Magnetic Moment of a Magnet of any Shape

The method just given involves the measurement of r, the distance between the centre of the magnet and that of the compass needle, and the assumption that this distance is great compared with the dimensions of the magnets, so that they may be treated as solenoidal. In practice these two conditions may not be possible. We might, for example, require to find the magnetic moment about a diameter of a large steel sphere magnetised in any manner.

Now the first equation we have used, viz.,

is true for any magnet, provided only that the amplitude of the oscillation is small, and may be applied to the case in point. To find, then, the value of M, determine H as in (d), using magnets of a suitable form and size. Suspend the given magnet so that it can oscillate about a suitable axis, and determine K either by calculation from its dimensions, or by observations as in §23; count also n, the number of transits per second of any fixed point on the magnet across some fixed mark. The formula will then give us M.