II
111
INDUCTION IN ROTATING SPHERES
2πack in consequence of self-induction, and in fact lags
behind the moving pole by this distance. The same is true of
the whole distribution near the pole.
For infinite velocities we get
1
Ω+
= -
=
1
;
2πτ
for very large values of 2πa/k
k
n
li (axan
H
Ω= -χ- 2πα
=
0
ζ
dn
1 hi n(5+c)
2πа г(r² — n²)'
+
1
k
nc
=
1
-
2πr 2πа +c²
Here also the abscissa of the point = 0, y = 0 is
η
2παι
;
k
but since this value is very large, and our formula holds only
for finite values of 7, the value of the distance must be regarded
as only an approximation.
The potential of the free electricity in the plate is
a
-
θε
(x+N)dg,
so that for small velocities
૦૬
=3 -a
ફ્
r(r+c)"