An introduction to the mathematical theory of attraction ...

200 Electric Images.
e, e 1 fl
but - and
r rr a r
whenc e a = 2 -f2)
ar3
then, as the potential is zero throughout the sphere, by
Art. 29, we have
R e (a - f2)
47 4 r3 (2)
Since f> a, it appears from (2) that R and a are both
negative, that is, if e be positive the charge on the sphere is
everywhere negative, and the force at its surface tends to
drive positive electricity towards the centre.
Since the potential in external space of the distribution
on the sphere is the same as that due to e at B, by Art. 37
the total charge on the sphere is e', that is, - e.
If the sphere be hollow, and the point A in its interior,
the potential is zero throughout external space (Art. 62), and
therefore if the direction of R be from C to P as before, we
have
R e a2-_f
a- Î4drw = r3 (3)
47r 44ra r3
Here a >f, and a, as before, is negative, but the force at
the inner surface of the sphere tends to drive positive electricity outwards.
In this case, since the potential in external space is zero,
the total charge on the sphere is - e.
112. Insulated Sphere.-If an insulated spherical conductor S, to which a charge E of electricity has been
imparted, be in the presence of an electrified point A, we
may suppose the sphere to have gone through a previous
process in which it is at first put to earth in the presence of
A and then insulated. It has now a charge Ei induced by
the charge e at A, and the potential is zero at each point of
S. Finally, we may suppose an additional charge E, to be