Historical burdens on physics
43 The field of permanent magnets
Subject:
In physics textbooks for the secondary school field line pictures of bar magnets are shown. Examples can be seen in Fig. 1.
Deficiencies:
In all the text books that I have consulted the corresponding pictures are
incorrect. (I have examined ten school
books, most of them German, some
American and one Italian). The errors
can be seen when comparing the
school book pictures of Fig. 1 with the
correct drawing of Fig. 2a (which was
taken from Sommerfeld [1]). The difference between Fig. 2a and the school
book pictures do not allow the excuse
that different pole distributions have
been presupposed, since there are no
pole distributions that correspond to
fields as shown in Fig. 1.
In the various text books different errors
can be detected.
1. Field lines exit or enter the magnet
only at the end faces, Figures 1a, 1b
and 1c. Actually they also do so at the
lateral faces.
2. Field lines exit the magnet only perpendicularly to the surface, Figures 1a
and 1b. Actually they are perpendicular
only at the center of the end faces.
3. Those field lines, which enter into or
exit from the magnet at the lateral faces
have an incorrect orientation, Figures
1d, 1e, 1f, 1g and 1h.
Similar errors can be found in the pictures of the magnetic field of the horseshoe magnets and of the Earth. Often, a
school book also shows a photograph
where the field lines are made visible by
means of iron filings. In such books one
may see on two figures that are side by
side the discrepancy between the real
field and what the field line picture pretends.
One of the pictures that I have found,
a
b
c
d
e
f
g
h
Fig. 1. Magnetic field lines of bar magnets, as shown in secondary school
books
displays even more crude errors:
Field lines do not only begin at
the north pole but also end there,
and the same happens at the
south pole.
a
Origin:
A graphical representation of a
physical phenomenon must not
necessarily be precise in every
respect. It must show and may
emphasize the essential. Unimportant details may be omitted for
the sake of clearness. In the present case, however, no simplification was made, but a message
was conveyed that is not correct.
It is not true that the students do
not perceive the incorrect claims.
One can easily convince oneself
that they keep them in mind. Indeed, many students believe,
that the field lines depart perpendicularly from the end faces of a
bar magnet. When asking a student to draw a field line picture of
a bar magnet, almost always an
incorrect picture or sketch is
drawn. Obviously, the students
draw something which they have
memorized.
b
c
Fig. 2. Bar magnet. (a) H and B field lines outside
the magnet; (b) B field lines; (c) H field lines
When asking for an explanation
or justification of the direction of the field lines, their reaction is perplexity.
Actually, the incorrect pictures have a certain plausibility.
The incorrect direction of the field lines that exit or enter at the lateral faces
might be justified in the following way: The students know that the B field is
divergence-free. The B field lines have no beginning and no end. Thus,
they can be completed or continued at the inside of the magnet. Now, they
make the incorrect hypothesis that the field lines have no kink when crossing the surface of the magnet. And indeed, in one of the text books, the field
lines had been drawn in this way, Fig. 1f. The field lines would be even
more “smooth”, if they left the magnet only at the end faces, as in Fig. 1b.
(The figures 1b and 1f are taken from the same book, but they do not agree
with one another.) The correct shape of the lines is shown in figure 2b. Notice the pronounced kinks of the lines at the lateral surfaces.
Those who let the lines enter and exit only at the end faces may believe
that inside they are identical with the magnetization lines, what is not true.
(The magnetization lines form a homogeneous field.)
Those who let the lines enter and exit perpendicularly to the surfaces may
believe, that a rule applies which we know from the electric field lines at the
surface of an electric conductor.
We were surprised to find that all the University text books that we had
consulted show the correct pictures, whereas all the school books show
incorrect pictures. Apparently there exists something like a “school physics”
that has its own life, independent from “University physics”. It also shows
that a “new” book in general is not really new. It contains the old errors in a
new packing.
Disposal:
Draw correct field lines. A help may be: Do not draw the B, but the H lines,
Fig. 2c. The magnetic poles are the sources of the H field lines. One may
imagine that the end faces are not magnetic poles but carry electric charge.
The problem of drawing the H field lines is the same as that of drawing the
electric field lines for the charged end faces.
[1] Sommerfeld, A.: Vorlesungen über Theoretische Physik, Band III, Elektrodynamik. – Akademische Verlagsgesellschaft,
Leipzig 1964. – S. 78
Friedrich Herrmann, Karlsruhe Institute of Technology