Download Historical burdens on physics 42 Magnetic poles

Historical burdens on physics
42 Magnetic poles
Subject:
A magnetic pole is either of two regions of a magnet, designated north and
south, where the magnetic field is strongest.
Deficiencies:
Magnetization is a vector field that describes the magnetic dipole density
within a material. The poles of a magnet are those regions where magnetization lines begin or end. The quantity that allows to describe magnetic
poles is the magnetic pole strength or magnetic charge Qm. The magnetic
charge density ρm is the source of the magnetic field H:
∇·H =
ρm
µ0
It is the magnetic analogue to the electric charge, or more exactly: to the
bound electric charge, as it appears at the surface of a polarized dielectric
material. Often, in physics textbooks the magnetic charge is not introduced.
Without it, however, it is difficult to describe a permanent magnet quantitatively.
The relation
F = Qm · H
which is the magnetic analogue of
F=Q·E
and which can easily be verified experimentally, cannot be treated. Coulomb’s law for magnetic poles is even not mentioned, although it is easier to
verify than the corresponding electric law. It is not even possible to define
the most fundamental property of a permanent magnet: i.e. that the total
magnetic charge of each magnet is zero. Instead, there only remains the
rather pale claim that a magnet has (at least) two poles.
For a normal bar magnet the magnetization lines end at the front faces.
That means that the magnetic charge is sitting at these surfaces. These,
however, are not identical with the regions “where the magnetic field is
strongest”, since there are field lines that leave the bar magnet at its lateral
faces, and as the well-known iron filings pictures show, the field intensity is
high at the ends of the lateral faces of the bar magnet. Indeed many students believe that the poles of a bar magnet are also at its sides, and that
the pole intensity decreases towards the middle of the magnet. This misconception is further supported by the customary green-red coloring of the
side faces of permanent magnets.
Origin:
Formerly, magnetic charge –also called magnetism or pole strength– was
introduced in every book about electrodynamics. Maxwell at the very be-
ginning of the second volume of his Treatise introduces Coulomb’s law for
magnetic poles, (it is the first equation in the book) and he states:
“In every magnet the total quantity of magnetism is zero.” [1]
Later the magnetic charge disappeared, due to a misunderstanding. From
the fact that no isolated magnetic monopoles, or particles, that carry a net
magnetic charge have been found, it was concluded that the quantity, that
allows for a description of such a charge does not exist either. However, a
physical quantity is not something that “exists” in nature. It is a tool for describing nature, “a free invention of the human mind”, as Einstein puts it [2].
Introducing or not a physical quantity is only a question of convenience.
And there is no doubt that it is convenient to introduce and to use the quantity “magnetic charge”. Without it, we cannot formulate Coulomb’s law for
magnetic systems, and we can even not pronounce quantitatively the fact
that magnets have two poles.
Disposal:
Introduce the extensive physical quantity magnetic charge. Formulate the
theorem: “The total magnetic charge of a magnet is zero.”
[1] James Clerk Maxwell, A Treatise on Electricity and Magnetism, Dover
Publications Inc., New York, 1954, p.4.
[2] Albert Einstein, Mein Weltbild, Ullstein Taschenbücher-Verlag, 1957, p.
115.
Friedrich Herrmann, Karlsruhe Institute of Technology