The voltage from the surface of the electrode to the point x is the line integral of ex with the lower limit equal
to the sphere's radius, r, and the upper limit equal to the distance, x:
As x becomes very large, E is closely approximated as
The resistance to the earth of the electrode is the resistance between the electrode and a very distant point;
the voltage drop between the electrode and a point infinitely distant,
the current entering the electrode,
earth resistivity, and
radius of hemisphere.
Rewriting Equation 2-7 as
shows that the resistivity can be determined by knowing r, E, and I.