Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/99

 Rh These results also enable us to understand why the magnetic moment of a permanent magnet can be made so much greater when the magnet has an elongated form. If we were to magnetize a disk with intensityI in a direction normal to its surface, and then leave it to itself, the interior particles would experience a constant demagnetizing force equal to 4πI, and this, if not sufficient of itself to destroy part of the magnetization, would soon do so if aided by vibrations or changes of temperature.

If we were to magnetize a cylinder transversely the demagnetizing force would be only 2πI.

If the magnet were a sphere the demagnetizing force would be $$\frac{4}{3}\pi I$$.

In a disk magnetized transversely the demagnetizing force is $$\pi^2 \frac{a}{c} I$$, and in an elongated ovoid magnetized longitudinally it is least of all, being $$4 \pi \frac{a^2}{c^2} I \log\frac{2c}{a}$$.

Hence an elongated magnet is less likely to lose its magnetism than a short thick one.

The moment of the force acting on an ellipsoid having different magnetic coefficients for the three axes which tends to turn it about the axis of x, is

Hence, if κ2 and κ3 are small, this force will depend principally on the crystalline quality of the body and not on its shape, provided its dimensions are not very unequal, but if κ2 and κ3 are considerable, as in the case of iron, the force will depend principally on the shape of the body, and it will turn so as to set its longer axis parallel to the lines of force.

If a sufficiently strong, yet uniform, field of magnetic force could be obtained, an elongated isotropic diamagnetic body would also set itself with its longest dimension parallel to the lines of magnetic force.

439.] The question of the distribution of the magnetization of an ellipsoid of revolution under the action of any magnetic forces has been investigated by J. Neumann. Kirchhoff has extended the method to the case of a cylinder of infinite length acted on by any force.