Magnetic field

From Wikipedia, the free encyclopedia

Jump to: navigation, search

This article may be too technical for a general
audience.
Please help improve this article by providing more
context and better explanations of technical details to make
it more accessible, without removing technical details. See below for
more information.

Electromagnetism

Electricity · Magnetism

Electrostatics

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

In physics,
a magnetic field is a force field that surrounds electric current
circuits. A magnetic field can also be found in the vicinity of ferromagnetic materials
such as iron. The existence of a magnetic field is ascertained by its effects.
The most important of these effects are (1) Force on a moving electrically
charged particle, (2) Force on a stationary charged particle when the
magnetic field is changing, (3) Mutual force acting between two objects or
electric current circuits that are surrounded by a magnetic field.

Contents

1 Definition

2 The Difference between B
and H

3 Magnetic field of current
flow of charged particles

4 Lorentz force on wire
segment

5 Properties

5.1 Magnetic field
lines

5.2 Pole labelling
confusions

6 Rotating magnetic
fields

7 Hall effect

8 Extension to the Theory of
Relativity

9 See also

10 References

11 Notes

12 External links

[edit]
Definition

The following equation for magnetic field
is a version of the Biot-Savart law and it
is a solution to Ampère's law.

where

is velocity
vector of the electric charge,
measured in metres per second

indicates a vector cross product

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

is the electric field vector 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.
The magnetic field vector is a pseudovector or axial
vector, rather than a simple vector, as it represents an axis.
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:

where

is the force vector produced, measured in newtons

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

is velocity
vector of the electric charge ,
measured in metres per second

Intuitively
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 ,
and the exact direction being at right angles to both the velocity of the
particle and .
The magnitude of
is the amount of force the magnetic field causes on the particle, per unit of
particle charge by particle speed. Another intuitive way to view
is as a bundle of lines of force that pull two unlike magnetic poles
together.

[edit]
The Difference between B and H

There are two quantities that physicists may refer to as the magnetic field,
notated
and .
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[1]

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 ρ 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.

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. 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]
Magnetic field of current flow of charged
particles

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

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

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

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

where

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

is velocity
of the electric charge q that is generating ,
measured in metres per second

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:

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 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]
Properties

[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.

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

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

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]
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.[2] 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).

(However, the Lorentz transformation cannot be applied to electric fields
unless it already presupposes the existence of magnetic fields and their inter
relationship with electric fields under the terms of Maxwell's equations. As
such, the magnetic field can hardly be considered as a by-product of the Lorentz
transformation.)

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". It is a relativistic
manifestation of the more fundamental electric field. 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-2·A-1. An
equivalent, but older, unit for 1 Tesla is Weber/m2.

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".

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]
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.

Electric motor — AC
motors used magnetic fields

Rapid-decay
theory - a creationist theory

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".

^ 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/wiki/Magnetic_field"

Categories: Wikipedia
articles that are too technical | Fundamental
physics concepts | Magnetostatics
| Magnetism |
Physical
quantity | Introductory
physics | Electromagnetism

Views

Article

Discussion

Edit
this page

History

Personal tools

Sign
in / create account

Navigation

Main
page

Contents

Featured
content

Current events

Random article

interaction

About Wikipedia

Community
portal

Recent
changes

Contact us

Make a donation

Help

Search

Toolbox

What
links here

Related
changes

Upload file

Special pages

Printable
version

Permanent
link

Cite
this article

In other languages

العربية

Català

Dansk

Deutsch

Eesti

Español

Français

Hrvatski

Italiano

עברית

Latviešu

Magyar

日本語

Polski

Português

Русский

Slovenčina

Slovenščina

Српски /
Srpski

ไทย

Tiếng Việt

Українська

This page was last modified 19:39, 1 May 2007.

All text is available under the terms of the GNU
Free Documentation License. (See Copyrights
for details.)
Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc., a
US-registered 501(c)(3) tax-deductible
nonprofit charity.

Privacy policy

About Wikipedia

Disclaimers