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In classical electromagnetism, **magnetization** or **magnetic polarization** is the vector field that expresses the density of permanent or induced magnetic dipole moments in a magnetic material. The origin of the magnetic moments responsible for magnetization can be either microscopic electric currents resulting from the motion of electrons in atoms, or the 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 ferromagnets. Magnetization is not always uniform 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 forces that result from those interactions. It can be compared to electric polarization, which is the measure of the corresponding response of a material to an electric field in electrostatics. Physicists and engineers usually define magnetization as the quantity of magnetic moment per unit volume.^{ [1] } It is represented by a pseudovector **M**.

**Classical electromagnetism** or **classical electrodynamics** is a branch of theoretical physics that studies the interactions between electric charges and currents using an extension of the classical Newtonian model. The theory provides a description of electromagnetic phenomena whenever the relevant length scales and field strengths are large enough that quantum mechanical effects are negligible. For small distances and low field strengths, such interactions are better described by quantum electrodynamics.

In vector calculus and physics, a **vector field** is an assignment of a vector to each point in a subset of space. A vector field in the plane, can be visualised as: a collection of arrows with a given magnitude and direction, each attached to a point in the plane. Vector fields are often used to model, for example, the speed and direction of a moving fluid throughout space, or the strength and direction of some force, such as the magnetic or gravitational force, as it changes from one point to another point.

The **density**, or more precisely, the **volumetric mass density**, of a substance is its mass per unit volume. The symbol most often used for density is *ρ*, although the Latin letter *D* can also be used. Mathematically, density is defined as mass divided by volume:

The magnetization field or **M**-field can be defined according to the following equation:

Where is the elementary magnetic moment and * is the volume element; in other words, the ***M**-field is the distribution of magnetic moments in the region or manifold concerned. This is better illustrated through the following relation:

The **magnetic moment** is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current, permanent magnets, elementary particles, various molecules, and many astronomical objects.

In mathematics, a **volume element** provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form

In mathematics, a **manifold** is a topological space that locally resembles Euclidean space near each point. More precisely, each point of an *n*-dimensional manifold has a neighbourhood that is homeomorphic to the Euclidean space of dimension *n*. In this more precise terminology, a manifold is referred to as an ** n-manifold**.

where **m** is an ordinary magnetic moment and the triple integral denotes integration over a volume. This makes the **M**-field completely analogous to the electric polarisation field, or **P**-field, used to determine the electric dipole moment **p** generated by a similar region or manifold with such a polarization:

In classical electromagnetism, **polarization density** is the vector field that expresses the density of permanent or induced electric dipole moments in a dielectric material. When a dielectric is placed in an external electric field, its molecules gain electric dipole moment and the dielectric is said to be polarized. The electric dipole moment induced per unit volume of the dielectric material is called the electric polarization of the dielectric.

The **electric dipole moment** is a measure of the separation of positive and negative electrical charges within a system, that is, a measure of the system's overall polarity. The SI units for electric dipole moment are coulomb-meter (C⋅m); however, the most commonly used unit in atomic physics and chemistry is the debye (D).

Where is the elementary electric dipole moment.

Those definitions of **P** and **M** as a "moments per unit volume" are widely adopted, though in some cases they can lead to ambiguities and paradoxes.^{ [1] }

The **M**-field is measured in * amperes per meter * (A/m) in SI units.^{ [2] }

The **ampere**, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

The magnetization is often not listed as a material parameter for commercially available ferromagnets. Instead the parameter that is listed is residual flux density, denoted . Physicists often need the magnetization to calculate the moment of a ferromagnet. To calculate the dipole moment **m** (A⋅m^{2}) using the formula:

- ,

we have that

- ,

thus

- ,

where:

- is the residual flux density, expressed in teslas (T).
- is the volume (m
^{3}) of the magnet. - H/m is the permeability of vacuum.
^{ [3] }

The behavior of magnetic fields (**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.

The magnetization defines the auxiliary magnetic field **H** as

- (SI units)

- (Gaussian units)

which is convenient for various calculations. The vacuum permeability μ_{0} is, by definition, 4π×10^{−7} V·s/(A·m).

A relation between **M** and **H** exists in many materials. In diamagnets and paramagnets, the relation is usually linear:

where *χ* is called the volume magnetic susceptibility.

In ferromagnets there is no one-to-one correspondence between **M** and **H** because of magnetic hysteresis.

The magnetization * M* makes a contribution to the current density

and for the *bound surface current*:

so that the total current density that enters Maxwell's equations is given by

where **J**_{f} 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**.

In the absence of free electric currents and time-dependent effects, Maxwell's equations describing the magnetic quantities reduce to

These equations can be solved in analogy with electrostatic problems where

In this sense −∇⋅**M** plays the role of a fictitious "magnetic charge density" analogous to the electric charge density *ρ*; (see also demagnetizing field).

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.

Magnetization reversal, also known as switching, refers to the process that leads to a 180° (arc) re-orientation of the magnetization vector with respect to its initial direction, from one stable orientation to the opposite one. Technologically, this is one of the most important processes in magnetism that is linked to the magnetic data storage process such as used in modern hard disk drives.^{ [5] } As it is known today, there are only a few possible ways to reverse the magnetization of a metallic magnet:

- an applied magnetic field
^{ [5] } - spin injection via a beam of particles with spin
^{ [5] } - magnetization reversal by circularly polarized light;
^{ [6] }i.e., incident electromagnetic radiation that is circularly polarized

Demagnetization is the reduction or elimination of magnetization.^{ [7] } One way to do this is to heat the object above its Curie temperature, where thermal fluctuations have enough energy to overcome exchange interactions, the source of ferromagnetic order, and destroy that order. Another way is to pull it out of an electric coil with alternating current running through it, giving rise to fields that oppose the magnetization.^{ [8] }

One application of demagnetization is to eliminate unwanted magnetic fields. For example, magnetic fields can interfere with electronic devices such as cell phones or computers, and with machining by making cuttings cling to their parent.^{ [8] }

Look up in Wiktionary, the free dictionary. magnetization |

In physics the **Lorentz force** is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge *q* moving with a velocity *v* in an electric field **E** and a magnetic field **B** experiences a force of

**Magnetism** is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. The most familiar effects occur in ferromagnetic materials, which are strongly attracted by magnetic fields and can be magnetized to become permanent magnets, producing magnetic fields themselves. Only a few substances are ferromagnetic; the most common ones are iron, cobalt and nickel and their alloys such as steel. The prefix *ferro-* refers to iron, because permanent magnetism was first observed in lodestone, a form of natural iron ore called magnetite, Fe_{3}O_{4}.

**Maxwell's equations** are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits. The equations provide a mathematical model for electric, optical, and radio technologies, such as power generation, electric motors, wireless communication, lenses, radar etc. Maxwell's equations describe how electric and magnetic fields are generated by charges, currents, and changes of the fields. One important consequence of the equations is that they demonstrate how fluctuating electric and magnetic fields propagate at a constant speed (*c*) in the vacuum, the "speed of light". Known as electromagnetic radiation, these waves may occur at various wavelengths to produce a spectrum from radio waves to γ-rays. The equations are named after the physicist and mathematician James Clerk Maxwell, who between 1861 and 1862 published an early form of the equations that included the Lorentz force law. He also first used the equations to propose that light is an electromagnetic phenomenon.

**Paramagnetism** is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds; they have a relative magnetic permeability slightly greater than 1 and hence are attracted to magnetic fields. The magnetic moment induced by the applied field is linear in the field strength and rather weak. It typically requires a sensitive analytical balance to detect the effect and modern measurements on paramagnetic materials are often conducted with a SQUID magnetometer.

A **magnetic field** is a vector field that describes the magnetic influence of electric charges in relative motion and magnetized materials. The effects of magnetic fields are commonly seen in permanent magnets, which pull on magnetic materials and attract or repel other magnets. Magnetic fields surround and are created by magnetized material and by moving electric charges such as those used in electromagnets. They exert forces on nearby moving electrical charges and torques on nearby magnets. In addition, a magnetic field that varies with location exerts a force on magnetic materials. Both the strength and direction of a magnetic field vary with location. As such, it is described mathematically as a vector field.

In classical electromagnetism, **Ampère's circuital law** relates the integrated magnetic field around a closed loop to the electric current passing through the loop. James Clerk Maxwell derived it using hydrodynamics in his 1861 paper "On Physical Lines of Force" and it is now one of the Maxwell equations, which form the basis of classical electromagnetism.

In electromagnetism, **permeability** is the measure of the ability of a material to support the formation of a magnetic field within itself, otherwise known as distributed inductance in transmission line theory. Hence, it is the degree of magnetization that a material obtains in response to an applied magnetic field. Magnetic permeability is typically represented by the (italicized) Greek letter *μ*. The term was coined in September 1885 by Oliver Heaviside. The reciprocal of magnetic permeability is magnetic reluctivity.

In electrodynamics, **Poynting's theorem** is a statement of conservation of energy for the electromagnetic field, in the form of a partial differential equation, due to the British physicist John Henry Poynting. Poynting's theorem is analogous to the work-energy theorem in classical mechanics, and mathematically similar to the continuity equation, because it relates the energy stored in the electromagnetic field to the work done on a charge distribution, through energy flux.

The term **magnetic potential** can be used for either of two quantities in classical electromagnetism: the *magnetic vector potential*, or simply *vector potential*, **A**; and the *magnetic scalar potential**ψ*. Both quantities can be used in certain circumstances to calculate the magnetic field **B**.

In physics, the **electric displacement field**, denoted by **D**, is a vector field that appears in Maxwell's equations. It accounts for the effects of free and bound charge within materials. "**D**" stands for "displacement", as in the related concept of displacement current in dielectrics. In free space, the electric displacement field is equivalent to flux density, a concept that lends understanding to Gauss's law. In the International System of Units (SI), it is expressed in units of coulomb per meter square (C⋅m^{−2}).

The **Curie constant** is a material-dependent property that relates a material's magnetic susceptibility to its temperature.

**Magnetostatics** is the study of magnetic fields in systems where the currents are steady. It is the magnetic analogue of electrostatics, where the charges are stationary. The magnetization need not be static; the equations of magnetostatics can be used to predict fast magnetic switching events that occur on time scales of nanoseconds or less. Magnetostatics is even a good approximation when the currents are not static — as long as the currents do not alternate rapidly. Magnetostatics is widely used in applications of micromagnetics such as models of magnetic storage devices as in computer memory. Magnetostatic focussing can be achieved either by a permanent magnet or by passing current through a coil of wire whose axis coincides with the beam axis.

**Lorentz–Heaviside units** constitute a system of units within CGS, named from Hendrik Antoon Lorentz and Oliver Heaviside. They share with CGS-Gaussian units the property that the electric constant *ε*_{0} and magnetic constant *µ*_{0} do not appear, having been incorporated implicitly into the unit system and electromagnetic equations. Lorentz–Heaviside units may be regarded as normalizing *ε*_{0} = 1 and *µ*_{0} = 1, while at the same time revising Maxwell's equations to use the speed of light *c* instead.

**Micromagnetics** is a field of physics dealing with the prediction of magnetic behaviors at sub-micrometer length scales. The length scales considered are large enough for the atomic structure of the material to be ignored, yet small enough to resolve magnetic structures such as domain walls or vortices.

In physics, magnetization dynamics is the branch of solid-state physics that describes the evolution of the magnetization of a material.

The **demagnetizing field**, also called the **stray field**, is the magnetic field (H-field) generated by the magnetization in a magnet. The total magnetic field in a region containing magnets is the sum of the demagnetizing fields of the magnets and the magnetic field due to any free currents or displacement currents. The term *demagnetizing field* reflects its tendency to act on the magnetization so as to reduce the total magnetic moment. It gives rise to *shape anisotropy* in ferromagnets with a single magnetic domain and to magnetic domains in larger ferromagnets.

**Multipole radiation** is a theoretical framework for the description of electromagnetic or gravitational radiation from time-dependent distributions of distant sources. These tools are applied to physical phenomena which occur at a variety of length scales - from gravitational waves due to galaxy collisions to gamma radiation resulting from nuclear decay. Multipole radiation is analyzed using similar multipole expansion techniques that describe fields from static sources, however there are important differences in the details of the analysis because multipole radiation fields behave quite differently from static fields. This article is primarily concerned with electromagnetic multipole radiation, although the treatment of gravitational waves is similar.

- 1 2 C.A. Gonano; R.E. Zich; M. Mussetta (2015). "Definition for Polarization P and Magnetization M Fully Consistent with Maxwell's Equations" (PDF).
*Progress in Electromagnetics Research B*.**64**: 83–101. doi:10.2528/PIERB15100606. - ↑ "Units for Magnetic Properties" (PDF). Lake Shore Cryotronics, Inc. Retrieved 2015-06-10.
- ↑ "K&J Magnetics - Glossary".
*www.kjmagnetics.com*. - ↑ A. Herczynski (2013). "Bound charges and currents" (PDF).
*American Journal of Physics*.**81**(3): 202–205. Bibcode:2013AmJPh..81..202H. doi:10.1119/1.4773441. - 1 2 3 Stohr, J.; Siegmann, H. C. (2006),
*Magnetism: From fundamentals to Nanoscale Dynamics*, Springer-Verlag, Bibcode:2006mffn.book.....S - ↑ Stanciu, C. D.; et al. (2007),
*Physical Review Letters 99, 217204* - ↑ "Magnetic Component Engineering". Magnetic Component Engineering. Retrieved April 18, 2011.
- 1 2 "Demagnetization".
*Introduction to Magnetic Particle Inspection*. NDT Resource Center. Retrieved April 18, 2011.

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