Download 127 Magnetic monopole and magnetic charge

127 Magnetic monopole and magnetic charge
Subject:
There are no particles that carry magnetic charge. It is said, that no
magnetic monopoles exist. It follows, so it is argued, that a physical quantity
„magnetic charge“ or „magnetic pole strength“ does not exist.
Deficiencies:
Let us first clarify two concepts:
Magnetic charge density ρm:
It is defined by
μ0 div H = ρm!
!
!
!
!
!
!
(1)
Thus, the magnetic charge density describes the sources of the H field.
Since we have
μ0 div H = – div M# #
#
#
#
#
#
(2)
it also signifies the sinks of the magnetization field. The volume integral of
the magnetic charge density is called magnetic pole strength, magnetic
charge or amount of magnetism.
Magnetic monopole:
The word is not used consistently.
When it is said that no magnetic monopoles exist, one refers to particles,
i.e. objects that carry magnetic charge (or whose pole strength is different
from zero). Such „monopoles“ have not been found so far.
But the word is also used as a name for the source of a magnetic „Coulomb
field“, i.e. a magnetic field, whose field strength H decreases as 1/r 2. Such
fields can be realized in any desired approximation. It is the field in the
vicinity of a pole of bar magnet that is long and thin.
Because of this ambiguity, in the following we shall not call a magnetically
charged particle a „monopole“ but a „monopole particle“.
To show the non-existence of the physical magnitude „magnetic charge“ it
is usually argued that no monopole particles have been found. However, in
order to explain what is meant by such a particle it is necessary to first
introduce the physical quantity magnetic charge, for instance by means of
equation (1).
It is not possible to deduce the existence or non-existence of a physical
quantity from an observation of nature. Physical quantities are human
constructs or creations [1]. A physical quantity is introduced when it is
advantageous; when it can serve for the description of natural phenomena.
Actually it is advantageous to introduce a quantity „magnetic charge“. It is
needed among other things:
• to describe the fact, that no magnetic monopole particles exist;
• to describe the fact, that the poles of a magnet carry equal and
opposite charges at their poles;
• to formulate Coulomb’s law for magnetic poles [2].
Certainly one could do without the introduction of magnetic charge. But
then, instead of saying that no particles exist that carry magnetic charge,
we had to formulate: „There are no particles for which the volume integral of
the divergence of the magnetic field strength over a region of space that
contains the particle is different from zero.“ By the way, one could get rid of
the electric charge in the same way. Obviously nobody would do so.
Origin:
Magnetic charge is a time-honored physical quantity, which has been used
with various names. At Coulomb’s time it was imagined that magnetism is
caused by two magnetic fluids (in analogy with the electric phenomena,
which were explained by two electric fluids).
For both, the electric and the magnetic fluids, Coulomb discovered the
inverse square law of the force [2].
Maxwell calls this quantity the „strength of a pole“ [3]:
The repulsion between two like poles is in the straight line joining them,
and is numerically equal to the product of the strengths of the poles
divided by the square of the distance between them.
On the next page he introduces the term „quantity of magnetism“, and he
states:
The quantity of magnetism at one pole of a magnet is always equal and
opposite to that at the other, or more generally thus:
In every Magnet the total quantity of Magnetism (reckoned algebraically)
is zero.
The term quantity of magnetism is also later used by Max Born [4].
Although it is easier to verify experimentally Coulomb’s law for magnetic
than that for electric charge, the quantity has today almost completely
disappeared from the text books. This happened together with the
marginalization of the magnetic field strength. If the field strength is not
used to describe a magnetic field the equation
!
μ0 div H = ρm
no longer can serve to get a feeling for the magnetic charge.
Disposal:
At school: Introduce magnetic charge right from the beginning of
magnetostatics as an independent extensive physical quantity, in the same
way as one introduces electric charge in electrostatics. The total magnetic
charge of a magnet is zero.
At university: First treat the relation
!
μ0 div H = – div M
Thereafter introduce magnetic charge as:
!
ρm = μ0 div H .
Friedrich Herrmann
[1] G. Falk und W. Ruppel: Mechanik, Relativität, Gravitation,
Springer-Verlag, Berlin 1973, p. 2
[2] C. A. Coulomb: Second Mémoire sur l’Électricitá et le Magnétisme, Où
l’on détermine, suivant quelles loix le Fluide magnétique, ainsi que le Fluide
électrique, agissent, soit par répulsion, soit par attraction. Mémoires de
l’Academie Royale des Sciences, 1785, p. 593
[3] J. C. Maxwell, A treatise on electricity and magnetism, Volume two,
Dover Publications, Inc, New York, 1954, p. 3-4
[4] M. Born, Die Relativitätstheorie Einsteins, Heidelberger Taschenbücher,
Springer-Verlag, Berlin 1969, p. 133