The Cambridge Handbook of Physics
Formulas
Index from 'Doppler effect' to 'Fraunhofer diffraction'
Doppler
effect (non-relativistic), 87
effect (relativistic) [3.22], 65
line broadening [8.116], 173
width [8.117], 173
DOPPLER EFFECT, 87
dot product [2.1], 20
double factorial, 48
double pendulum [3.183], 76
DRAG, 85
drag
on a disk || to flow
[3.310],
85
on a disk ^ to flow
[3.309],
85
on a sphere [3.308], 85
drift velocity (electron) [6.61], 132
Dulong and Petit's law [6.46], 130
Dynamics and Mechanics, 63-88
DYNAMICS DEFINITIONS, 68
e (exponential constant), 9
e TO 1000 DECIMAL PLACES, 18
Earth (motion relative to) [3.38], 66
EARTH DATA, 176
eccentricity
of conic section, 38
of orbit [3.108], 71
of scattering hyperbola [3.120], 72
ECLIPTIC COORDINATES, 178
ecliptic latitude [9.14], 178
ecliptic longitude [9.15], 178
Eddington limit [9.59], 181
edge dislocation [6.21], 128
effective
area (antenna) [7.212], 153
distance (Fresnel diffraction) [8.48],
166
mass (in solids) [6.86], 134
wavelength [9.40], 179
efficiency
heat engine [5.10], 107
heat pump [5.12], 107
Otto cycle [5.13], 107
refrigerator [5.11], 107
Ehrenfest's equations [5.53], 109
Ehrenfest's theorem [4.30], 91
eigen -functions (quantum) [4.28], 91
Einstein
A coefficient [8.119], 173
B coefficients [8.118], 173
diffusion equation [5.98], 113
field equation [3.59], 67
lens (rings) [9.50], 180
tensor [3.58], 67
EINSTEIN COEFFICIENTS, 173
Einstein-de Sitter model [9.104], 185
elastic
collisions, 73
media (isotropic), 81
modulus (longitudinal) [3.241], 81
modulus [3.234], 80
potential energy [3.235], 80
elastic scattering, 72
ELASTIC WAVE VELOCITIES, 82
Elasticity, 80
ELASTICITY DEFINITIONS (GENERAL), 80
ELASTICITY DEFINITIONS (SIMPLE), 80
electric current [7.139], 147
electric dipole, see dipole
electric displacement (dimensions), 16
electric displacement, D [7.86], 142
electric field
around objects, 138
energy density [7.128], 146
static, 136
thermodynamic work [5.7], 106
wave equation [7.193], 152
electric field from
A and f[7.41],
139
charge distribution [7.6], 136
charge-sheet [7.32], 138
dipole [7.31], 138
disk [7.28], 138
line charge [7.29], 138
point charge [7.5], 136
sphere [7.27], 138
waveguide [7.190], 151
wire [7.29], 138
electric field strength (dimensions), 16
ELECTRIC FIELDS, 138
electric polarisability (dimensions), 16
electric polarisation (dimensions), 16
electric potential
from a charge density [7.46], 139
Lorentz transformation [7.75], 141
of a moving charge [7.48], 139
short dipole [7.82], 142
electric potential difference (dimensions), 16
electric susceptibility, cE[7.87],
142
electrical conductivity, see conductivity
ELECTRICAL IMPEDANCE, 148
electrical permittivity, e, er[7.90],
142
electromagnet (magnetic flux density) [7.38], 138
electromagnetic
boundary conditions, 144
constants, 7
fields, 139
wave speed [7.196], 152
waves in media, 152
electromagnetic coupling constant, see fine structure constant
ELECTROMAGNETIC ENERGY, 146
Electromagnetic fields (general), 139
ELECTROMAGNETIC FORCE AND TORQUE, 145
ELECTROMAGNETIC PROPAGATION IN COLD PLASMAS, 157
Electromagnetism, 135-160
electron
charge, 6, 7
density of states [6.70], 133
diamagnetic moment [7.108], 144
drift velocity [6.61], 132
g-factor [4.143], 100
gyromagnetic ratio [4.140], 100
heat capacity [6.76], 133
intrinsic magnetic moment [7.109], 144
mass, 6
radius (equation) [7.238], 155
radius (value), 8
scattering cross-section [7.238], 155
spin magnetic moment [4.143], 100
thermal velocity [7.257], 156
velocity in conductors [6.85], 134
ELECTRON CONSTANTS, 8
ELECTRON SCATTERING PROCESSES, 155
Electrons in solids, 132
electronvolt (unit), 5
electronvolt (value), 6
electrostatic potential [7.1], 136
ELECTROSTATICS, 136
elementary charge, 6, 7
elements (periodic table of), 124
ellipse, 38
(semi) centre of mass [3.178], 76
area [2.268], 37
moment of inertia [3.166], 75
perimeter [2.267], 37
semi-latus-rectum [3.109], 71
semi-major axis [3.106], 71
semi-minor axis [3.107], 71
ellipsoid
moment of inertia of solid [3.163], 75
the moment of inertia [3.147], 74
volume [2.269], 37
elliptic integrals [2.398], 45
elliptical orbit [3.104], 71
ELLIPTICAL POLARISATION, 170
elliptical polarisation [8.80], 170
ellipticity [8.82], 170
E = mc2 [3.72], 68
emission coefficient [5.174], 120
emission spectrum [7.291], 159
emissivity [5.193], 121
energy
density
blackbody
[5.192],
121
dimensions, 16
elastic wave [3.281],
83
electromagnetic
[7.128],
146
radiant
[5.148],
118
spectral
[5.173],
120
dimensions, 16
dissipated in resistor [7.155], 148
distribution (Maxwellian) [5.85], 112
elastic [3.235], 80
electromagnetic, 146
equipartition [5.100], 113
Fermi [5.122], 115
first law of thermodynamics [5.3], 106
Galilean transformation [3.6], 64
kinetic , see kinetic energy
Lorentz transformation [3.19], 65
loss after collision [3.128], 73
mass relation [3.20], 65
of capacitive assembly [7.134], 146
of capacitor [7.153], 148
of charge distribution [7.133], 146
of electric dipole [7.136], 146
of inductive assembly [7.135], 146
of inductor [7.154], 148
of magnetic dipole [7.137], 146
of orbit [3.100], 71
potential , see potential energy
relativistic rest [3.72], 68
rotational kinetic
rigid body
[3.142],
74
w.r.t. principal axes
[3.145],
74
thermodynamic work, 106
ENERGY IN CAPACITORS, INDUCTORS AND RESISTORS, 148
energy-time uncertainty relation [4.8], 90
ENSEMBLE PROBABILITIES, 114
enthalpy
definition [5.30], 108
Joule-Kelvin expansion [5.27], 108
entropy
Boltzmann formula [5.105], 114
change in Joule expansion [5.64], 110
experimental [5.4], 106
fluctuations [5.135], 116
from partition function [5.117], 115
Gibbs formula [5.106], 114
of a monatomic gas [5.83], 112
entropy (dimensions), 16
e, er
(electrical permittivity) [7.90], 142
EQUATION CONVERSION: SI TO GAUSSIAN UNITS, 135
equation of state
Dieterici gas [5.72], 111
ideal gas [5.57], 110
monatomic gas [5.78], 112
van der Waals gas [5.67], 111
equipartition theorem [5.100], 113
error function [2.391], 45
errors, 60
escape velocity [3.91], 70
estimator
kurtosis [2.546], 57
mean [2.542], 57
skewness [2.545], 57
standard deviation [2.544], 57
variance [2.543], 57
Euler
angles [2.101], 26
constant
expression
[2.120],
27
value, 9
differential equation [2.351], 43
formula [2.217], 34
relation, 38
strut [3.261], 82
Euler's equation (fluids) [3.289], 84
Euler's equations (rigid bodies) [3.186], 77
Euler's method (for ordinary differential equations) [2.597],
62
Euler-Lagrange equation
and lagrangians [3.214], 79
calculus of variations [2.335], 42
even functions, 53
EVOLUTIONARY TIMESCALES, 181
exa, 5
exhaust velocity (of a rocket) [3.93], 70
exitance
blackbody [5.191], 121
luminous [5.162], 119
radiant [5.150], 118
exp(x) [2.133], 29
expansion coefficient [5.19], 107
EXPANSION PROCESSES, 108
expansivity [5.19], 107
EXPECTATION VALUE, 91
expectation value
Dirac notation [4.37], 92
from a wavefunction [4.25], 91
explosions [3.331], 87
exponential
distribution [2.552], 58
integral [2.395], 45
series expansion [2.133], 29
exponential constant (e), 9
extraordinary modes [7.271], 157
extrema [2.336], 42
f-number [8.69], 168
Fabry-Perot etalon
chromatic resolving power [8.21], 163
free spectral range [8.23], 163
fringe width [8.19], 163
transmitted intensity [8.17], 163
FABRY-PEROT ETALON, 163
face-centred cubic structure, 127
factorial [2.410], 46
factorial (double), 48
Fahrenheit conversion [1.2], 15
faltung theorem [2.517], 55
farad (unit), 4
Faraday constant, 6, 9
Faraday constant (dimensions), 16
Faraday rotation [7.273], 157
Faraday's law [7.55], 140
fcc structure, 127
Feigenbaum's constants, 9
femto, 5
Fermat's principle [8.63], 168
Fermi
energy [6.73], 133
temperature [6.74], 133
velocity [6.72], 133
wavenumber [6.71], 133
fermi (unit), 5
Fermi energy [5.122], 115
FERMI GAS, 133
Fermi's golden rule [4.162], 102
Fermi-Dirac distribution [5.121], 115
fermion statistics [5.121], 115
fibre optic
acceptance angle [8.77], 169
dispersion [8.79], 169
numerical aperture [8.78], 169
Fick's first law [5.92], 113
Fick's second law [5.95], 113
field equations (gravitational) [3.42], 66
FIELD RELATIONSHIPS, 139
fields
depolarising [7.92], 142
electrochemical [6.81], 133
electromagnetic, 139
gravitational, 66
static E and B, 136
velocity [3.285], 84
Fields associated with media, 142
film reflectance [8.4], 162
fine-structure constant
expression [4.75], 95
value, 6, 7
finesse (coefficient of) [8.12], 163
finesse (Fabry-Perot etalon) [8.14], 163
first law of thermodynamics [5.3], 106
fitting straight-lines, 60
fluctuating dipole interaction [6.50], 131
fluctuation
of density [5.137], 116
of entropy [5.135], 116
of pressure [5.136], 116
of temperature [5.133], 116
of volume [5.134], 116
probability (thermodynamic) [5.131],
116
variance (general) [5.132], 116
Fluctuations and noise, 116
Fluid dynamics, 84
fluid stress [3.299], 85
FLUID WAVES, 86
flux density [5.171], 120
flux density-redshift relation [9.90], 184
flux linked [7.149], 147
flux of molecules through a plane [5.91], 113
flux-magnitude relation [9.32], 179
focal length [8.64], 168
focus (of conic section), 38
force
and acoustic impedance [3.276], 83
and stress [3.228], 80
between two charges [7.119], 145
between two currents [7.120], 145
between two masses [3.40], 66
central [4.113], 98
centrifugal [3.35], 66
Coriolis [3.33], 66
critical compression [3.261], 82
definition [3.63], 68
dimensions, 16
electromagnetic, 145
Newtonian [3.63], 68
on
charge in a field [7.122],
145
current in a field [7.121],
145
electric dipole [7.123],
145
magnetic dipole [7.124],
145
sphere (potential flow)
[3.298],
84
sphere (viscous drag)
[3.308],
85
relativistic [3.71], 68
unit, 4
Force, torque and energy, 145
FORCED OSCILLATIONS, 78
form factor [6.30], 128
formula (the) [2.456], 50
Foucault's pendulum [3.39], 66
four-parts formula [2.260], 36
four-scalar product [3.27], 65
four-vector
electromagnetic [7.79], 141
momentum [3.21], 65
spacetime [3.12], 64
FOUR-VECTORS, 65
Fourier series
complex form [2.479], 52
real form [2.477], 52
FOURIER SERIES, 52
Fourier series and transforms, 52
FOURIER SYMMETRY RELATIONSHIPS, 53
Fourier transform
cosine [2.510], 54
definition [2.483], 52
derivatives
and inverse
[2.503],
54
general
[2.499],
53
Gaussian [2.508], 54
Lorentzian [2.506], 54
shah function [2.511], 54
shift theorem [2.502], 54
similarity theorem [2.501], 54
sine [2.509], 54
step [2.511], 54
top hat [2.512], 54
triangle function [2.513], 54
FOURIER TRANSFORM, 52
FOURIER TRANSFORM PAIRS, 54
FOURIER TRANSFORM THEOREMS, 53
Fourier's law [5.94], 113
Frames of reference, 64
Fraunhofer diffraction, 164