Physics for university students (Volume 2) online

tion when freelv suspended horizontally. It has no fixed
poles and no equator.

( )tlier substances attracted by a magnet are nickel, cobalt,
manganese, chromium, and cerium. Only nickel and cobalt
show decided magnetic properties comparable with iron.
Some gases are feebly magnetic, and liquid oxygen exhibits
conspicuous magnetic properties.

Another class of substances are apparently repelled by a
magnet. These are called <liama</itrttc to distinguish them
from paramagnetic bodies like iron and nickel. Among
them are bismuth, antimony, tin, copper, and some others
in a less marked degree. Paramagnetic bodies are often
designated simply by the word magnetic.''

256. Magnetic Induction. When a magnet attracts
a piece of soft iron, the iron first be-
comes a temporary magnet by induction.

Magnetic induction is analogous to

electrostatic induction, and takes place

along lines of induction or lines of

magnetic force. When one piece of

iron has been attached to the pole of

a magnet, it may in turn act inductively

on a second one, and so on in a series Fig - I3L

of temporary magnets of decreasing strength (Fig. 131).




308 ELECTRICITY AND MAGNETISM.

But if the magnet be detached from the first piece and be

slowly withdrawn, all the small
iron cylinders will fall apart, and
they will not again attract one
another till they are once more
brought under the inductive in-

Fig. 132.

fluence of a magnet. A bar of iron

near a magnet is attracted because it becomes a temporary
magnet by induction, with the pole nearest to the pole of
the inducing magnet of the opposite kind or sign (Fig.
132). Induction thus precedes attraction.

257. Permanent and Temporary Magnets. - - Per-
manent and temporary magnets differ only in degree. The
softest iron retains a small amount of magnetism after it
has been brought under the action of a magnetizing force,
while hardened steel retains a large proportion of it. The
latter loses some of its magnetism as soon as the magnet-
izing force is withdrawn, while the former loses the larger
part. A much larger magnetizing force is required to
magnetize hard steel than soft iron to the same magnetic
strength. The relation between the part lost and the part
retained depends on the quality and hardness of the iron
and on the after treatment which it receives. Cast-iron
retains an appreciable fraction of the magnetism induced in
it, and this property is utilized in starting the excitation of
dynamo machines. The property of resisting magnetiza-
tion or demagnetization is called retentivity. The reten-
tivity of hardened steel is much greater than that of soft
iron.

258. Magnetic Field. Magnetic induction, like elec-
trostatic induction, is exerted through the agency of the



PROPERTIES OF MAGNETS.



309



surrounding medium. Evidence in support of this asser-
tion will accumulate as we advance in the study of the
subject. It would be unphilosophical to imagine an inde-
pendent medium or ether for every kind of action propa-
L^ated through space; it is therefore assumed that the ether
concerned r nagnetic induction is the same as that essential
to the phenomena of light and electrostatics. The ether
about a magnet is under magnetic stress, since the space
there is traversed by magnetic forces. Such a region, in
which a magnetic pole tends to move in a definite direction,
is a magnetic field.

Lines of magnetic force, or magnetic induction, are lines
ah nig which a single ideal magnetic pole would tend to
move. The positive direction along a line of force is the



1







Fig. 133.

direction toward which a free X-seeking pole is urged. If
an observer stands with his back to a X-seeking pole, he is
looking in the positive direction of the lines of force coming
from that pole.

Paramagnetic substances like iron tend to move from the
weak to the strong parts of a magnetic field, while dia-
magnetir substances like bismuth tend to move from the
strong to the weak parts of the field.



310



ELECTRICITY AND MAGNETISM.



259. Magnetic Figures. Magnetic figures, or a map
of the lines of magnetic force about a magnet, have been
known from early times. Fig. 133 shows the forms assumed




Fig. 134.



by iron filings sifted on a glass plate over a bar magnet.
When the plate is gently tapped the filings arrange them-
selves in curved lines running between the N and S poles.
Since the field is symmetrical about the magnetic axis, such
a figure may be obtained in any plane passing through the




Fig. 135.



axis. Each particle of iron is magnetized by induction
and sets itself along a line of force. The whole field about
such a magnet is therefore pervaded by lines of force.



PROPERTIES OF MAGXETS. 311

They form closed curves ; through the magnet they run from
the S to the X pole, while they complete their circuit in the
air from the X around to the S pole.

Fig. 134 was taken from the unlike poles of two similar
magnets. The lines of force stretch across from one to the
other. \o\v, lines of force show a tendency to shorten.
They act like .stretched elastic cords mutually repelling one
another. Hence these two poles of opposite sign are drawn
together.

Fig. loo was made from two like poles. X"o lines extend
Mcinss tVoni (me t< the other. Moreover, the elasticity or
resiliency of these lines under distortion is plainly such
;is to force the magnets apart, so that the lines may recover
their normal distribution about each pole.

260. Magnetic Shielding (J.J.T., 261). Magnetic
attraction and repulsion, and magnetic induction take place
through all non-magnetic substances as if nothing were
interposed. Suspend a small piece of magnetized watch-
spring by a silk fibre inside a glass bottle or a large test-
tulx'. It is affected hy
external iron or mag-
nets as if the glass were
not present. The free-
dom thus secured from
drafts of air makes this
a good magnetoscope.

.Magnetic forces act
across all substances,

except iron or other magnetic materials if of sufficient thick-
ness. A conductor is a perfect screen from electrostatic
action for bodies within it. A magnetic needle in a hollow-
iron ball is screened in like manner from another system of




312 ELECTRICITY AXD MAGNETISM.

magnetic forces, but only imperfectly. Consider a magnetic
needle inside an iron shell placed in a uniform magnetic
field; that is, a field consisting of a system of parallel equi-
distant lines of force. When the ball is introduced into
this field it is no longer uniform, but the lines pass through
the iron in preference to the air. Thus in Fig. 136 let P
be the needle within the shell. The lines of force crowd
into the iron. They are thus deflected toward the iron
within and without. A few will still traverse the hollow
space, but the number of these may be made indefinitely
small with a sufficient thickness of soft iron. If the inner
radius of the shell is one-half the outer, it may easily be
that the magnetic force inside is not more than -%fa of that
outside. The ratio depends on the quality of the iron, or
on what may here be called its specific conductivity for
lines of force (309).

261. Consequent Poles. A bar of steel may be mag-
netized in such a way that it will have a succession of

poles alternating

^\N s N s\ in sign. Thus in

Fig. 137 there are
north poles at N,

N, and south poles at /S, 8. The lines of force do not run
entirely through the length of the magnet, but the N's are
centres from which they emerge from the magnet and the
S's are centres to which they converge. A consequent
pole forms a part of two magnetic circuits. Such poles
are often used in dynamo-electric machines.

A ring may be magnetized either so as to present con-
sequent poles, or in such a way that it will exhibit no
external magnetic effects. Fig. 138 shows the lines of
force about a ring with consequent poles at 1 and 3. In



PROPERTIES OF MAGXETS.



313



Fig. 180 there are no poles ; that is, there are no points

at which the

lines of force

pass from the

iron into the air.

Tli is ring con-
stitutes a closed

magnetic cir-
cuit, or one in

which the lines

of force are

wholly in the

iron. Such a

ring has no ex-
ternal magnetic

effect, so long as

there is no

change in its

magnetism, because there are no external lines of force.

Closed magnetic circuits are more
retentive of magnetism than open
ones.




Fig. 138.




262. Effects of Heat on Mag-
netism. - - If a permanent mag-
net be heated to a bright-red
heat, all signs of magnetism dis-
appear. Up to 680 C. iron shows
but a slight change in its mag-
netic properties ; above this a rapid decrease in magnetic
susceptibility takes place, so that at about 750 C. it ceases
entirely to be magnetic and is quite indifferent toward a
magnet. Iron has therefore a magnetic limit, determined



Fig. 139.



314



ELECTRICITY AND MAGNETISM.



by temperature, and beyond this limit it is not affected by
magnetism. Nickel loses its magnetic properties at about
350 C. Chromium ceases to be magnetic at about 500.
The temperature at which magnetic susceptibility reap-
pears when the temperature is reduced is lower than the
critical temperature at which it
disappears when the temperature is
raised.

Manganese is magnetic only at
temperatures near C. Accord-
ing to Dewar, when iron is cooled
to about 200 C. in liquid oxygen
its susceptibility is twice as great
as at C.

The loss of magnetization by
heat in the case of nickel is beau-
tifully shown by the simple appa-
ratus of Fig. 140, designed by
Bidwell. A thin tongue of nickel
is soldered to a copper disk and the
whole is blackened and suspended
by silk threads. A permanent mag-
net M is held in such a position that
it retains the nickel tongue just over
the flame of the alcohol lamp. When

the nickel is heated to the proper temperature the magnet
releases it and the nickel-copper bob swings as a pendulum.
During one or two vibrations it loses sufficient heat by
radiation . and convection to recover its magnetism; it is
then attracted again and held by the magnet. This opera-
tion is repeated as soon as the nickel is again heated by
the lamp.




Fig. 140.



PROPERTIES OF MAGNETS. 315

263. Strength of Pole. The strength of pole, or
degree of magnetization, of a magnet is defined by means
of its effect on another magnet. Thus, if at the same
distance the N pole of magnet A repels the N pole of
magnet B with a force/, and magnet C repels B with a
force '2f, then C is said to have twice the strength of pole
of A. Strength of pole is denoted by the letter m.

264. Unit Pole. Consider two long, slender, uni-
formly magnetized needles with their similar poles A and
B placed at a distance of one centimetre in air, the other
poles being so far away that they exert no appreciable
influence in the neighborhood of A and B. Then if A and
B are equal poles and the force between them is one dyne,
both A and B are poles of unit strength. A unit pole
repels an equal awl similar pole at a distance of one centi-
metre in air with a force of one dyne. It is necessary to add
the qualifying phrase " in air," because the force would
not be one dyne if a magnetic substance intervened.

A pole of strength 2 would repel a unit pole at unit
distance with a force of two dynes. Hence if m and w'are
the strengths of t-wo poles, the distance between them being
unity, the repulsion between the two is mm' dynes. If the
poles are of opposite signs mm' is negative, or a negative
force means an attraction.

The strength or intensity of a magnetic field at any point
is the force exerted on unit pole placed at the point, the
introduction of this pole not being supposed to influence
the field. Strength of field, or the flux of magnetic force
IM-I square centimetre, is conventionally denoted by the
number of lines of force passing through one square centi-
metre at right angles to the direction of the field. It is
designated by the letter ,



316



ELECTRICITY AND MAGNETISM.



Imagine a sphere of unit radius described about a unit
pole as a centre. Then the intensity of the field at every
point on the surface of this sphere is unity, or one line
passes through every square centimetre. Therefore the
number of lines belonging to unit pole is 4?r, since the
surface of the sphere is 4?r square centimetres ; and for a
pole of strength m the number of lines radiating is 47rw.

265. Magnetic Moment. The moment of a magnet
is the product of the strength of its poles and the distance
between them, or

= ml.



Let the dotted lines (Fig. 141) be the direction of the field
of unit strength, and let ns be a magnet whose strength of
pole is m. Then the fqrce on either
pole is m and the two forces consti-
tute a couple. The moment of this
couple when the magnetic axis of ns
is perpendicular to the lines of force
of the field is ml, and this is the mag-
netic moment.




Fig. 141.



266. Intensity of Magnetization.
Intensity of magnetization is the
magnetic moment per unit of volume
of the magnet. It must be regarded as having not only
magnitude but direction, its direction being that of the
axis of the magnet. If s is the sectional area of a long
uniform rod and I its length, then

x _ ml __ m
~~~*



Intensity of magnetism is the pole-strength per unit of area.



PROPERTIES OF MAGNETS. 317

267. Second Law of Magnetic Force. - - The first
law (-54) is qualitative. Coulomb, by means of his tor-
sion balance applied to magnetic poles instead of to electric
charges, gave quantitative expression to the law of mag-
netic force as affected by the distance between the poles :

The force between two magnetic poles is proportional to
the product of their strengths and inversely proportional
to the square of the distance between them.

This distance must be so great that the poles may be
regarded as mere points. Then from the definition of unit
pole we may write



268. Theory of Magnetic Figures. - - The law of
inverse squares can now be applied to elucidate the form
of the curves developed about a magnet by means of iron
filings. Let NS (Fig. 142) be a long thin magnet, and
let P be a X-pointing pole in the field of NS. It will be
attracted by S and repelled by N along the lines PS and
PX respectively. | The forces will be inversely as the
squares of these distances, and may be represented by
the lines PA and PB. \ Both forces act on the same pole.
Complete the par-
allelogram, and
the diagonal PC
is the resultant
force. Since an

equal and oppo- _

site force acts on Fjg |42

the south pole of

the same small magnet represented by a short iron fil-
ing, the two forces compose a couple tending to set the
particle of iron or other small magnet along the diagonal




318



ELECTRICITY AND MAGNETISM.



of the parallelogram. This line is therefore tangent to
the curved line of force passing through P.

If another point P' be chosen, equidistant from N and 8,
the two forces of attraction and repulsion on either pole at
P' are equal and the diagonal is parallel to the axis of NS.
Continuing in this way, the direction of the intensity of the
field may be found at many points, and the directions com-
bined as tangents to a curve will map out lines of force.

269. Magnetic Forces by Method of Deflections.
Two methods of making magnetic measurements are
worthy of discussion here. In the first a magnetic deflect-
ing force is compared with the intensity of the field in
which the magnet is placed by observing the angle of
deflection. If a magnetic needle be poised on a sharp
point or be suspended by a fine fibre, and if it be de-
flected by any means from the magnetic meridian, the
forces tending to bring it back consti-
tute a couple; and for equilibrium this
couple must be equal to the one pro-
-<Fwducing the deflection.

Let NS (Fig. 143) be the direction
of the magnetic field, and let the magnet
be deflected by some force f at right an-
gles to the field of force. Then the forces
acting on the pole of the magnet are 8&m
in the direction of the field and fm at right
angles to the field. The moment of the
first force tending to replace the magnet
in the direction of the field is &6ml sin 0,
where 8 is the intensity of the field, m is the strength
of pole of the needle, I is the half-length of the needle, and
I sin is the lever arm AB. The moment of cfm is



OCm




Fig. 143.



PROPERTIES OF MAGNETS.



319



ffm x B = fml cos 6. Equating the two moments
and

S8ml sin 6 = ffml cos

or & = &6 tan 0.

The magnetic force producing a deflection is equal to
the product of the strength of field and the tangent of the
angle of deflection.

27O. Method of Oscillations. When a suspended
magnetic needle is disturbed from its position of equilib-
rium it describes a series of oscillations like a pendulum.
If the angular deflection be small the vibrations will all
be accomplished in the same period. The law of the
vibration of such a needle is the same as that of the pen-
dulum (I., 71), since the restoring couple is proportional
to the sine of the angle of deflection 6 (Fig.
144) ; and when this angle is small the mo-
tion is simple harmonic.

We may therefore write for the period of a
complete vibration



T=



7T



where K is the moment of inertia of the needle,
rH3 the intensity of the field, and 3115 is the
product ml corresponding to M h in the case
of the pendulum.
From this equation

^-rfKn*
T 1 ''



00



F.g. 144.



or the intensity of the field is proportional to the square of
the vibration-frequency.

The fields at two places may be compared by observing



$20 ELECTRICITY AND MAGNETISM.

the number of vibrations made by the same magnet in
equal times, first at the one place and then at the other.
Then

B6_ = T^ = r^_

BS'~ ' T- n' 2 '

271. Comparison of Pole-strengths by Oscillations.
- Let one of the magnets to be compared be placed in the
same magnetic meridian with the oscillating needle, and
let the field produced by it at the needle be A t . Then



If the first magnet be replaced by the second one at the
same distance from the needle, then



Ari! 2 .... 0)
Subtract (a) from (ft) and (<?) and

= A(n\ rc 2 ),



TTTI

Whence



This equation gives the ratio of the pole-strengths of the
two magnets which produce fields h { and Ji., at the needle if
the distance be constant.

The law of inverse squares can be demonstrated in a
similar way by observing the oscillations of a needle first in
the earth's field alone, and then in the earth's field plus
that of the influencing magnet placed at successive distances
from the needle.

272. Magnetization and Mechanical Stress. Joule
observed that an iron rod increases in length when



PROPERTIES OF MAGNETS. 321

magnetized, but that no change of volume takes place.
Hence the rod must contract in sectional area. He con-
cluded that if a rod be magnetized circularly, that is, so
that the lines of magnetization are circles around the axis
of the rod, it should contract in length. This conclusion
he verified by experiment.

Bid well 1 has extended Joule's observations by showing
that at a certain magnetization the elongation reaches a
maximum, and that for magnetizing forces beyond that the
elongation is less and less until the magnet finally remains
unaffected; any increase of the magnetizing force beyond
this point causes the rod to shorten. Effects of the same
kind occur in rings forming closed magnetic circuits ; the
diameter is increased by small magnetizing forces and is
decreased with larger ones.

The mechanical extension of a wire produces increase of
magnetization with small magnetizing forces ; but Villari
found that when the field is sufficiently intense, extension
causes a decrease of magnetization. This effect is called
the Villari reversal. Compression produces the opposite
effects to extension.

A circularly magnetized iron wire, when twisted, becomes
magnetized longitudinally ; and, conversely, torsion in weak
fields diminishes longitudinal magnetization and produces
circular magnetization. We may therefore conclude that
the superposition of both circular and longitudinal mag-
netizations will cause torsional strain. Wiedemann has
demonstrated this to be true in the case of iron. With
small magnetizing forces the twist is in one direction, but
when the magnetizing forces are large there is a reversal of
the direction of the twist. Nickel also exhibits a Villari
critical point and reversal for its residual magnetism; but

l Proc. Boy. Soc., XL., pp. 109, 257.



322 ELECTRICITY AND MAGNETISM.

for large magnetizing forces extension diminishes its mag-
netization and compression increases it.

273. Magnetism Molecular. Numerous facts point
to the conclusion that magnetism is a molecular phenome-
non. If - a piece of magnetized watch-spring be broken in
two, each half will be a magnet with its poles pointing in
the same direction as in the original magnet. Smaller
subdivision of the watch-spring simply increases the number
of poles without destroying the magnetism. It is therefore
inferred that the ultimate particles or molecules of steel
and iron are magnets, and that they are naturally and
permanently such. If a glass tube be filled with fine iron
filings, it may be magnetized ; if it be then shaken so as to
rearrange the particles, all signs of magnetization disappear.
The demagnetization produced by vibrating an iron bar is
a phenomenon of similar character. If iron be cast in an
intense magnetic field it is found to be strongly magnetized.
Beetz deposited iron electrolytically in a thin line on silver
parallel to the lines of force in a strong magnetic field.
The iron was found to be so highly magnetized that no
more permanent magnetism could be induced in it.

Weber's hypothesis is that the molecules of iron and
other paramagnetic substances are natural magnets, but in
the unmagnetized state of the mass their axes lie in all
directions indifferently; when subjected to a magnetizing
force the magnetic axes of the molecules turn round more
or less in the direction of the axis of magnetization.
When they have all been turned in this direction the iron
is saturated and its magnetization can receive no further
increase. As soon as the magnetizing force is withdrawn,
the molecules spring back partly toward their former posi-
tions ; thus, some of the magnetism is temporary, or the



PROPERTIES OF MAGNETS. 323

magnet has been supersaturated. In soft iron the mole-
cules offer less resistance to this molecular motion or rear-
rangement than in steel. Hence hardened steel possesses
greater coercive force and greater retentivity. To Weber's
theory Maxwell made the addition that the magnetized
molecules are rotating around their longer axes.

274. Swing's Theory of Magnetism. Instead of sup-
posing that in the unmagnetized state the molecular mag-
netic axes are turned criss-cross, Ewing has shown that
the particles are arranged so as to form closed magnetic
circuits, or, at least, stable configurations under the action
of their mutual forces. A group of such molecules will
arrange themselves so as to satisfy their relative attractions
and repulsions. To illustrate his theory Ewing constructed
a model, consisting of short lozenge-shaped magnets piv-
oted on points and arranged at equal distances in a hori-
zontal plane. Any small number of these may group
themselves in several stable configurations. When they
are simply agitated they settle down into groups of equi-
librium. With a small external magnetizing force these
needles turn through a small angle only; when the force
reaches a larger value, some of the needles suddenly turn
round and new groupings result, with most of the needles
pointing in the direction of the magnetizing force ; any
further increase of the magnetizing force produces but
little effect. These three stages correspond to three similar
ones often observed in magnetizing iron (316).

275. The Earth a Magnet. Since a suspended mag-
netic needle tends to set itself in a definite direction, it
follows that the space about the earth is a magnetic field.
A small magnet shows that a couple acts on it to bring its



324 ELECTRICITY AND MAGNETISM.

axis into a definite azimuth, but no force tends to produce
motion of translation. This relation is due to the fact that
the magnetic pole of the earth is so far distant in compari-
son with the length of the small magnet that the forces
on the two poles of the latter are rigorously equal and in
opposite directions. The same condition may be described