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| {{about|magnetization as it appears in Maxwell's equations of classical electrodynamics|a microscopic description of how magnetic materials react to a magnetic field|magnetism|mathematical description of fields surrounding magnets and currents|magnetic field}}
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| {{Electromagnetism|cTopic=Magnetostatics}}
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| In classical [[electromagnetism]], '''magnetization''' <ref>American spelling. The British spelling is '''magnetisation'''.</ref> or '''magnetic polarization''' is the [[vector field]] that expresses the [[density]] of permanent or induced [[magnetic dipole moment]]s in a magnetic material. The origin of the magnetic moments responsible for magnetization can be either microscopic [[electric current]]s resulting from the motion of [[electron]]s in [[atom]]s, or the [[Spin (physics)|spin]] of the electrons or the nuclei. Net magnetization results from the response of a material to an external [[magnetic field]], together with any unbalanced magnetic dipole moments that may be inherent in the material itself; for example, in [[ferromagnet]]s. Magnetization is not always [[homogeneity (physics)|homogeneous]] within a body, but rather varies between different points. Magnetization also describes how a material responds to an applied [[magnetic field]] as well as the way the material changes the magnetic field, and can be used to calculate the [[force]]s that result from those interactions. It can be compared to [[Polarization density|electric polarization]], which is the measure of the corresponding response of a material to an [[electric field]] in [[electrostatics]]. Physicists and engineers define magnetization as the quantity of [[magnetic moment]] per unit volume. It is represented by a vector M.
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| ==Definition==
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| Magnetization can be defined according to the following equation:
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| :<math>\mathbf{M}=\frac{N}{V}\mathbf{m}=n\mathbf{m}</math>
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| Here, '''M''' represents magnetization; '''m''' is the [[Euclidean vector|vector]] that defines the [[magnetic moment]]; V represents volume; and ''N'' is the number of magnetic moments in the sample. The quantity ''N/V'' is usually written as ''n'', the number density of magnetic moments. The M-field is measured in [[amperes]] per meter (A/m) in SI units.<ref>{{cite web|url=http://www.magneticmicrosphere.com/resources/Units_for_Magnetic_Properties.pdf|title=Units for Magnetic Properties|publisher=Lake Shore Cryotronics, Inc.|accessdate=2009-10-24}}</ref>
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| ==Magnetization in Maxwell's equations==
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| The behavior of [[magnetic field]]s ('''''B''''', '''''H'''''), [[electric fields]] ('''''E''''', '''''D'''''), [[charge density]] (''ρ''), and [[current density]] ('''''J''''') is described by [[Maxwell's equations]]. The role of the magnetization is described below.
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| ===Relations between B, H, and M===
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| {{main|Magnetic field}}
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| The magnetization defines the auxiliary magnetic field '''''H''''' as
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| :<math>\mathbf{B}=\mu_0\mathbf{(H + M)}</math> ([[SI units]])
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| :<math>\mathbf{B} = (\mathbf{H} + 4 \pi \mathbf{M} )</math> ([[Gaussian units]])
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| which is convenient for various calculations. The [[vacuum permeability]] μ<sub>0</sub> is, by definition, {{val|4|end= π|e=-7}} [[Volt|V]]·[[Second|s]]/([[Ampere|A]]·[[Metre|m]]).
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| A relation between '''''M''''' and '''''H''''' exists in many materials. In [[diamagnet]]s and [[paramagnet]]s, the relation is usually linear:
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| :<math>\mathbf{M} = \chi_m\mathbf{H}</math>
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| where ''χ''<sub>m</sub> is called the [[magnetic susceptibility|volume magnetic susceptibility]].
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| In [[ferromagnet]]s there is no one-to-one correspondence between '''''M''''' and '''''H''''' because of [[Magnetic hysteresis]].
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| ===Magnetization current===
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| The magnetization '''''M''''' makes a contribution to the [[current density]] '''''J''''', known as the '''magnetization current''' or '''bound current''':
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| :<math> \mathbf{J_m} = \nabla\times\mathbf{M} </math>
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| so that the total current density that enters Maxwell's equations is given by
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| :<math> \mathbf{J} = \mathbf{J_f} + \nabla\times\mathbf{M} + \frac{\partial\mathbf{P}}{\partial t}</math>
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| where '''''J'''''<sub>f</sub> is the electric current density of free charges (also called the '''free current'''), the second term is the contribution from the magnetization, and the last term is related to the [[electric polarization]] '''''P'''''.
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| ===Magnetostatics===
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| {{Main|Magnetostatics}}
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| In the absence of free electric currents and time-dependent effects, [[Maxwell's equations]] describing the magnetic quantities reduce to
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| :<math>\begin{align}
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| \mathbf{\nabla\cdot H} &= -\nabla\cdot\mathbf{M}\\
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| \mathbf{\nabla\times H} &= 0
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| \end{align}</math>
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| These equations can be easily solved in analogy with [[electrostatic]] problems where
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| :<math>\begin{align}
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| \mathbf{\nabla\cdot E} &= \frac{\rho}\epsilon_0\\
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| \mathbf{\nabla\times E} &= 0
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| \end{align} </math>
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| In this sense <math>-\nabla\cdot\mathbf{M}</math> plays the role of a "magnetic charge density" analogous to the electric charge density <math>\rho</math> (see also [[demagnetizing field]]).
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| Magnetization is volume density of [[magnetic moment]]. That is: if a certain volume has magnetization <math>\mathbf{M}</math> then the volume element <math>d V</math> has a magnetic moment of <math>d\mathbf{m} = \mathbf{M} \, dV</math>
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| ==Magnetization dynamics==
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| ::''Main article: [[Magnetization dynamics]]''
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| The time-dependent behavior of magnetization becomes important when considering nanoscale and nanosecond timescale magnetization. Rather than simply aligning with an applied field, the individual magnetic moments in a material begin to precess around the applied field and come into alignment through relaxation as energy is transferred into the lattice.
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| ==Demagnetization==
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| In addition to magnetization, there is also demagnetization. Demagnetization is the process by which the magnetic field of an object is reduced or eliminated.<ref>{{cite web|title=Magnetic Component Engineering|url=http://www.mceproducts.com/knowledge-base/article/article-dtl.asp?id=90|publisher=Magnetic Component Engineering|accessdate=April 18, 2011}}</ref> The process of demagnetizing can be accomplished in many ways. One technique used for demagnetization is to heat the object above its [[Curie Temperature]]. The reason for this is that when a magnetic material is heated to its Curie Temperature, thermal fluctuations have enough energy to overcome the [[exchange interactions]] which cause ferromagnetism, and magnetic ordering is destroyed. One other way of achieving demagnetization is to use an electric coil. If the object is retracted out of a coil with alternating current running through it, the object's dipoles will become randomized and the object will be demagnetized.<ref name="NDT">{{cite web|title=Demagnetization|url=http://www.ndt-ed.org/EducationResources/CommunityCollege/MagParticle/Physics/Demagnetization.htm|work=Introduction to Magnetic Particle Inspection|publisher=NDT Resource Center|accessdate=April 18, 2011}}</ref>
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| ===Applications of Demagnetization===
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| One application of demagnetization is to eliminate unwanted magnetic fields. The reason for doing this is that magnetic fields can have unwanted effects on different devices. In particular magnetic fields can affect electronic devices such as cell phones or computers. If such a device is going to be coming into contact with other possibly magnetic objects, the magnetic fields might need to be reduced in order to protect the electronic device. Therefore demagnetization is sometimes used to keep magnetic fields from damaging electrical devices.<ref name="NDT"/>
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| ==See also==
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| * [[Permeability (electromagnetism)]]
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| * [[Magnetic susceptibility]]
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| * [[Earth's magnetic field]]
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| * [[Geomagnetic reversal]]
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| * [[Geomagnetic excursion]]
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| * [[Orbital magnetization]]
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| {{Wiktionary-inline}}
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| ==Sources==
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| <references/>
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| [[Category:Electric and magnetic fields in matter]]
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