$ , measured in metres per second

Because magnetic field is the relativistic product of Lorentz transformations, the force it produces is called the Lorentz force.

The force due to the magnetic field is different in different frames — moving magnetic field (as well as changing magnetic field) transforms partially or fully back into electric field under Lorentz transformations. This results in Faraday's law of induction.

[edit] The Difference between 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. 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.

The electric current equation can be viewed as a convective current of electric charge that involves linear motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the $\mathbf{B}$ vector. The magnetic inductive current represents lines of force. In particular, it represents lines of inverse square law force.

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

[edit] Magnetic field of current flow of charged particles

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

Substituting into the definition of magnetic field

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

the proper electric field of point-like charge (see Coulomb's law)

$\mathbf{E} = { 1 \over 4 \pi \epsilon_0} {q \over r^2} \hat{r}= {10^{-7}}{c^2} {q \over \ {r}^2} \hat{r}$

results in the equation of magnetic field of moving charge, which is usually called the Biot-Savart law:

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

where

q

is electric charge, whose motion creates the magnetic field, measured in coulombs

$\mathbf{v}$ is velocity of the electric charge

q

that is generating $\mathbf{B}$ , measured in metres per second

$\mathbf{B}$ is the magnetic field (measured in teslas)

[edit] 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:

$F = I l \times B \,$

where

F = forces, measured in newtons

I = current in wire, measured in amperes

B = magnetic field, measured in teslas

$\times$ = vector cross-product

l = length of wire, measured in metres

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 Laplace force.

[edit] Symbols and terminology

Magnetic field is usually denoted by the symbol $\mathbf{B} \$ . Historically, $\mathbf{B} \$ was called the magnetic flux density or magnetic induction. A distinct quantity, $\mathbf{H}$ , 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 permeability µ). Otherwise, however, this distinction is often ignored, and both quantities are frequently referred to as "the magnetic field." (Some authors call $\mathbf{H}$ the auxiliary field, instead.) In linear materials, such as air or free space, the two quantities are linearly related:

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

where

$\ \mu$ is the magnetic permeability of the medium, measured in henries per metre.

In SI units, $\mathbf{B} \$ and $\mathbf{H} \$ are measured in teslas (T) and amperes per metre (A/m), respectively; or, in cgs units, in gauss (G) and oersteds (Oe), respectively. Two parallel wires carrying an electric current in the same direction will generate a magnetic field that will cause a force of attraction between them. This fact is used to define the value of an ampere of electric current. 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.

[edit] Properties

Maxwell did much to unify static electricity and magnetism, producing a set of four equations relating the two fields. However, under Maxwell's formulation, there were still two distinct fields describing different phenomena. It was Albert Einstein who showed, using special relativity, that electric and magnetic fields are two aspects of the same thing (a rank-2 tensor), and that one stationary 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 thought experiment one can do to show this is with two identical infinite and parallel lines of charge having no motion relative to each other but moving together relative to an observer. Another observer is moving alongside the two lines of charge (at the same velocity) and observes only electrostatic repulsive force and acceleration. The first or "stationary" observer seeing the two lines (and second observer) moving past with some known velocity also observes that the "moving" observer's clock is ticking more slowly (due to time dilation) and thus observes the repulsive acceleration of the lines more slowly than that which the "moving" observer sees. The reduction of repulsive acceleration can be thought of as an attractive force, in a classical physics context, that reduces the electrostatic repulsive force and also that is increasing with increasing velocity. This pseudo-force is precisely the same as the electromagnetic force in a classical context.

A changing magnetic field is mathematically the same as a moving magnetic field (see relativity of motion). Thus, according to Einstein's field transformation equations (that is, the Lorentz transformation of the field from a proper reference frame to a non-moving reference frame), part of it is manifested as an electric field component. This is known as Faraday's law of induction and is the principle behind electric generators and electric motors.

[edit] Magnetic field lines

Magnetic field lines shown by iron filings

The direction of the magnetic field vector follows from the definition above. It coincides with the direction of orientation of a magnetic dipole, such as a small magnet, a small loop of current in the magnetic field, or a cluster of small particles of ferromagnetic material (see figure).

[edit] Pole labelling confusions

See also Magnetic North Pole and Magnetic South Pole.

The end of a compass needle that points north was historically called the "north" magnetic pole of the needle. Since dipoles are vectors and align "head to tail" with each other, the magnetic pole located near the geographic North Pole is actually the "south" pole.

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

Earth's magnetic field is probably produced by electric currents in its liquid core.

Electrostatics

Electromagnetism
Electricity · Magnetism
Electric charge
Coulomb's law
Electric field
Gauss's law
Electric potential
Electric dipole moment
Magnetostatics
Ampère's law
Magnetic field
Magnetic dipole moment
Electrodynamics
Electric current
Lorentz force law
Electromotive force
(EM) Electromagnetic induction
Faraday-Lenz law
Displacement current
Maxwell's equations
(EMF) Electromagnetic field
(EM) Electromagnetic radiation
Electrical Network
Electrical conduction
Electrical resistance
Capacitance
Inductance
Impedance
Resonant cavities
Waveguides
This box: view • talk • edit

Current (I) flowing through a wire produces a magnetic field ( $\mathbf{B}$ ) around the wire. The field is oriented according to the right-hand rule.

For other senses of this term, see magnetic field (disambiguation).

[edit] Definition

The following term in Lorentz transformation of the electric field E of a charge moving with velocity v is called the magnetic field B:

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

where

$\mathbf{v} \$ is velocity of the electric charge, measured in metres per second

$\times \$ indicates a vector cross product

c is the speed of light in a vacuum measured in metres per second

$\mathbf{E}$ is the electric field measured in newtons per coulomb or volts per metre

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

where

$\mathbf{F}$ is the force produced, measured in newtons

$q \$ is electric charge that the magnetic field is acting on, measured in coulombs

$\mathbf{v} \$ is velocity of the electric charge $q \$ , measured in metres per second

Because magnetic field is the relativistic product of Lorentz transformations, the force it produces is called the Lorentz force.

[edit] The Difference between B and H

(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

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

[edit] Magnetic field of current flow of charged particles

Substituting into the definition of magnetic field

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

the proper electric field of point-like charge (see Coulomb's law)

$\mathbf{E} = { 1 \over 4 \pi \epsilon_0} {q \over r^2} \hat{r}= {10^{-7}}{c^2} {q \over \ {r}^2} \hat{r}$

results in the equation of magnetic field of moving charge, which is usually called the Biot-Savart law:

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

where

q

is electric charge, whose motion creates the magnetic field, measured in coulombs

$\mathbf{v}$ is velocity of the electric charge

q

that is generating $\mathbf{B}$ , measured in metres per second

$\mathbf{B}$ is the magnetic field (measured in teslas)

[edit] 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:

$F = I l \times B \,$

where

F = forces, measured in newtons

I = current in wire, measured in amperes

B = magnetic field, measured in teslas

$\times$ = vector cross-product

l = length of wire, measured in metres

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 Laplace force.

[edit] Symbols and terminology

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

where

$\ \mu$ is the magnetic permeability of the medium, measured in henries per metre.

[edit] Properties

[edit] Magnetic field lines

Magnetic field lines shown by iron filings

[edit] Pole labelling confusions

See also Magnetic North Pole and Magnetic South Pole.

Earth's magnetic field is probably produced by electric currents in its liquid core.

[edit] Magnetic flux density

Magnetic flux density, is essentially what is commonly thought of as magnetic field — akin to a gravitational or electric field. It is a response of a medium to the presence of a magnetic field. The SI unit of magnetic flux density is the tesla. 1 tesla = 1 weber per square metre.

It can be more easily explained if one works backwards from the equation:

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

where

B is the magnitude of flux density, measured in SI as teslas

F is the force experienced by a wire, measured in Newtons

I is the current, measured in amperes

L is the length of the wire, measured in metres

Demonstration of Fleming's left hand rule

For a magnetic flux density to equal 1 tesla, a force of 1 newton must act on a wire of length 1 metre carrying 1 ampere of current.

1 newton of force is not easily accomplished. For example: the most powerful superconducting electromagnets 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 — hence 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 coulombs, and

v is the velocity of that charge in metres per second.

Fleming'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 be remembered in the following way. The digits from the thumb to second finger indicate 'Force', 'B-field', and 'I(Current)' respectively, or F-B-I in short. For professional use, the right hand grip rule is used instead which originated from the definition of cross product in the right hand system of coordinates.

Other units of magnetic flux density are

1 gauss = 10^-4 teslas = 100 microteslas (µT)

1 gamma = 10^-9 teslas = 1 nanotesla (nT)

[edit] Historical Information

The difference between the B field and the H field can be historically traced back to Maxwell's concept of a sea of molecular vortices. See his original 1861 paper 'On Physical Lines of Force'.

Within that context, H represented pure vorticity (spin), whereas B was a weighted vorticity that was weighted for the density of the vortex sea. Maxwell considered magnetic permeability to be a measure of the density of the vortex sea. Hence the relationship,

(1) Magnetic Induction Current

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

was essentially an angular analogy to the linear electric current relationship,

(2) Electric Convection Current

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

B was seen as a kind of magnetic current of vortices aligned in their axial planes, with H being the circumferential velocity of the vortices.

The electric current equation can be viewed as a convective current of electric charge that involves motion. By analogy, the magnetic equation is an inductive current involving spin. There is no linear motion in the inductive current along the direction of the 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 B is to H, and where J is to v, then it necessary follows from Gauss's law and from the equation of continuity of charge that D is to E. Ie. B parallels with D, whereas H parallels with E.

[edit] Rotating magnetic fields

Main article: Alternator

The rotating magnetic field is a key principle in the operation of alternating-current motors. A permanent magnet in such a field will rotate so as to maintain its alignment with the external field. This effect was conceptualized by Nikola Tesla, and later utilised in his, and others, early AC (alternating-current) electric motors. A rotating magnetic field can be constructed using two orthogonal coils with 90 degrees phase difference in their AC currents. However, in practice such a system would be supplied through a three-wire arrangement with unequal currents. This inequality would cause serious problems in standardization of the conductor size and so, in order to overcome it, three-phase systems are used where the three currents are equal in magnitude and have 120 degrees phase difference. Three similar coils having mutual geometrical angles of 120 degrees will create the rotating magnetic field in this case. The ability of the three-phase system to create a rotating field, utilized in electric motors, is one of the main reasons why three-phase systems dominate the world's electrical power supply systems.

Because magnets degrade with time, synchronous motors and induction motors use short-circuited rotors (instead of a magnet) following the rotating magnetic field of a multicoiled stator. The short-circuited turns of the rotor develop eddy currents in the rotating field of the stator, and these currents in turn move the rotor by the Lorentz force.

In 1882, Nikola Tesla identified the concept of the rotating magnetic field. In 1885, Galileo Ferraris independently researched the concept. In 1888, Tesla gained U.S. Patent 381968 for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.

[edit] 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 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).

[edit] Extension to the Theory of Relativity

Einstein explained in 1905 that a magnetic field is the relativistic part of an electric field.^[3] It arises as a mathematical by-product of Lorentz coordinate transformation of electric field from one reference frame to another (usually from co-moving with the moving charge reference frame to the reference frame of non-moving observer). 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, and it must be computed using the Lorentz transformations. One of the products of these transformations is the part of the electric field which only acts on moving charges — and we call it 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 which is the consequence that a magnetic field is the result of motion of electric field.

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.

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". We use the symbol $\mathbf{B}$ for the magnetic field and for the sake of mathematical simplicity (one symbol instead of seven). Intuitively $\mathbf{B}$ 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 $\mathbf{B}$ , and the exact direction being at right angles to both the velocity of the particle and $\mathbf{B}$ . The magnitude of $\mathbf{B}$ is the amount of force per unit of charge multiplied by the speed of the particle.

[edit] See also

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.
Magnetohydrodynamics — the academic discipline which studies the dynamics of electrically conducting fluids.
Magnetic flux
Magnetic monopole
SI electromagnetism units

Mathematics

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

Applications

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

[edit] References

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.

[edit] 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 B as the primary field feel obliged to call it the magnetic induction because the name magnetic field was historically preempted by H. This seems clumsy and pedantic. If you go into the laboratory and ask a physicist what causes the pion trajectories in his bubble chamber to curve, he'll probably answer "magnetic field," not "magnetic induction." You will seldom hear a geophysicist refer to the earth's magnetic induction, or an astrophysicist talk about the magnetic induction of the galaxy. We propose to keep on calling B the magnetic field. As for H, although other names have been invented for it, we shall call it "the field H" or even "the magnetic field H".
^ The standard graduate textbook by Jackson follows this usage. Edward Purcell, in Electricity and Magnetism, McGraw-Hill, 1963, writes, Even some modern writers who treat B as the primary field feel obliged to call it the magnetic induction because the name magnetic field was historically preempted by H. This seems clumsy and pedantic. If you go into the laboratory and ask a physicist what causes the pion trajectories in his bubble chamber to curve, he'll probably answer "magnetic field," not "magnetic induction." You will seldom hear a geophysicist refer to the earth's magnetic induction, or an astrophysicist talk about the magnetic induction of the galaxy. We propose to keep on calling B the magnetic field. As for H, although other names have been invented for it, we shall call it "the field H" or even "the magnetic field H".
^ On the Electrodynamics of Moving Bodies

[edit] 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.

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).

Retrieved from "http://en.wikipedia.org../../../m/a/g/Magnetic_field.html"

Magnetic field

From Wikipedia, the free encyclopedia

Contents

[edit] Definition

[edit] The Difference between B and H

[edit] Magnetic field of current flow of charged particles

[edit] Lorentz force on wire segment

[edit] Symbols and terminology

[edit] Properties

[edit] Magnetic field lines

[edit] Pole labelling confusions

[edit] Definition

[edit] The Difference between B and H

[edit] Magnetic field of current flow of charged particles

[edit] Lorentz force on wire segment

[edit] Symbols and terminology

[edit] Properties

[edit] Magnetic field lines

[edit] Pole labelling confusions

[edit] Magnetic flux density

[edit] Historical Information

[edit] Rotating magnetic fields

[edit] Hall effect

[edit] Extension to the Theory of Relativity

[edit] See also

[edit] References

[edit] Notes

[edit] External links

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