Physics for Geologists, Second edition

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76 Electricity and magnetism electric insulators are also heat insulators. Most minerals are bad conductors of electricity and heat. A good conductor requires free electrons. Electricity can be made to flow down a wire and made to do work at some distance from where it is generated. An electric current flowing down a wire generates a magnetic field around it. This process is reversible, and a changing magnetic field can generate an electric current. The main topics we are interested in are 1 the electrical conductivity and resistivity of materials; 2 the fields associated with electric currents, and the analogy with water flow. Conductivity and resistivity: potential Conductivity is a measure of the ease with which an electric current passes through unit volume of a substance: resistivity is the inverse. Conductance and resistance are the absolute measures of a articular volume of substance. The unit of resistance is the ohm, Q(VA- ); the unit of resistivity is the ohm-rnetre, ohm-m, or Q m (V A-l m2 m-l = v A-* m). So the resistance between two electrodes 2 m apart in material of resistivity 1 Q m will be 2 Q if the cross-sectional area remains constant. Ohm's Law states that for a given conductive material, the ratio of the voltage (potential or energy) across the ends and the current in the conductor is constant within certain limits, and this is called the resistance of the material: V (volts) = constant = resistance R (ohms). I (amps) If the cross-sectional area S is uniform, the resistance is proportional to the length, 1, and inversely proportional to the cross-sectional area. Resistivity is thus related to resistance, R, by: where p is the resistivity of the material. (These symbols are not entirely standard: R commonly stands for resistivity in electrical borehole logging studies.) In practice, a known current is passed between two electrodes placed in the material (Figure 8.1), and the potential difference between two others is measured. The principle of reciprocity means that if the current is passed between M and N, and the voltage (potential difference) is measured between A and B, the result will be the same. This is very important in the tools used for measuring the resistivity of rocks around boreholes. Copyright 2002 by Richard E. Chapman P
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
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Physics for Geologists Second editi
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Copyright 2002 by Richard E. Chapma
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... vlii Contents Polarization 47 L
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Figures Copyright 2002 by Richard E
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Tables Copyright 2002 by Richard E.
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xiv Preface waves diminishes with d
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xvi Preface provides. This book is
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xviii Acknowledgements to K. Whaler
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xx Symbols mass refractive index bu
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2 Basic concepts Table 1.1 Dimensio
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4 Basic concepts Table 1.2 Basic SI
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6 Basic concepts pascal (Pa) and si
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8 Basic concepts all the relevant d
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10 Basic concepts relating them by
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2 Force The dimensions of force are
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14 Force The ratio of the Moon's ac
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16 Force Figure 2.1 The sum of the
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18 Force When a motorcycle takes a
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20 Force Figure 2.3 Torque is the p
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22 Force How does momentum differ f
Page 41 and 42: 24 Force the weights - that is, the
Page 43 and 44: 26 Force Figure 2.6 Wall-sticking i
Page 45 and 46: 3 Gravity Universal gravity When di
Page 47 and 48: 30 Gravity are significant to geolo
Page 49 and 50: 32 Gravity Figure 3.2 The tractive,
Page 51 and 52: 34 Gravity Mean sea level It might
Page 53 and 54: 36 Gravity The benefits of space fl
Page 55 and 56: 38 Gravity Figure 3.6 Profile of th
Page 57 and 58: 40 Gravity Figure 3.8 The siphon at
Page 59 and 60: 4 Optics Light is an electromagneti
Page 61 and 62: 44 Optics Figure 4.2 Refraction. (a
Page 63 and 64: 46 Optics The coeficient of reflect
Page 65 and 66: 48 Optics only the light oscillatin
Page 67 and 68: 50 Optics called Iceland Spar. Two
Page 69 and 70: 52 Optics Diffraction If you shine
Page 71 and 72: 54 Optics Figure 4.7 Geometrical op
Page 73 and 74: 56 Optics Figure 4.9 The mirrors in
Page 75 and 76: 5 Atomic structure and age-dating P
Page 77 and 78: 60 Atomic structure and age-dating
Page 83 and 84: 66 Electromagnetic radiation radiat
Page 85 and 86: 68 Electromagnetic radiation Source
Page 87 and 88: Heat and heat flow The noun heat ha
Page 89 and 90: 72 Heat and heat flow Second Law: A
Page 91: 8 Electricity and magnetism Electri
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99 and 100: Electricity and magnetism 83 is kno
Page 101 and 102: 9 Stress and strain Pressure, p, is
Page 103 and 104: Stress and strain 87 than some natu
Page 105 and 106: These three elastic constants are r
Page 107 and 108: Stress and strain 91 Figure 9.1 New
Page 109 and 110: Stress and strain 93 Figure 9.2 Com
Page 111 and 112: Stress and strain 95 Figure 9.3 Ide
Page 113 and 114: Fracture Stress and strain 97 We fo
Page 115 and 116: Stress and strain 99 from which we
Page 117 and 118: 10 Sea waves The nature of water wa
Page 119 and 120: Sea waves 103 Figure 10.1 Wave moti
Page 121 and 122: Sea waves 105 refraction by islands
Page 123 and 124: Acoustics: sound and other waves 10
Page 125 and 126: Acoustics: sound and other waves 10
Page 127 and 128: 12 Fluids and fluid flow Introducti
Page 129 and 130: Fluids and fluid flow 1 13 Figure 1
Page 131 and 132: Fluids and fluid flow 115 Figure 22
Page 133 and 134: Fluids and fluid flow 117 and the f
Page 135 and 136: water above a vertical thickness h
Page 137 and 138: Fluids and fluid flow 121 where V i
Page 139 and 140: Fluids and fluid flow 123 ardentes,
Page 141 and 142: Fluids and fluid flow 125 Figure 12
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- 14 $ 12 E 10 K .- 3 8 r cll + 6 0
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Fluids and fluid flow 129 the liqui
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Some dangers of mathematical statis
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Appendix 139 What would happen if y
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Notes 141 and since x is very large
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References Allum, J. A. E. (1966) P
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References 145 -(1950) 'Mechanism o
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Further reading 147 Trigg, G. L. an
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Physics for Geologists, Second edition

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