(5) Calculate the total magnetic flux in the air-gap of the inductor from the relation

Inferences.

Show how the relation given in (5) can be

obtained, and state any assumptions made in obtaining it. Is any correction required for high accuracy in the relation for F?

85. Determination of the Relative Inductivities of Materials

(Induction Balance Method).

Introduction.-The form of induction balance which will be used in the following tests is the one introduced by Hughes, a description of which will be found on p. 356. The extreme sensitiveness of the induction balance to minute differences of electric conductivity and magnetic permeability enable a very interesting and instructive series of observations to be carried out. The relative effects and inductivities will be determined by what we may term the "zero" telephone method, i.e. by balancing each material in the same way and against the same arrangement, so that no sound occurs in the telephones.

Apparatus. Hughes' induction balance complete, with two telephones, battery, interrupter, and materials to be experimented upon.

Observations.--(1) Connect the two telephones in parallel, and across the two terminals of the secondary coils marked S.

Join the two terminals of the primary coils marked P in simple series with the battery and interrupter, which should be placed as far away from the balance as possible, so as not to interfere with the hearing at the telephones. A long length of flexible twin electric lighting lead should be used for the purpose. Wind the interrupter up if necessary, but not to the full extent, so as not to overwind it.

(2) Start the interrupter, by turning the lever controlling its clockwork, place a telephone to each ear, and with no metal in or near the coils of the balance, adjust the small ivory set screw which raises or lowers the top right-hand coil until no sound is heard in the telephones. The balance is now adjusted to "zero."

(3) Place the metal wedge with its attached millimetre scale between the guides of the left-hand top coil and a wooden cup in the other top coil. Insert one of the discs, all of which are of the same diameter and thickness, in the cup. Now slowly slide the metal wedge along the guides until just no sound is heard in the telephones. Note the scale-reading d1, and then slide the wedge further on, and gradually bring it back until again no sound is heard; note the scale-reading d. and the metal used.

(4) Repeat (3) for each of the metals provided, noting whether the same kind of sound occurs in each case, and tabulate as follows:

Metal tested.

di.

d2.

Mean,
4(d1 + d2).

N.B. If the arrangement is not sufficiently sensitive, increase the battery power. It will be observed that each metal disc being balanced against the same zinc wedge, the scale-readings will give a measure of the disturbing effects of these materials.

(5) Replace the wooden cup by the coil of insulated wire and remove the wedge, and note the effect, (a) when the ends of the coil are "free," (b) when they are joined together.

(6) Again insert the cup, and note the effect, (c) when a disc of non-magnetic material, (d) when one of magnetic material, is inserted with its plane perpendicular to that of the coils.

(7) Insert the two plugs, containing iron wires, in the two cups

placed in the respective secondaries, and move the one which has no handle attached to it up and down until no sound is heard in the telephones. Note the effect of slightly twisting the other wire by means of the handle.

Inferences.

State very clearly all the inferences which you can deduce from the results of the preceding experiments, suggesting the causes of the various phenomena observed.

86. Magnetic Permeability and Hysteresis (Absolute and Comparative Measurements).

Introductory.-Before proceeding to the actual methods of measuring the various magnetic properties of materials, it may be advisable to first give a brief résumé on some of the principles underlying such determinations.

Every magnet is surrounded by or sets up a magnetic field composed of lines of magnetic force, and the intensity of the magnetic field at any point can be measured by the number of lines of force passing through a square centimetre of surface placed across the field. If a magnetic pole is surrounded by a sphere of unit radius, and therefore containing 4 sq. cms. of surface, there will be 4 lines of force emanating from the pole if of unit strength. In other words, there will be one line of force per square centimetre, which represents unit field.

Thus a magnet of pole strength m has 4 lines of force emanating from it. A uniformly wound solenoid of turns per unit length and carrying a current A, will therefore exert a magnetic force = 47(An). Suppose now we have a straight bar of length / cms. and section s sq. cms., uniformly magnetized and possessing a pole strength m. Then M = ml is called its M ml m

magnetic moment; and if V = its volume, then- =

V

sl

=
S

=

I

And further, if this is

is the intensity of magnetization of the bar. produced by a magnetic field or magnetizing force of intensity H,

I

then is termed the susceptibility K or coefficient of magneti

H

zation. Again, let B stand for the magnetic induction or number

L

of lines of force per square centimetre in the bar. Then B = 4πΙ +H, and the ratio between the magnetizing force H and the internal induction which it produces in the bar is called the B

magnetic permeability μ of the material. Thus μ = H

The permeability of any magnetic material is therefore a property which it possesses, in virtue of which a given magnetizing force is able to produce a certain magnetic induction in the material. A certain magnetizing force is unable to produce the same magnitude of induction in different materials having the same size and form. This is owing to one material being more permeable, or offering greater facilities to the passage of magnetic lines of force through it, than the other, consequently, although the same number of lines are generated by the force in each case, they will gather up in and flow through that material which has the greater permeability, in larger numbers than in the other. For cores of air or non-magnetic materials, B x H directly, μ being = I approximately. The dimensions of either H, B, or I are of the (mass)+ The methods for

order

force

or

pole strength' (length) (time)'

measuring permeability may be classified as follows:

A. Magnetometric or steady deflection methods.

B. Balance or null deflection methods, applicable to comparative tests of two or more samples of material.

C. Ballistic or inductive methods.

D. Traction methods.

E. Optical methods, which are suited for measuring the permeability in intense magnetic fields.

In the following pages we shall only consider methods A, B, and C, and these we may now proceed with.

87. Measurement of Magnetic Permeability (Magnetometer Method).

Introduction. This method, which is very generally associated now with the name of Professor Ewing, who has employed it in a large amount of research work in magnetism undertaken by him,

is one in which the magnetic qualities to be measured are deduced from the steady deflections of a suitable magnetometer needle, affected by the specimen to be tested. It is only applicable to long straight rods of the material for the following reasons. When a rod of magnetic material is uniformly wound with insulated wire and magnetized by a current sent through the coil, it develops free magnetism and definite polarity at its ends, which exerts a demagnetizing influence or force, opposing the main magnetizing force due to the coil. This effect becomes less marked as the rod is longer, owing to the ends, in which the free magnetism chiefly resides, being too far away from the middle regions to affect the magnetic force there. If the rod is very long (300 to 400 diameters), the magnetization will be practically uniform throughout a considerable portion of its middle region, though falling off towards the ends. In such cases no correction, i.e. deduction, need be applied to the magnetizing force, as calculated in the ordinary way from the current-turns, in order to obtain the actual magnetizing force producing a given induction. Hence the importance of using long straight rods. We must now see what the numerical value is of the correction to be applied when the rod is not long enough to neglect the demagnetizing action of its ends. The correction may be obtained approximately by treating the long cylindrical rod as a very long ellipsoid. Thus, if n is a number depending on the relation of the length of the ellipsoid to its transverse dimensions, and if H = the effective magnetizing force producing an induction B, and H1 = the total magnetizing force as would be obtained from the ampere turns in the usual way, and I = intensity of magnetization

netic lines of force, B will be large compared with H.

n

The following table gives a few values of n and

worked