MAGNETIC TUBES
145
!#l "*oi n(i
' ‘ * fc
:0ftk
aaetIC «ajyk;
l P* e Peiod^
be capable j>
^^ndamental 4"
; ? er ' Wbffli;-
Jt)
№ ' * • l l
; indtiettj'u
given by
. fj
terpretation of tie
te quanta tfe
eflned by A/i. 1
0 divide exactly®
nay represent is
t of two current'1'
meal model * retire
constructed on tfe
It has been W
ose analogy to tit
f with tic P® 1
4. Quantum Magnetic Tubes for any Number of Circuits
By making appropriate assumptions the results which we
have obtained for a single current circuit and for two current
circuits may be extended to any number of current circuits. In
the case of a heavy atom Bohr’s later theory postulates the exist
ence of a large number of independent electron orbits. There
is a certain amount of evidence from the work of Ellis and others
that quantum relations hold even within the nucleus, which may
be composed of positive electrons (protons) and negative elec
trons (corpuscles) in orbital motion. On this view an atomic
and also a molecular system is an extremely complex system of
orbits, in which positively or negatively electrified particles are
circulating at high speed, thus virtually constituting a system
of current circuits.
Let us consider a single Faraday tube of magnetic induction
linked with any number of current circuits, i lt i 2 , i 3 . . . i n .
wH 2
The energy per unit volume in the magnetic field is iL—. If
on
A is the area of cross-section of the tube at any point and ds
is an element of its length we get for the energy in an element
of the tube,
and the energy associated with the whole tube can be expressed
as
the integral extending for the whole length of the tube. Now
we know that ¿itHA is constant along the tube, for the magnetic
flux is the same throughout, we therefore write for the energy
Since the tube is linked with several current circuits we have
where proper attention must be paid to the signs of these quan
tities. Consequently the energy is
' ‘ * fc
aaetIC «ajyk;
l^onio:^,
l P* e №%
be capable®;
^^ndamental 4"
; ? er ' When we i--
* * • l l
; indtiettju
given by
. J):j
terpretation of tie
ite quantum tube:
eflned byJ/i. 1
0 divide exactly®
4
nay represent is
t of two curat i
meal model * repre
constructed on i
It has been to®
ose anal®’ to ®
f with tic P® 1
T — l^uHA^' 1 + ¿2 + H + • • • + k)
• 10 : 39