Measuring Magnetic Moments and Field Strengths

For this we have only to combine the results of the observations in (b), and determine the moment of inertia of the magnet about the axis of rotation. Thus, weigh the magnet and let its mass be m grammes; measure its length with a rule, the calipers, or the beam compass, as may be most convenient; let it be l cm. Determine, by means of the screw gauge, its diameter if it be a circular cylinder, let it be c cm; or if it be rectangular in shape, the length of that side of the rectangle which is horizontal when it is swinging, let this be a cm. Then it can be shown, by the use of the integral calculus, that in the first case, if the section be circular,

and in the second, if it be rectangular,

⁽¹⁾

Thus K can be determined in either case, supposing the stirrup to be so light in comparison with the magnet that its effect may be neglected.

If K cannot be found by direct measurement, we must have recourse to the methods of observation described in §23.

Thus, K being determined, we know all the quantities involved in the two equations of (b), with the exception of M and H.

The two equations are

and from these we obtain by multiplication,

whence

and by division,

or

This is the method actually employed in many unifilar magnetometers, to determine the horizontal intensity of the earth's magnetic force, the only difference consisting in the very delicate arrangements for the accurate determination of the quantities to be measured.

(1)	Routh's Rigid Dynamics, chapter 1. See also above, p. 145. .