Page:A Treatise on Electricity and Magnetism - Volume 2.djvu/40

Meaning of the term 'Magnetic Polarization.'

382.] In speaking of the state of the particles of a magnet as magnetic polarization, we imply that each of the smallest parts into which a magnet may be divided has certain properties related to a definite direction through the particle, called its Axis of Magnetization, and that the properties related to one end of this axis are opposite to the properties related to the other end.

The properties which we attribute to the particle are of the same kind as those which we observe in the complete magnet, and in assuming that the particles possess these properties, we only assert what we can prove by breaking the magnet up into small pieces, for each of these is found to be a magnet.

Properties of a Magnetized Particle.

383.] Let the element dxdydz be a particle of a magnet, and let us assume that its magnetic properties are those of a magnet the strength of whose positive pole is m, and whose length is ds. Then if P is any point in space distant r from the positive pole and r' from the negative pole, the magnetic potential at P will be ${\frac {m}{r}}$ due to the positive pole, and $-{\frac {m}{r'}}$ due to the negative pole, or

$V={\frac {m}{rr'}}(r-r').$

(1)

If dS, the distance between the poles, is very small, we may put

$(r-r')ds\cos \epsilon \,.$

(2)

where ε is the angle between the vector drawn from the magnet to P and the axis of the magnet, or

$V={\frac {m}{rr'}}\cos \epsilon .$

(3)

Magnetized Moment.

384.] The product of the length of a uniformly and longitudinally magnetized bar magnet into the strength of its positive pole is called its Magnetic Moment.

Intensity of Magnetization.

The intensity of magnetization of a magnetic particle is the ratio of its magnetic moment to its volume. We shall denote it by $I$.

The magnetization at any point of a magnet may be defined by its intensity and its direction. Its direction may be defined by its direction-cosines λ, μ, ν.