An introduction to the mathematical theory of attraction ...

Electrified Point. 197
CHAPTER VI.
ELECTRIC IMAGES.
107. Conductor put to Earth.-When a conductor C
in connexion with the ground is in electric equilibrium, its
potential is the same as that of the surface of the earth. If
the connexion be made by means of a thin wire, and if the
distance of C from the earth's surface be large compared
with the dimensions and mutual distances of C and the other
conductors in the vicinity, the potential of the electricity
distributed on the entire system of conductors is approximately
zero at all points of C. Hence we may assume that a conductor in connexion with the ground, when in a state of
electric equilibrium, is at potential zero.
Such a conductor is said to be put to earth.
108. Electrified Point.-If a body A charged with
electricity be brought into the presence of a conductor C
which is put to earth, the potential of the electric mass on A
is not zero at C, and in order that the total potential at C
should be zero there must be a separation and distribution
of electric mass on C, such that the potential at C due to this
distribution along with that on A is zero. This distribution
on C is said to be in&dced by A.
If A be a conductor the distribution induced on C disturbs the previously existing constancy of the potential at A,
and the problem presented for solution is to find the distribution of a given charge on A, and the charge and distribution
on C, so that the potential due to the two distributions shall
be constant at the surface of A and zero at the surface
of C.
In order to simplify the problem we may, for mathematical purposes, suppose the body A to shrink to a point, whilst
the electric mass which it contains remains finite. This
hypothesis cannot be realized in nature, but is analogous