23
THE TERRESTRIAL MAGNETIC FIELD
(a) Gyration, which we have just described and which takes place at the frequency
Ib' whose magnitude depends upon the local value of the induction.
- This frequency increases from the magnetic equator to the poles along anyone
line of force, as can easily be seen from the formulas given above.
- On the other hand, it decreases with altitude, as does B. It is possible to draw up a
map of h (,\, r) for each type of charged particle.
(b) The north-south oscillation of the guiding center along a line of force, and thus
from one hemisphere to the other.
Let us try to explain this motion.
o Magnetic induction
o -o
(-)
(a)
E
(+)
(+)
--
Grad.S (-)
&QJt t JtQJC
Cd)
(-)
&QJL!:olff ~+)E.-JjGr;d.8,. ~
(-)
(b)
(+)
~
(-)
~1JUUl:
~
(e)
(c)
Fig. 7. Drift motions of electrically charged particles in a magnetic field under the influence of an
additional force. (a) F=O. Simple gyration. (b) F is due to an electric field E. Protons and electrons
drift in the same direction. (c) F is of mechanical origin. Protons and electrons drift in opposite
directions. (d) The force F results from the fact that the induction B is not uniform. The drifts are
again in opposite directions. (e) F is due to the simultaneous presence of an electric field E and an
inhomogeneity in the magnetic induction. The' spirals' become more open for both protons and
electrons. The drifts are in opposite directions.
As we have said, the kinetic energy W of the charged particle remains constant, but
now there is a force in the direction of B. It arises from the fact that the induction
varies along the line of force. The velocity (and therefore the energy) along B is no
longer constant. Since W = W II +W 1., the energy W 1. in the direction perpendicular to
B changes also. And therein lies the new phenomenon.
To specify how the energies W II and W 1. are exchanged in the course of the motion,
it is sufficient to realize that the moment IIII of the particle remains invariant. Referring
to Figure 6, which defines the angle 8 between the velocity v and the induction B, we
see that VI =V sin 8; thus our condition IIlI =const. can be written
sin 2 8 = C I
B
'
where C I is a constant.