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§7. –ACTION OF A NEUTRAL CLOSED CURRENT OR
OF A MAGNET
ON AN ION
IN MOTION
WALTER RITZ
Translated from Recherches
critiques sur l'Ėlectrodynamique Générale,
Annales de Chimie et de Physique, Vol. 13, p. 145, 1908.
We observe this action in the study of cathode rays and canal rays,
where the speed v of the ion e in motion, while remaining very
much inferior to that of light, is very large in relation to the speed of the
ions of the closed current, then in Hall’s phenomena, the Zeeman effect and
the magnetic rotation of the polarization plane of light.
Let us keep the notations of the preceding section; the action
undergone by e will be the sum of the actions of the positive and
negative charges  of all the elements of volume of the current. The conductor
itself, in these experiments, is at rest; thus V'=0,  and the speed v' of the negative ions, the only ones mobile by
hypothesis, is small in relation to v. The general formula (13) gives
for a linear element ds' of the closed current, and the abstraction made
from the electrostatic term and
Annales 238
the accelerations,
(Oeuvres
395) Beside the terms
proportional to v, v', the
terms in  disappear because  is very small; it is the same for the terms in  for they relate to the electrostatic action of the charges E' of the current as , that is they are very small. There remain the terms
proportional to v and v' which may be written
This is formula (25) in a different notation. The current ds' being closed, we may, as we have done previously,
integrate in relation to s', and
we will again obtain
Annales 239
the result that
the action of a magnet or a closed current at rest, on an ion in movement
is the same as in Lorentz’s theory.
If v becomes smaller and comparable to v', all the terms of (27) become very small, and the
phenomenon necessitates, in order to be observed, very delicate means of
investigation. This is what takes place when in placing a plate carrying a
current between the poles of an electromagnet, one observes, when the magnet
is energized, a difference of potential between the two sides of the current
(the Hall effect). The electrostatic action of the magnet being negligible,
it is a fortiori the same for terms in E' of formula (27); thus there will be, firstly, an
action proportional to J' and v', which is the same, as we have seen, in both
theories; there is, moreover, the force
The latter depends, as does Hall’s phenomenon itself (and contrary to
the forces studied until now) on the hypotheses made on the movement of ions:
it would be sensibly nil if the positive and negative ions of the
electromagnet had equal speeds (Oeuvres 396)
and opposite signs. Formula (20) of Lorentz gives analogous forces:
The term in v'2
has the nature of an electric force performed by the elements of volume of
the magnet independently of their orientation (the molecular currents being
considered as permanent and simply oriented by the magnetization). These
actions, independent of the sign of the magnetic field and of the existence
of a current in
Annales 240
the plate, will
no doubt escape even the most delicate observations. As to the terms
containing the accelerations of the ions of the current, and which are the
same in both theories, they are equally negligible for analogous motives.
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