42
II
INDUCTION IN ROTATING SPHERES
KU =
-
Эф
მე:
+X‚¹
Әф
κα
-
ду
KW =
-
მი
+Z;
Əz
further, since the currents are steady, we have inside
Ju dv дго
Əz
=
0,
+ +
Эх ду
ux +vy + wz = 0.
and for p = R and p=r,
Hence we have these conditions for :-
inside,
元
​²
+ +
дх ду
Əz'
and at the surface,
26
=
рар
· xX+yY+zZ,
which determine ø, with one additive constant arbitrary.
The potential of the magnets in internal and external
space we assume to be developed in the series of spherical
harmonics
+∞o
=
81
We take each term by itself and thus put the external
potential = Xn
Then we have
X = wx
Əz
= wy
dz
ལྤ
= ―
wy-2
by
-
wx Xxx
Xn
=w2-
wnXn
дх
Əz
1 Using the unit previously employed for ø.