92 
THE QUANTUM 
[vn. i 
We assume that the intensity of the magnetic field increases 
from zero to some final value H g , and that the time required to 
reach this value is long in comparison with the periodic time of 
the electron in its orbit. We seek to find the change in the 
magnetic moment due to this applied field, and we shall assume 
as the result of a more exact investigation that the variation 
in the radius of the orbit is so small as to be negligible. In 
consequence of the variation in the strength of the magnetic 
field there will be an electromotive force E in the orbit, equal 
to the rate of decrease of the magnetic flux, i.e. 
E = - ^-(Hnr*) 
Cli 
In one revolution the electron must do an amount of work eE. 
As the electron is revolving so rapidly the value of dH/dt changes 
very slightly in this revolution. We may then regard the work 
done by the electron as done against a constant force F = eE/2nr. 
The equation of motion of the electron along the tangent to 
the orbit is therefore 
or 
Hence 
Integrating this equation from the time t = o, when H = 0 
to the time when the magnetic field is established, we find for 
the whole change in the magnetic moment 
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We notice that this change in the magnetic moment is 
independent of co, and has the same sign for all the orbits even 
though the electrons may be revolving in opposite directions. 
If there are N orbits in unit volume and r is the mean square 
radius of an orbit, the intensity of magnetization acquired is 
Since k is negative, the substance will appear diamagnetic. 
We may draw attention to the fact that the change in the