Magnetization

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.It is represented by a pseudovector M. The magnetization field or M-field can be defined according to the following equation: Where d m {displaystyle mathrm {d} mathbf {m} } is the elementary magnetic moment and d V {displaystyle mathrm {d} V} 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: 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: Where d p {displaystyle mathrm {d} mathbf {p} } 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. The M-field is measured in amperes per meter (A/m) in SI units. 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 B r {displaystyle scriptstyle mathbf {B} _{r}} . Physicists often need the magnetization to calculate the moment of a ferromagnet. To calculate the dipole moment m (A⋅m2) using the formula: