An introduction to the mathematical theory of attraction ...

Sphere in Field of Uiiform Force. 203
This is the potential due to a mass La at C, together with a
mass - - at B. Accordingly
ea ea
E = La -, and La= E + -
1' f
113. Sphere with Electrified Point in its Interior.-If a charge e be at a point A in the interior of a
hollow charged insulated spherical conductor, the distribution
of mass on the interior surface of this conductor is given
by (3), Art. 111, the total mass being - e, and on the external surface there is a uniform distribution of the total mass
E + e, where E is the charge which was imparted to the
conductor.
At an internal point Q, the potential V is given by the
equation
E~+e e ea 1
V- + AQ- f BQ (9)
where B is the image of A in the sphere.
At an external point the potential is that due to a charge
E + e at the centre of the sphere.
114. Sphere in Field of Uniform Force.-If the
force throughout a certain region of space be of uniform
magnitude F and parallel to a fixed direction, it may be
regarded as due to an infinite mass 1, situated at an infinite
distance R in a direction opposite to that of the force, provided -= F
B 2
If now an insulated sphere, whose centre is C, be placed
in the field, a distribution of electricity is induced on its
surface, whose potential U in external space can be deduced
from (5) by supposing E= O in that equation. In the present
a2
case e = Mf, / = R, and CB is given by the equation CB = R.
Hence
e. CB= - =F3;
and, accordingly, in external space the potential due to the