Physics for Geologists, Second edition

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84 Electricity and magnetism Important electrical definitions ohm The unit of resistance. It is the resistance of an electric circuit in which an electric potential difference of one volt produces a current of one amp (ampere). Or, equivalently, it is the resistance in which one watt is dissipated when a current of one amp flows through it. Its symbol is Q, the Greek letter omega. volt Unit of potential difference and electromotive force. It is the potential difference across a resistance of one ohm when one ampere is flowing through it. Or, equivalently, it is the difference in potential between two points on a conductor carrying a current of one ampere when the power dissipated between the points is one watt. ampere Unit of electric current (coulomb per second). It is the current pro- duced by a potential difference of one volt across a resistance of one ohm. Or, equivalently, it is the constant current that, if maintained in two parallel, straight, conductors of infinite length and negligible circular cross-sectional area, placed 1 m apart in a vacuum, would produce a magnetic force between the two conductors equal to 20 x lo6 N per metre of length. watt Unit of power (joule per second). It is the power dissipated in an electric conductor carrying a current of one ampere between two points at one volt potential difference. coulomb The electric charge which repels an identical charge one metre away with a force of 10 x lo9 N. siemens The conductance of a conductor in which a current of one ampere is generated by a potential difference of one volt. Potential (Electric) The potential difference, or voltage, between two points is the work required to move unit positive charge from one point to another against the electric forces of the field. Dielectric material An insulating material. Permittivity We need not be concerned about this, but it is a measure of the ability of a substance to store electrical energy, and its value in vacuum is 8.854 x 10-12. The dielectric constant is the ratio of the permittivity of the dielectric material to the permittivity of vacuum or free space, that is, k = E /E~. Conductance/conductivity Conductance is a measure of the ease with which an electric current passes through a particular volume of substance. The unit is the siemens. 1 S = 1/Q. Conductivity is the conductance of unit volume of substance. Resistance/resistivity Resistance is the inverse of conductance, and resistivity is the resistance of unit volume of substance. Increasing temperature increases resistance, and as the temperature approaches 0 K, resistance vanishes. Hence the work on superconductors. Copyright 2002 by Richard E. Chapman
9 Stress and strain Pressure, p, is a surface force divided by the area on which the force is exerted [MLT-~/L~ = ML-~T-~]. Stress, S or a, is also a force divided by the area it acts on, but it is three-dimensional. More properly in some contexts, pressure and stress are the limiting value of the ratio as the area becomes very small, S = lim (@/&A). GA-too Force, as we saw on page 12, is a vector and we can resolve a force into its x, y, z components by vector arithmetic. A surface force can be resolved into a normal component on the surface, and a shear component in the surface. Can we resolve a stress? Yes, but not by vector arithmetic. In fact, six components are needed to define a stress completely, and stresses are tensors. Tensors cannot be resolved by vector arithmetic. Take a cube and apply a pressure between two opposing faces. Within the cube there will be a state of stress in three dimensions. More generally, the cube may have any orientation with respect to the force applied. On each face there will be a normal and two possible shear directions in the co-ordinate system, giving eighteen in all. The cube is in equilibrium, so we need only consider the forces acting on three sides, giving nine components as in the following matrix: a, tXy t,, acting along the x axis ty, ay tyZ acting along the y axis t,, tZy aZ acting along the z axis. These further reduce to six quantities because tXy = ty,, txz = t,, and ty, = tZy when the object is not subjected to a net turning couple. The stress ellipsoid is a convenient way of describing the state of stress in a solid. The stress ellipsoid is defined by three mutually perpendicular axes and the stresses along them. The axes are called the principal directions, and the magnitudes of the stresses in these directions are called the principal stresses, designated a,, a, and a, (z being by convention vertical). These 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
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24 Force the weights - that is, the
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26 Force Figure 2.6 Wall-sticking i
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3 Gravity Universal gravity When di
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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 and 92: 8 Electricity and magnetism Electri
Page 93 and 94: Electricity and magnetism 77 Figure
Page 95 and 96: Electricity and magnetism 79 rivett
Page 97 and 98: Electricity and magnetism 8 1 defin
Page 99: Electricity and magnetism 83 is kno
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
Page 143 and 144: - 14 $ 12 E 10 K .- 3 8 r cll + 6 0
Page 145 and 146: Fluids and fluid flow 129 the liqui
Page 147 and 148: Some dangers of mathematical statis
Page 149 and 150: Some dangers of mathematical statis
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Some dangers of mathematical statis
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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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