Electrical and electromagnetic methods - Geophysics for the Mineral Exploration Geoscientist - page 238

against the action of an electric field, for example when a
positive charge is moved closer to another positive charge
so that the repulsive force between them increases. The
direction a charge moves to minimise its energy de nes
the lines of force or the imaginary field lines of the electric
field. By convention, the field lines are sketched with arrows
showing the direction of the field pointing from positive to
negative, i.e. the direction of movement of a positive charge.
The field lines radiate from the pole and are everywhere
normal to the equipotential surfaces. Since the pole may be
positive or negative, the direction of the field lines may
diverge or converge at the pole, respectively. In the latter
case, this field is analogous to a gravity field ( Fig. 5.2a ).
Electrical charges arrange themselves to minimise their
electrical potential energy, evident by the fact that like
charges repel and unlike charges attract each other. If they
are free to move through a body the potential is uniform
throughout. However, if their movement is inhibited, or
there is an external electric field causing displacement of
the charges within the body, different parts of a body
acquire different electrical potentials and it is then electric-
ally polarised, as

Unlike gravity fields, the variation of an electric field is
signi cantly affected by the properties of the materials
through which it passes. However, this is only signi cant
for geophysical methods using very high-frequency elec-
tromagnetic waves (see online Appendix 5 ) .

5.2.1.2 Potential difference, current and resistance
It is convenient to describe the properties of electric
currents using the analogy of a flow of water through the
simple plumbing system shown in Fig. 5.3a . Clearly, if the

a)

Lower water
pressure

Higher water
pressure

V a lve (open)

Pipe

Pump

Constant direction
and rate of flow of
wa ter through the pipe

b)

Va lve (open)

Pump

is for example the H 2 O molecule

Core sample

( Figs. 5.2b and c ).
When two electrical poles are in proximity, the resulting
field around them is simply that which results from sum-
ming the potentials from the two poles. For the case of two
poles of opposite polarity, the resultant field forms an
electric dipole ( Fig. 5.2d ). Note how the field lines diverge
away from the two point poles, a feature useful for geo-
physical surveying because an electric current follows the
field lines, spreading out and interacting with a large
volume of the intervening geology.
The magnitude of the force between electrically charged
bodies is described in a similar way to gravitational forces,
being proportional to the product of the electrical charges
and inversely proportional to the square of the distance
between them. The proportionality constant linking the
charges and their separation to the force, i.e. equivalent
to the gravitational constant in Section 3.2.1.1 , is1

Water flows
through pore space

c)

Higher
potential

Lower
pot ential

Battery
(d.c.)

Switch
(closed)

e -

Wire

V

I

Potential difference

I I

Constant direction and rate
of flow of current through wire

d)

Battery

Switch (closed)

e -

I

L

Resistor

I I

=ð 4 πε 0 Þ

r

where ε 0 is known as the dielectric permittivity of free

space, i.e. of a vacuum. The dielectric permittivity (

Current flows
through resistor

)of
different materials varies according to their ability to
become electrically polarised. The ratio of a material

ε

Figure 5.3 Simple plumbing systems (a and b) and d.c. electrical
circuits (c and d). (a) Water driven around a closed plumbing system
by a pump. (b) Plumbing system in (a) with a porous-rock core
sample included through which the water is forced. (c) Electrical
circuit comprising a battery and closed loop of wire around which
the current

s
permittivity to that of free space is known as the dielectric
constant (

'

κ

) and given by the expression:

flows. (d) Electrical circuit in (c) with the addition of a
resistor, hindering the

κ ¼ ε
ε 0

flow of current, and analogous to the
plumbing system in (b). V

ð : Þ

5 1

- voltage, and I - current.