Explanation
In electromagnetism, the auxiliary magnetic field H represents how a magnetic field B influences the organization of magnetic dipoles in a given medium, including dipole migration and magnetic dipole reorientation. Its relation to permeability is
where the permeability, μ, is a scalar if the medium is isotropic or a second rank tensor for an anisotropic medium.
In general, permeability is not a constant, as it can vary with the position in the medium, the frequency of the field applied, humidity, temperature, and other parameters. In a nonlinear medium, the permeability can depend on the strength of the magnetic field. Permeability as a function of frequency can take on real or complex values. In ferromagnetic materials, the relationship between B and H exhibits both non-linearity and hysteresis: B is not a single-valued function of H, but depends also on the history of the material. For these materials it is sometimes useful to consider the incremental permeability defined as
This definition is useful in local linearizations of non-linear material behavior, for example in a Newton-Raphson iterative solution scheme that computes the changing saturation of a magnetic circuit.
Permeability is the inductance per unit length. In SI units, permeability is measured in henrys per metre (H·m−1 = J/(A2·m) = N A−2). The auxiliary magnetic field H has dimensions current per unit length and is measured in units of amperes per metre (A m−1). The product μH thus has dimensions inductance times current per unit area (H·A/m2). But inductance is magnetic flux per unit current, so the product has dimensions magnetic flux per unit area. This is just the magnetic field B, which is measured in webers (volt-seconds) per square-metre (V·s/m2), or teslas (T).
B is related to the Lorentz force on a moving charge q:
- .
The charge q is given in coulombs (C), the velocity v in meters per second (m/s), so that the force F is in newtons (N):
H is related to the magnetic dipole density. A magnetic dipole is a closed circulation of electric current. The dipole moment has dimensions current times area, units ampere square-metre (A·m2), and magnitude equal to the current around the loop times the area of the loop. The H field at a distance from a dipole has magnitude proportional to the dipole moment divided by distance cubed, which has dimensions current per unit length.
Read more about this topic: Permeability (electromagnetism)
Famous quotes containing the word explanation:
“There is no explanation for evil. It must be looked upon as a necessary part of the order of the universe. To ignore it is childish, to bewail it senseless.”
—W. Somerset Maugham (1874–1965)
“Herein is the explanation of the analogies, which exist in all the arts. They are the re-appearance of one mind, working in many materials to many temporary ends. Raphael paints wisdom, Handel sings it, Phidias carves it, Shakspeare writes it, Wren builds it, Columbus sails it, Luther preaches it, Washington arms it, Watt mechanizes it. Painting was called “silent poetry,” and poetry “speaking painting.” The laws of each art are convertible into the laws of every other.”
—Ralph Waldo Emerson (1803–1882)
“What causes adolescents to rebel is not the assertion of authority but the arbitrary use of power, with little explanation of the rules and no involvement in decision-making. . . . Involving the adolescent in decisions doesn’t mean that you are giving up your authority. It means acknowledging that the teenager is growing up and has the right to participate in decisions that affect his or her life.”
—Laurence Steinberg (20th century)