Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/98

 Rh (2) When κ is a large positive quantity, the magnetization depends principally on the form of the body, and is almost independent of the precise value of κ, except in the case of a longitudinal force acting on an ovoid so elongated that Nκ is a small quantity though κ is large.

(3) If the value of κ could be negative and equal to $$\frac{1}{4 \pi}$$ we should have an infinite value of the magnetization in the case of a magnetizing force acting normally to a flat plate or disk. The absurdity of this result confirms what we said in Art. 428.

Hence, experiments to determine the value of κ may be made on bodies of any form provided κ is very small, as it is in the case of all diamagnetic bodies, and all magnetic bodies except iron, nickel, and cobalt.

If, however, as in the case of iron, κ is a large number, experiments made on spheres or flattened figures are not suitable to determine κ; for instance, in the case of a sphere the ratio of the magnetization to the magnetizing force is as 1 to 4.22 if κ = 30, as it is in some kinds of iron, and if K were infinite the ratio would be as 1 to 4.19, so that a very small error in the determination of the magnetization would introduce a very large one in the value of κ.

But if we make use of a piece of iron in the form of a very elongated ovoid, then, as long as Nκ is of moderate value com pared with unity, we may deduce the value of κ from a determination of the magnetization, and the smaller the value of N the more accurate will be the value of κ.

In fact, if Nκ be made small enough, a small error in the value of N itself will not introduce much error, so that we may use any elongated body, such as a wire or long rod, instead of an ovoid.

We must remember, however, that it is only when the product Nκ is small compared with unity that this substitution is allowable. In fact the distribution of magnetism on a long cylinder with flat ends does not resemble that on a long ovoid, for the free mag netism is very much concentrated towards the ends of the cylinder, whereas it varies directly as the distance from the equator in the case of the ovoid.

The distribution of electricity on a cylinder, however, is really comparable with that on an ovoid, as we have already seen, Art. 152.