Physics II: Chapter 8

ReferenceBeginning Physics II




Magnetization, Orbital Motion, Spin, Diamagnetic Material, Paramagnetic Material, Ferromagnetism, Magnetic Poles, Magnetization Vector, Magnetic Intensity Vector, Magnetic Susceptibility, Superconductor



For details on the following concepts, please consult Chapter 8.

A magnetic field can change the properties of the material in which it is created, and result in having the material produce its own field, which has to be added to the original field. This modification of the properties of a material is called “magnetization” of the material.

In order for a magnetic field to have any effect, a material must consist of moving charged particles. All materials consist of a collection of atoms and molecules. The orbital motion may be thought of as electrons circulating about a nucleus within an atom.

In addition to orbiting the nucleus, the electrons spin on their axes and, as a consequence, have an additional “spin” angular momentum and “spin” electric current loops. In either case, orbital or spin, magnetic fields can be set up by the atomic current loops, and an external magnetic field can exert forces on the electrons, and thereby modify their motion.

An external magnetic field generally induces      currents and associated magnetic moments in the atoms of a material. These magnetic moments, in turn, produce their own magnetic fields, which, by Lenz’s law, are in a direction opposite to the original field. The materials in which this is the dominant effect are called diamagnetic materials, in the same manner as materials that produce electric fields opposed to the original electric field are dielectric materials. In general, such induced magnetic fields in an atom are very small and the external field is reduced by a tiny amount as a consequence of diamagnetism. While diamagnetism is present in all atoms, it dominates only in those atoms in which the orbital and spin angular moments average out to zero.

In paramagnetic materials there is a net orbital and/or spin angular momentum and a net effective current loop for the atom. Such an “effective” current loop gives the atom a definite overall magnetic dipole moment. An external magnetic field exerts a torque on such a magnetic moment and the torque tries to line up the moment parallel to the magnetic field. The lined-up moments will then produce their own magnetic field in the same direction as the original field, thus increasing the magnetic field. Paramagnetic materials are more common than diamagnetic materials, especially since they dominate in materials where both effects are present.

Certain materials, notably iron, nickel and cobalt, exhibit ferromagnetism at room temperature. This means that the magnetic interactions between the magnetic moments of neighboring atoms is strong enough, even at room temperature, to align the moments in the same direction. If an external field is applied to the ferromagnetic material it has the effect of causing the domains of aligned moments to rotate and point in the same direction, the direction of the magnetic field. Once they have been aligned, they tend to remain aligned even if the external field that originally caused them to align is removed. The material has now become a permanent magnet.

The field produced by a solenoid is nearly the same in shape as the electric field produced by oppositely charged particles located at the ends of the bar. We therefore often talk of the bar as being composed of two opposite magnetic poles (the substitute for electric charges), one called a north pole and the other called a south pole.

The north pole is the apparent source of magnetic field lines (as is a positive charge for electric field lines), and the south pole is a sink for the lines. In actuality the lines do not terminate at the poles, but continue in straight lines within the material, forming closed loops. The designation of north or south pole arises from the fact that the bar tends to line up in the magnetic field of the earth with the north pole facing in the northerly direction. As in the case of electric charges, opposite poles attract, and similar poles repel each other.

The magnetization vector, M, is the total magnetic moment per unit volume. Thus, a material in a magnetic field can become magnetized, with a magnetization M = ΣM/V). The magnetic field, BM produced by the magnetic dipoles in the material is related to the magnetization as follows.

It is the part of the magnetic field in a material that arises from an external current and is not intrinsic to the material itself. The definition of H is:

H = B/μ0 − M

where B is the actual magnetic field within a material considered as a concentration of magnetic field lines per unit cross-sectional area; μ0 is the magnetic permeability; and M is the magnetization vector. The magnetic field H might be thought of as the magnetic field produced by the flow of current in wires and the magnetic field B as the total magnetic field including also the contribution M made by the magnetic properties of the materials in the field. When a current flows in a wire wrapped on a soft-iron cylinder, the magnetizing field H is quite weak, but the actual average magnetic field (B) within the iron may be thousands of times stronger because B is greatly enhanced by the alignment of the iron’s myriad tiny natural atomic magnets in the direction of the field.

In general, except for material that becomes a permanent magnet, the magnetization is proportional to the magnetic field, and therefore to the magnetic intensity as well. We can therefore write that,

Where χ is called the magnetic susceptibility of the material. Then

where μ is the permeability of the material, κm, is the relative permeability of the material, and μ = μ0κm, with κm = 1 + χ. This means that for these materials, we can calculate B if we know H, merely by multiplying H by μ.

Some materials, at sufficiently low temperatures lose all their resistivity. These materials are called superconductors. They also set up surface currents in a magnetic field, which themselves produce an exactly opposite field, and thereby cancel any field which tries to be established in its interior. Thus, a superconductor can be considered to be a perfect diamagnet.


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