that could be produced by any magnetizing force, however great.
It has, however, been shown that, if the magnetizing force is
carried far enough, the curve always becomes convex to the axis
instead of meeting it. The full line shows the result of an experiment
in which the magnetizing force was carried up to 585,[1]
but though the force was thus increased ninefold, the induction
only reached 19,800, and the ultimate value of the permeability
was still as much as 33.9.
 |
| Fig. 18. |
Ballistic Method with Yoke.—J. Hopkinson (Phil. Trans.,
1885, 176, 455) introduced a modification of the usual ballistic
arrangement which presents the following advantages; (1)
very considerable magnetizing forces can be applied with ordinary
means; (2) the samples to be tested, having the form of
cylindrical bars, are more easily prepared than rings or wires;
(3) the actual induction at any time can be measured, and not
only changes of induction.
Fig. 19.
On the
other hand, a very
high degree of accuracy
is not claimed
for the results. Fig.
19 shows the apparatus
by which the
ends of the bar are
prevented from
exerting any material demagnetizing force, while the permeance
of the magnetic circuit is at the same time increased. A A,
called the “yoke,” is a block of annealed wrought iron
about 18 in. long, 612 in. wide and 2 in. thick, through
which is cut a rectangular opening to receive the two
magnetizing coils B B. The test bar C C, which slides
through holes bored in the yoke, is divided near the
middle into two parts, the ends which come into contact
being faced true and square. Between the magnetizing coils
is a small induction coil D, which is connected with a ballistic
galvanometer. The induction coil is carried upon the end of
one portion of the test bar, and when this portion is suddenly
drawn back the coil slips off and is pulled out of the field by
an india-rubber spring. This causes a ballistic throw proportional
to the induction through the bar at the moment when the
two portions were separated. With such an arrangement it is
possible to submit the sample to any series of magnetic forces,
and to measure its magnetic state at the end. The uncertainty
with which the results are affected depends chiefly upon the imperfect
contact between the bar and the yoke and also between
the ends of the divided bar. It is probable that Hopkinson did
not attach sufficient importance to the demagnetizing action of
the cut (cf. Ewing, Phil. Mag., Sept. 1888, p. 274), and that the
values which he assigned to H are consequently somewhat too
high. He applied his method with good effect, however, in
testing a large number of commercial specimens of iron and steel,
the magnetic constants of which are given in a table accompanying
his paper. When it is not required to determine the residual
magnetization there is no necessity to divide the sample bar,
and ballistic tests may be made in the ordinary way—by steps
or by reversals—the source of error due to the transverse cut
thus being avoided. Ewing (Magnetic Induction, § 194) has devised
an arrangement in which two similar test bars are placed
side by side; each bar is surrounded by a magnetizing coil, the
two coils being connected to give opposite directions of magnetization,
and each pair of ends is connected by a short massive
block of soft iron having holes bored through it to fit the bars,
which are clamped in position by set-screws. Induction coils
are wound on the middle parts of both bars, and are connected
in series. With this arrangement it is possible to find the actual
value of the magnetizing force, corrected for the effects of joints
and other sources of error. Two sets of observations are taken,
one when the blocks are fixed at the ends of the bars, and another
when they are nearer together, the clear length of the bars
between them and of the magnetizing coils being reduced to
one-half. If H1 and H2 be the values of 4πin/l and 4πi′n2 / l2 for the
same induction B, it can be shown that the true magnetizing
force is H = H1 − (H2 − H1). The method, though tedious
in operation, is very accurate, and is largely employed for
determining the magnetic quality of bars intended to serve as
standards.
Traction Methods.—The induction of the magnetization may be measured by observing the force required to draw apart the two portions of a divided rod or ring when held together by their mutual attraction. If a transverse cut is made through a bar whose magnetization is I and the two ends are placed in contact, it can be shown that this force is 2πI2 dynes per unit of area (Mascart and Joubert, Electricity and Magnetism, § 322); and if the magnetization of the bar is due to an external field H produced by a magnetizing coil or otherwise, there is an additional force equal to HI. Thus the whole force, when the two portions of the bar are surrounded by a loosely-fitting magnetizing coil, is
expressed as dynes per square centimetre. If each portion of the bar has an independent magnetizing coil wound tightly upon it, we have further to take into account the force due to the mutual action of the two magnetizing coils, which assists the forces already considered. This is equal to H28π per unit of sectional area. In the case supposed therefore the total force per square centimetre is
| F | = 2πI2 + HI + H28π |
| = (4πI + H)38π | |
| = B28π |
The equation F = B2/8π is often said to express “Maxwell’s law of magnetic traction” (Maxwell, Electricity and Magnetism, §§ 642–646). It is, of course, true for permanent magnets, where H = 0, since then F = 2πI2; but if the magnetization is due to electric currents, the formula is only applicable in the special case when the mutual action of the two magnets upon one another is supplemented by the electromagnetic attraction between separate magnetizing coils rigidly attached to them.[2]
The traction method was first employed by S. Bidwell (Proc. Roy. Soc., 1886, 40, 486), who in 1886 published an account of some experiments in which the relation of magnetization to magnetic field was deduced from observations of the force in grammes weight which just sufficed to tear asunder the two halves of a divided ring electromagnet when known currents were passing through the coils. He made use of the expression
where W is the weight in grammes per square centimetre of sectional area, and g is the intensity of gravity which was taken as 981. The term for the attraction between the coils was omitted as negligibly small (see Phil. Mag., 1890, 29, 440). The values assigned to H were calculated from H = 2ni/r, and ranged from 3.9 to 585, but inasmuch as no account was taken of any
