THE SMOOTH SOUNDING GRAPH. A Manual for Field Work ... - BGR

5
where R is the resistance [Ohm] of the wire, U is the voltage [Volt]
measured between the wire-ends when a current of an intensity I [Am-
pere] flows through the wire.
Fig.1
This means: the longer
the wire, the greater the
resistance, but the
resistance decreases,
when the cross-section is
enlarged. The influence
of the material of the
wire (iron, copper) is
expressed by a material constant ρ, i.e. the resistivity of the wire
measured in [Ohm.m] or [Ωm]. This dimension can easily be proved from
equation (1) in order to have equal dimensions on both sides.
Now we have to change our mind from the wire to the half-space. Some
difficulties arise, because the infinite half-space possesses neither a
length nor a cross-section. We also do not know in which direction the
current flows. Obviously this problem depends on the points of grounding
the electrodes. Between which points the voltage U has to be recorded?
We now shall reduce these difficulties step by step. Starting from formula
(1) valid for the wire (Fig. 1) we try to remove the length a and the cross-
section q from this formula, transforming it into
U
a
=
I
ρ
q
(2)
At the left side appears a voltage normalized to the unit length and ex-
pressing the intensity E of the electric field. E has the dimension [Volt/m].
At the right side the quotient current/cross-section expresses nothing else
then the density of the current within the wire.