II
59
INDUCTION IN ROTATING SPHERES
the free
We determine also the potential of the free electricity. Potential of
This follows from the expression for the spherical shell by electricity.
means of the very same substitutions that we have used all
along.
We thus find
1. Neglecting self-induction,
10
$
rax
= a dr.
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2. Taking it into account
= α
"α(x + n)
d‡.
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The case is of interest when the velocity a becomes infinite.
If we assume x to be symmetrical with respect to the n-axis,
and restrict our considerations to a limited region, we have
for a = ∞
k
roxan,
Ω+χ=
2πα δζ
and hence
10
+=
-
1: a
2π
η
=
k rax
2π
dn.
dnds
Thus approaches a definite finite limit when the velocity
increases.
B. Rotating Discs.
We again
discs.
We next consider the neighbourhood of the pole, and thus Rotating
obtain the theory of an infinite rotating disc.
suppose the inducing magnets to be inside the sphere. The
propositions we must employ are quite analogous to those of
the previous case.
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