A convenient and rapid method of estimating a magnetic moment has been devised by H. Armagnat.[18] The magnet is laid on a table with its north pole pointing northwards, A compass having a very short needle is placed on the line which bisects the axis of the magnet at right angles, and is moved until a neutral point is found where the force due to the earth’s field H is balanced by that due to the magnet. If 2l is the distance between the poles m and −m, d the distance from either pole to a point P on the line AB (fig. 5), we have for the resultant force at P
R = −2 cos θ × m / d² = −2lm / d³ = -M / d³.
When P is the neutral point, H is equal and opposite to R; therefore M = Hd³, or the moment is numerically equal to the cube of the distance from the neutral point to a pole, multiplied by the horizontal intensity of the earth’s force. The distance between the poles may with sufficient accuracy for a rough determination be assumed to be equal to five-sixths of the length of the magnet.
Measurement of Magnetization and Induction.—The magnetic condition assumed by a piece of ferromagnetic metal in different circumstances is determinable by various modes of experiment which may be classed as magnetometric, ballistic, and traction methods. When either the magnetization I or the induction B corresponding to a given magnetizing force H is known, the other may be found by means of the formula B = 4πI + H.
Magnetometric Methods.—Intensity of magnetization is most directly measured by observing the action which a magnetized body, generally a long straight rod, exerts upon a small magnetic needle placed near it. The magnetic needle may be cemented horizontally across the back of a little plane or concave mirror, about ¼ or 3⁄8 in. in diameter, which is suspended by a single fibre of unspun silk; this arrangement, when enclosed in a case with a glazed front to protect it from currents of air, constitutes a simple but efficient magnetometer. Deflections of the suspended needle are indicated by the movement of a narrow beam of light which the mirror reflects from a lamp and focusses upon a graduated cardboard scale placed at a distance of a few feet; the angular deflection of the beam of light is, of course, twice that of the needle. The suspended needle is, in the absence of disturbing causes, directed solely by the horizontal component of the earth’s field of magnetic force HE, and therefore sets itself approximately north and south. The magnetized body which is to be tested should be placed in such a position that the force HP due to its poles may, at the spot occupied by the suspended needle, act in a direction at right angles to that due to the earth—that is, east and west. The direction of the resultant field of force will then make, with that of HE, an angle θ, such that Hp / HE = tan θ, and the suspended needle will be deflected through the same angle. We have therefore
HP = HE tan θ.
The angle θ is indicated by the position of the spot of light upon the scale, and the horizontal intensity of the earth’s field HE is known; thus we can at once determine the value of HP, from which the magnetization I of the body under test may be calculated.
In order to fulfil the requirement that the field which a magnetized rod produces at the magnetometer shall be at right angles to that of the earth, the rod may be conveniently placed in any one of three different positions with regard to the suspended needle.
| Fig. 6. |
(1) The rod is set in a horizontal position level with the suspended needle, its axis being in a line which is perpendicular to the magnetic meridian, and which passes through the centre of suspension of the needle. This is called the “end-on” position, and is indicated in fig. 6. AB is the rod and C the middle point of its axis; NS is the magnetometer needle; AM bisects the undeflected needle NS at right angles. Let 2l = the length of the rod (or, more accurately, the distance between its poles), v = its volume, m and −m the strength of its poles, and let d = the distance CM. For most ordinary purposes the length of the needle may be assumed to be negligible in comparison with the distance between the needle and the rod. We then have approximately for the field at M due to the rod