Note Sheet for Fall 2004 Qualifying Exam
Vector Identities: (a, b, c and d are vector fields and ψ is a scalar field)
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Vector Differential Operators in Non-Cartesian Coordinates:
Cylindrical Coordinates:
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Spherical Coordinates:
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Solar-System Physical Data:
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Earth Mass: 5.98×1024 kg |
Moon Mass: 7.35×1022 kg |
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Earth Radius: 6.38×106 m |
Moon Radius: 1.74×106 m |
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Mean Earth-Sun Distance: 1.50×1011 m |
Mean Moon-Earth Distance: 3.85×108 m |
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Solar Mass: 1.99×1030 kg |
Solar Radius: 6.96×108 m |
Fundamental Constants:
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Gravitational constant |
G = 6.673×10–11 N·m2/kg2 |
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Coulomb constant (k = 1/4πε0) |
k = 8.9876×109 N·m2/C2 |
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Planck’s constant |
h = 6.6262×10–34 J·s |
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Boltzmann constant |
kB = 1.3086×10–23 J/K |
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Speed of light in vacuum |
c = 2.9979×108 m/s |
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Proton charge |
e = 1.6022×10–19 C |
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Proton rest mass |
mp = 1.6726×10–27 kg |
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Electron rest mass |
me = 9.1096×10–31 kg |
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Avogadro’s number |
NA = 6.0222×1023 |
Pauli Spin Matrices:
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