Comparing Magnetic Moments

(1) Suspend the magnet in its stirrup under the bell jar, as in fig. 51, and when it is in equilibrium make a mark on the glass opposite to one end. Displace the magnet slightly from this position, and count the number of times the end crosses the mark in a known interval of time, say one minute - a longer interval will be better if the magnet continue swinging. Divide this number by the number of seconds in the interval, 60 in the case supposed, the result is the number of transits in one second. Call this n. There will be two transits to each complete oscillation, for the period of an oscillation is the interval between two consecutive passages of the needle through the resting point in the same direction, and all transits, both right to left and left to right, have been taken; n/2 is therefore the number of complete oscillations in one second, and the periodic time is found by dividing one second by the number of oscillations in one second. Hence, T being the periodic time,

But we have shown (p. 366) that

Hence

and

Now K depends only on the form and mass of the magnet, which are not altered by magnetisation; H is the strength of the field in which it hangs, which is also constant; so that if M₁, M₂, &c. be the magnetic moments after different treatments, n₁, n₂, &c. the corresponding number of transits per second,

We thus find the ratio of M₁ to M₂.

(2) We can do this in another way as follows:

Take a compass needle, A B (fig. 53) provided with a divided circle, by means of which its direction can be determined, and note its position of equilibrium. Place the magnet at some distance from the compass needle, with its end pointing towards the centre of the needle and its centre east or west of that of the needle. Instead of a compass needle we may use a small magnet and mirror, with a beam of light reflected on to a scale, as already described (p. 367). The centre of the magnet should be from 40 to 50 cm from the needle. The needle will be deflected from its position of equilibrium. Let the deflection observed be θ₁; reverse the magnet so that its north pole comes into the position formerly occupied by the south pole, and vice versa. The needle will be deflected in the opposite direction (fig. 53 [2]). Let the deflection be θ₂. If the magnet had been uniformly magnetised and exactly reversed we should find that θ₁ and θ₂ were the same. Let the mean of the two values be θ; so that θ is the deflection produced on a magnetic needle by a bar magnet of moment M when the line joining the centres of the two is east and west, and is in the same straight line as the axis of the bar magnet. But under these circumstances we have shown (p. 364) that, if r be the distance between their centres,

If another magnet of moment M' be substituted for the first, and a deflection θ' be observed, the distance between the centres being still r, we have

Hence

We can thus compare the moments of the same magnet under different conditions, or of two different magnets.