II
109
INDUCTION IN ROTATING SPHERES
a
X' = X - w~(Vx – Uy),
a
y' = F - ∞
Y -
(Vx -
W (V - Uy),
oy
–
-
a
Z' = Z – w — (Vx – Uy).
dz
But we saw on p. 67, that for all U, V, W occurring in
the investigation
$ = w(Vx - Uy).
We see at once that we may retain the previous solutions
unaltered as regards u, v, w, y, N. The only alteration which
must be made is to put for p', the potential of the free
electricity,
p' = const,
and, when free electricity was not present originally,
' = 0.
On an infinite sphere or plane plate we must have always
$' = 0.
If we
Maxwell obtained the same result, starting from the
formula of the potential law for conductors at rest.
reject the terms aU+BV+yW in the expressions for the
electromotive forces in conductors in motion, the equations for
conductors at rest must also be altered, and the equation
then no longer holds.
$ = 0
9. SPECIAL CASES AND APPLICATIONS.
In conclusion, the formulæ obtained will be applied to
some particular cases.
a plane
1. A single magnetic pole of strength 1 moves in a straight Magnetic
line parallel to an infinitely thin plane plate. Let the origin pole above
of E, n, be taken at the foot of the perpendicular from the plate.
pole on the plate, and let the negative n-axis be parallel to