Physics for Geologists, Second edition

Electricity and magnetism 77
Figure 8.1 Resistivity. The resistivity of a block of material can be measured by
passing a current through two electrodes, and measuring the voltage
between the other two. The dimensions of the block between the
electrodes are also required (Equation 8.2).
Electric fields
When two electrodes are placed in a homogeneous, isotropic material, and
a current is passed from one to the other, an electric field is created that
occupies the material (Figure 8.2). The field consists of lines of force, or flow
paths, radiating out from the positive electrode A normal to the surfaces
of equal potential (equipotential surfaces), and converging into the negative
electrode B. There is also a line of force or a flow path from A that is diamet-
rically opposed to the direct path to B. Indeed, the direct path is but one path,
and the reason is simple. By creating a potential difference between A and
B, the energy of the charges forming the electric current is greatest at A, and
decreases in all directions away from A. This is exactly what happens if the
electrodes are replaced by water wells in a homogeneous, isotropic reservoir,
pumping down at A at the same rate as pumping up at B. The energy of the
water is greatest at A and water flows radially outwards, following paths to
B, where the energy is least.
Electric fields exist whether or not currents exist between the electrodes
and charges are moving. If currents exist (the charges are moving) there is
an associated magnetic field. Consequently, if a magnetic field changes, it
will cause charges to move and so generate currents.
The field can be mapped and measured if electrodes can be inserted
into the medium and the potential difference measured. This is a prop-
erty of the medium and of the potential difference. The same is true of
groundwater: wells drilled in an aquifer would indicate the distribution of
Copyright 2002 by Richard E. Chapman