Information about Magnetic Field
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Magnetic field lines shown by iron filings
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In physics, the magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.
When placed in a magnetic field, magnetic dipoles align their axes to be parallel with the field lines, as can be seen when iron filings are in the presence of a magnet. Magnetic fields also have their own energy and momentum, with an energy density proportional to the square of the field intensity. The magnetic field is measured in the units of teslas (SI units) or gauss (cgs units).
There are some notable specific incarnations of the magnetic field. For the physics of magnetic materials, see magnetism and magnet, and more specifically ferromagnetism, paramagnetism, and diamagnetism. For constant magnetic fields, such as are generated by stationary dipoles and steady currents, see magnetostatics. For magnetic fields created by changing electric fields, see electromagnetism.
The electric field and the magnetic field are components of the electromagnetic field.
Definition
In classical physics, the magnetic field
is a vector field (that is, some vector at every point of space and time), with SI units of Tesla (one Tesla is one newton-second per coulomb-metre) and cgs units of gauss. As a vector field, it has the property of being solenoidal.
The field
can be both defined and measured by means of a small magnetic dipole (i.e., bar magnet). The magnetic field exerts a torque on magnetic dipoles that tends to make them point in the same direction as the magnetic field (as in a compass), and moreover the magnitude of that torque is proportional to the magnitude of the magnetic field. Therefore, in order to measure the magnetic field at a particular point in space, you can put a small freely-rotating bar magnet (such as a compass) there: the direction it winds up pointing is the direction of ; and the ratio of the maximum magnitude of the torque to the dipole moment of the bar magnet is the magnitude 
.
(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.)
It follows from any of these definitions that the magnetic field vector (being a vector product) is a pseudovector (also called an axial vector).
B and H
There are two quantities that physicists may refer to as the magnetic field, notated
and . The vector field
is known among electrical engineers as the magnetic field intensity or magnetic field strength also known as auxiliary magnetic field or magnetizing field. The vector field is known as magnetic flux density or magnetic induction or simply magnetic field, as used by physicists, and has the SI units of Tesla (T), equivalent to webers (Wb) per square metre or volt second per square metre. Magnetic flux has the SI units of webers so the field is that of its areal density. [1][2][3][4][1] The vector field has the SI units of amperes per metre and is something of the magnetic analog to the electric displacement field represented by 
, with the SI units of the latter being ampere-seconds per square metre. Although the term "magnetic field" was historically reserved for , with being termed the "magnetic induction", is now understood to be the more fundamental entity, and most modern writers refer to as the magnetic field, except when context fails to make it clear whether the quantity being discussed is or . See: [2]
The difference between the
and the 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, represented pure vorticity (spin), whereas 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
was essentially a rotational analogy to the linear electric current relationship,
(2) Electric convection current
where
is electric charge density. was seen as a kind of magnetic current of vortices aligned in their axial planes, with being the circumferential velocity of the vortices. With µ representing vortex density, we can now see how the product of µ with vorticity leads to the term magnetic flux density which we denote as .
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
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
is to , and where 
is to ρ, then it necessarily follows from Gauss's law and from the equation of continuity of charge that 
is to . Ie. parallels with , whereas parallels with .
In SI units,
and 
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.
The fields
and are also related by the equation
(SI units)
(cgs units),
is magnetization.
Force due to a magnetic field
Force on a charged particle
where
- q is the electric charge of the particle (in coulombs)
- and × is the cross product.
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:
where
- F = forces, measured in newtons
- I = current in wire, measured in amperes
- B = magnetic field, measured in teslas
= vector cross-product
- l = length of wire, measured in meters, vector direction along wire, aligned with positive current.
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.
Direction of force
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Demonstration of Fleming's left hand rule
The direction of force is determined by the above equations, in particular using the right-hand rule to evaluate the cross product. Equivalently, one can use Fleming's left hand rule for motion, current and polarity to determine the direction of any one of those from the other two, as seen in the example. It can also be remembered in the following way. The digits from the thumb to second finger indicate 'Force', 'B-field', and 'I(Current)' respectively, or F-B-I in short. Another similar trick is the right hand grip rule.
Magnetic field of a steady current
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Current (I) through a wire produces a magnetic field (math:B/3B9826C13A288E712F1D0DB6.gif) around the wire. The field is oriented according to the right hand grip rule.
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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
(in SI units), where
is a differential element of current,
is the resulting differential contribution to the magnetic field,
is the magnetic constant,
is the unit displacement vector from the current element to the field point, and
is the distance from the current element to the field point.
This is a consequence of Ampere's law, one of the four Maxwell's equations. Alternatively, it can be thought of as a true, empirical law in its own right, which contributes to the derivation of Maxwell's equations. From a practical point of view, though, the law is true and useful regardless of its philosophical origin.
Properties
Magnetic field lines
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, or a small loop of current in the magnetic field. So, a cluster of small particles of ferromagnetic material being brought in the magnetic field can be used to show the direction of magnetic field lines (see figure). A trajectory of charged particle (electron Such motion of Solar wind plasma in the magnetic field of Earth results in Northern Lights (and Southern Lights) - spots of glow in upper atmosphere above magnetic poles of Earth where energetic electrons and protons can reach air and ionize nitrogen and oxygen molecules.Pole labelling confusions
See also North Magnetic Pole and South Magnetic 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 to minimize their magnetic potential energy, 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.
Rotating magnetic fields
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 381,968 for his work. Also in 1888, Ferraris published his research in a paper to the Royal Academy of Sciences in Turin.
Hall effect
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).
Special relativity and electromagnetism
According to special relativity, electric and magnetic forces are part of a single physical phenomenon, electromagnetism; an electric force perceived by one observer will be perceived by another observer in a different frame of reference as a mixture of electric and magnetic forces. A magnetic force can be considered as simply the relativistic part of an electric force when the latter is seen by a moving observer.
More specifically, rather than treating the electric and magnetic fields as separate fields, special relativity shows that they naturally mix together into a rank-2 tensor, called the electromagnetic tensor. This is analogous to the way that special relativity "mixes" space and time into spacetime, and mass, momentum and energy into four-momentum.
Magnetic field shapes descriptions
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Schematic quadrupole magnet("four-pole") magnetic field. There are four steel pole tips, two opposing magnetic north poles and two opposing magnetic south poles.
- An azimuthal magnetic field is one that runs east-west.
- A meridional magnetic field is one that runs north-south. In the solar dynamo model of the Sun, differential rotation of the solar plasma causes the meridional magnetic field to stretch into an azimuthal magnetic field, a process called the omega-effect. The reverse process is called the alpha-effect.[3]
- A radial magnetic field is one seen around a straight wire carrying a current. The magnetic field strength decreases with the square of the radial distance from the wire.
- A dipole magnetic field is one seen around a charged particle, or around a bar magnetic.
- A quadruple magnetic field is one seen between two sets (ie four) bar magnets poles. The quadrupole magnet 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 magnetic is replaces by a hollow electromagnetic coil magnet.
- A toroidal magnetic field occurs in a doughnut-shaped coil, the electric current spiraling around the tube-like surface, and is found, for example, in a tokamak.
- A poloidal magnetic field is generated by a current flowing in a ring, and is found, for example, in a tokamak.
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 — hypothetical physical quantity which would cause nonzero divergence of magnetic field.
- SI electromagnetism units
- 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.
- Helmholtz coil — a device for producing a region of nearly uniform magnetic field.
- Maxwell coil — a device for producing a large volume of almost constant magnetic field.
- Earth's magnetic field — a discussion of the magnetic field of the Earth.
- Dynamo theory — a proposed mechanism for the creation of the Earth's magnetic field.
- Electric motor — AC motors used magnetic fields
- Rapid-decay theory - a creationist theory
- Stellar magnetic field — a discussion of the magnetic field of stars.
- Teltron Tube
References
Web-
id="CITEREFNave">Nave, R., Magnetic Field Strength H, <[5] (retrieved on 2007-06-04)
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id="CITEREFKeitch">Keitch, Paul, Magnetic Field Strength and Magnetic Flux Density, <[6] (retrieved on 2007-06-04)
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id="CITEREFOppelt">Oppelt, Arnulf (2006-11-02), magnetic field strength, <[7] (retrieved on 2007-06-04)
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id="CITEREF">magnetic field strength converter, <[8] (retrieved on 2007-06-04)
Books- Durney, Carl H. and Johnson, Curtis C. (1969). Introduction to modern electromagnetics. McGraw-Hill. ISBN 0-07-018388-0.McGraw-Hill">
- Rao, Nannapaneni N. (1994). Elements of engineering electromagnetics (4th ed.). Prentice Hall. ISBN 0-13-948746-8.
- Griffiths, David J. (1999). Introduction to Electrodynamics (3rd ed.). Prentice Hall. ISBN 0-13-805326-X.
- Jackson, John D. (1999). Classical Electrodynamics (3rd ed.). Wiley. ISBN 0-471-30932-X.Wiley">
- 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
1. ^ Magnetic Field Strength is also sometimes called Magnetic Field Intensity. For more information reference the sources Durney and Johnson, and also Rao.
2. ^ 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".
3. ^ 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.
- Jiles, David (1994). Introduction to Electronic Properties of Materials (1st ed.). Springer. ISBN 0-412-49580-5.
- "Rotating magnetic fields". Integrated Publishing.
- "Introduction to Generators and Motors", rotating magnetic field. Integrated Publishing.
- "Induction Motor-Rotating Fields".
- McCulloch, Malcolm,"A2: Electrical Power and Machines", Rotating magnetic field. eng.ox.ac.uk.
- "AC Motor Theory" Figure 2 Rotating Magnetic Field. Integrated Publishing.
- 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).
Electromagnetism is the physics of the electromagnetic field: a field which exerts a force on particles that possess the property of electric charge, and is in turn affected by the presence and motion of those particles.
..... Read more.Electricity (from New Latin ēlectricus, "amberlike") is a general term for a variety of phenomena resulting from the presence and flow of electric charge. This includes many well-known physical phenomena such as lightning, electromagnetic fields and electric currents,
..... Read more.magnetism is one of the phenomena by which materials exert attractive or repulsive forces on other materials. Some well known materials that exhibit easily detectable magnetic properties (called magnets) are nickel, iron and their alloys; however, all materials are influenced to
..... Read more.Electrostatics (also known as static electricity) is the branch of physics that deals with the phenomena arising from what seem to be stationary electric charges. This includes phenomena as simple as the attraction of plastic wrap to your hand after you remove it from a
..... Read more.Flavour in particle physics
..... Read more.Coulomb's law, developed in the 1780s by French physicist Charles Augustin de Coulomb, may be stated as follows:- The magnitude of the electrostatic force between two points electric charges is directly proportional to the product of the magnitudes of each
..... Read more.electric field. This electric field exerts a force on other electrically charged objects. The concept of electric field was introduced by Michael Faraday.
The electric field is a vector field with SI units of newtons per coulomb (N C−1
..... Read more.In physics and mathematical analysis, Gauss's law is the electrostatic application of the generalized Gauss's theorem giving the equivalence relation between any flux, e.g.
..... Read more.Electric potential is the potential energy per unit of charge associated with a static (time-invariant) electric field, also called the electrostatic potential, typically measured in volts. It is a scalar quantity.
..... Read more.In physics, the electric dipole moment (or electric dipole for short) is a measure of the polarity of a system of electric charges.
In the simple case of two point charges, one with charge and one with charge , the electric dipole moment is:
..... Read more.Magnetostatics is the study of static magnetic fields. In electrostatics, the charges are stationary, whereas here, the currents are stationary. As it turns out magnetostatics is a good approximation even when the currents are not static as long as the currents do not
..... Read more.Magnetic flux, represented by the Greek letter Φ (phi), is a measure of quantity of magnetism, taking account of the strength and the extent of a magnetic field.
..... Read more.The Biot-Savart Law is an equation in electromagnetism that describes the magnetic field vector B in terms of the magnitude and direction of the source electric current, the distance from the source electric current, and the magnetic permeability weighting factor.
..... Read more.In physics, the magnetic moment or magnetic dipole moment is a measure of the strength of a magnetic source. In the simplest case of a current loop, the magnetic moment is defined as:
..... Read more.Classical electromagnetism (or classical electrodynamics) is a theory of electromagnetism that was developed over the course of the 19th century, most prominently by James Clerk Maxwell.
..... Read more.Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.Definition
The amount of electric current (measured in amperes) through some surface, e.g.
..... Read more.Lorentz force is the force exerted on a charged particle in an electromagnetic field. The particle will experience a force due to electric field of qE, and due to the magnetic field qv × B.
..... Read more.Electromotive force (emf, ) is a term used to characterize electrical devices, such as voltaic cells, thermoelectric devices, electrical generators and transformers, and even resistors.
..... Read more.For magnetic induction, see .Electromagnetic induction is the production of voltage across a conductor situated in a changing magnetic field or a conductor moving through a stationary magnetic field.
..... Read more.Faraday's law of induction (more generally, the law of electromagnetic induction) states that the induced emf (electromotive force) in a closed loop equals the negative of the time rate of change of magnetic flux through the loop.
..... Read more.Displacement current is a quantity related to changing electric field. It occurs in dielectric materials and also in free space.
In the particular case of when it occurs in free space, it is not believed to involve the motion of electric charge as is the case with
..... Read more.For thermodynamic relations, see .In electromagnetism, Maxwell's equations are a set of four equations that were first presented as a distinct group in 1884 by Oliver Heaviside in conjunction with Willard Gibbs.
..... Read more.The electromagnetic field is a physical field produced by electrically charged objects. It affects the behaviour of charged objects in the vicinity of the field.
..... Read more.Electromagnetic (EM) radiation is a self-propagating wave in space with electric and magnetic components. These components oscillate at right angles to each other and to the direction of propagation, and are in phase with each other.
..... Read more.Electrical resistance is a measure of the degree to which an object opposes an electric current through it. The SI unit of electrical resistance is the ohm. Its reciprocal quantity is electrical conductance measured in siemens.
..... Read more.Capacitance is a measure of the amount of electric charge stored (or separated) for a given electric potential. The most common form of charge storage device is a two-plate capacitor.
..... Read more.inductance, or more accurately self-inductance of the circuit. The term was coined by Oliver Heaviside in February 1886. It is customary to use the symbol for inductance, possibly in honour of the physicist Heinrich Lenz.
..... Read more.Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal alternating current (AC). Electrical impedance extends the concept of resistance to AC circuits, describing not only the relative magnitudes of the voltage and current, but also the
..... Read more.A resonator is a device or system that exhibits resonance or resonant behavior. Many objects that use resonant effects are referred to simply as resonators. Examples of resonators are discussed in this article.
..... Read more.theory of relativity, or simply relativity, refers specifically to two theories: Albert Einstein's special relativity and general relativity.
The term "relativity" was coined by Max Planck in 1908 to emphasize how special relativity (and later, general relativity)
..... Read more.
-
id="CITEREF">magnetic field strength converter, <[8] (retrieved on 2007-06-04)
-
id="CITEREFOppelt">Oppelt, Arnulf (2006-11-02), magnetic field strength, <[7] (retrieved on 2007-06-04)
-
id="CITEREFKeitch">Keitch, Paul, Magnetic Field Strength and Magnetic Flux Density, <[6] (retrieved on 2007-06-04)