II
41
INDUCTION IN ROTATING SPHERES
law
=
-
Əz
эх ду
aw av
א
Z
=a
Əz მე:
dy
Əz
au aw'
These are the expressions given by Jochmann. The change
produced in the results by the formula of the dynamical
theory will be discussed in § 8.
If, in addition to the currents u, v, w, there are components
of magnetisation λ, μ, v, then in this part of the induction in
the above formulæ we must replace
ƏM ƏN ƏN
әм
ƏL ƏL ƏM
U, V, W by
Əz Əy' Əx
Əz' ay
ду
əx
The formulæ thus obtained still hold when the magnets
are on the inside of the rotating mass.
all outside, since inside the mass
If the magnets are
V²L=0, V2M = 0, V2N = 0,
xx
we have
22
=
Z
дх
Əz
дх
дх
= a
dy
-
-
a
ax
дх
-B-
ax
And for the elements of our sphere
@= -
wy, B = wx,
y = 0.
§ 2. SOLUTION NEGLECTING SELF-INDUCTION.
In this paragraph the problem will be solved in the case
where the effect of self-induction may be neglected.
components of current u, v, w these equations hold:-
For the
SCIENCE ENGINEERING LU-