II
49
INDUCTION IN ROTATING SPHERES
Secondly, let n be negative, then
Hence, for a positive n,
and for a negative n,
Xndp
=
- Ex..
OXn dp
>
მთ
W
зв
ax
Xn dp.
K
მთა
These expressions admit of summation at once, and we get Summation
the following second form for the solution :-
If x, denote the part of the potential due to internal, and
Xi
X, the part due to external magnets, then
Xe
зв
∞
==
K
ω θ
მთა
Χο. αρ
-
Χι. αρ
of spherical
harmonics.
Similarly
$
=
-
@ sin e
Ә
0
Jx-4x-4)
dp - [x.dp}.
For an infinitely thin spherical shell of radius R
$ =
зв
=
·
ய
R
dp
όχι
山
​dp},
1/2+-/2+).
K მთ
- w sin
R
axe do
R
dp
მთ
Xi dp
00
Hence we get this relation between and
მა
аф
+ K sin
дов
= 0.
дв
E
M. P.
SCIENCE ENGINEERING LL