Il
=
107
INDUCTION IN ROTATING SPHERES
To determine so that in external space
=
Απε ax
2wz
1 + 4πε
2w-
dz
and at the surface
$
= const.
We easily find
$
‚R² – p² ƏX₂
=
W
2n+1 Əz
Απε
1 + 4πε
Hence follows the rate of increase of potential at the
earth's surface
Эф
др
=
Απε
1 + 4πε
2RwZ
1 όχι
2n+1 dz
- 2, or at any rate is small.
There-
Much the greater part of the earth's magnetic force is due
to terms for which n =
fore we may write approximately
Эф
др
-
=
Απε
1+ 4πε
Rw.
dx
Iz
ax/az is the component of the earth's magnetic force in
the direction of the north pole of the heavens.
If we assume that for interplanetary space 4πe/(1+4πе)
is very nearly 1, we get for the electromotive forces values of
the order of 1 Daniell in 50 m., that is, very small values.
However, a term of the form const/p may have to be added
to the above value of 4. Its value depends on the quantity
of free electricity on the earth, although it does not vanish
with this quantity; but the order of magnitude of the cal-
culated forces is not altered by the presence of this term.
III.
When a sphere of any arbitrary magnetic properties rotates Spherical
in a liquid, which is itself a conductor, and makes electric magnet in a
liquid.
contact with the surface of the sphere, the sphere will induce
currents in the liquid. In general these no longer flow in
concentric spherical shells, but traverse the magnet.