DIMENSIONS AND UNITS To get the value of a quantity in Gaussian units, multiply the value ex- pressed in SI units by the conversion factor. Multiples of 3 in the conversion factors result from approximating the speed of light c = 2.9979 1010 cm/sec × 3 1010 cm/sec. ≈ × Dimensions Physical Sym- SI Conversion Gaussian Quantity bol SI Gaussian Units Factor Units t2q2 Capacitance C l farad 9 1011 cm ml2 × m1/2l3/2 Charge q q coulomb 3 109 statcoulomb t × q m1/2 Charge ρ coulomb 3 103 statcoulomb 3 3/2 density l l t /m3 × /cm3 tq2 l Conductance siemens 9 1011 cm/sec ml2 t × 2 tq 1 9 1 Conductivity σ siemens 9 10 sec− 3 ml t /m × q m1/2l3/2 Current I,i ampere 3 109 statampere t t2 × q m1/2 Current J, j ampere 3 105 statampere 2 1/2 2 density l t l t /m2 × /cm2 m m 3 3 3 Density ρ kg/m 10− g/cm l3 l3 q m1/2 Displacement D coulomb 12π 105 statcoulomb l2 l1/2t /m2 × /cm2 1/2 ml m 1 4 Electric field E volt/m 10− statvolt/cm t2q l1/2t 3 × 2 1/2 1/2 ml m l 1 2 Electro- , volt 10− statvolt 2 motance EmfE t q t 3 × ml2 ml2 Energy U, W joule 107 erg t2 t2 m m Energy w,ǫ joule/m3 10 erg/cm3 2 2 density lt lt 10 Dimensions Physical Sym- SI Conversion Gaussian Quantity bol SI Gaussian Units Factor Units ml ml Force F newton 105 dyne t2 t2 1 1 Frequency f,ν hertz 1 hertz t t 2 ml t 1 11 Impedance Z ohm 10− sec/cm tq2 l 9 × 2 2 ml t 1 11 2 Inductance L henry 10− sec /cm q2 l 9 × Length l l l meter (m) 102 centimeter (cm) 1/2 q m 3 Magnetic H ampere– 4π 10− oersted 1/2 intensity lt l t turn/m × ml2 m1/2l3/2 Magnetic flux Φ weber 108 maxwell tq t m m1/2 Magnetic B tesla 104 gauss tq l1/2t induction l2q m1/2l5/2 Magnetic m,µ ampere–m2 103 oersted– t t moment cm3 1/2 q m 3 Magnetization M ampere– 4π 10− oersted lt l1/2t turn/m × q m1/2l1/2 4π Magneto- , ampere– gilbert 2 motance MmfM t t turn 10 Mass m, M m m kilogram 103 gram (g) (kg) ml ml Momentum p, P kg–m/s 105 g–cm/sec t t m m 2 1 2 Momentum kg/m –s 10− g/cm –sec l2t l2t density ml 1 Permeability µ 1 henry/m 107 — q2 4π × 11 Dimensions Physical Sym- SI Conversion Gaussian Quantity bol SI Gaussian Units Factor Units t2q2 Permittivity ǫ 1 farad/m 36π 109 — ml3 × q m1/2 Polarization P coulomb/m2 3 105 statcoulomb l2 l1/2t × /cm2 2 1/2 1/2 ml m l 1 2 Potential V,φ volt 10− statvolt t2q t 3 × ml2 ml2 Power P watt 107 erg/sec t3 t3 m m Power watt/m3 10 erg/cm3–sec lt3 lt3 density m m Pressure p, P pascal 10 dyne/cm2 lt2 lt2 2 q 1 9 1 Reluctance ampere–turn 4π 10− cm− 2 R ml l /weber × 2 ml t 1 11 Resistance R ohm 10− sec/cm tq2 l 9 × 3 ml 1 9 Resistivity η,ρ t ohm–m 10− sec tq2 9 × ml ml Thermal con- κ, k watt/m– 105 erg/cm–sec– 3 3 ductivity t t deg (K) deg (K) Time t t t second (s) 1 second (sec) ml m1/2l1/2 Vector A weber/m 106 gauss–cm potential tq t l l Velocity v m/s 102 cm/sec t t m m Viscosity η,µ kg/m–s 10 poise lt lt 1 1 1 1 Vorticity ζ s− 1 sec− t t ml2 ml2 Work W joule 107 erg t2 t2 12 INTERNATIONAL SYSTEM (SI) NOMENCLATURE6 Physical Name Symbol Physical Name Symbol Quantity of Unit for Unit Quantity of Unit for Unit *length meter m electric volt V potential *mass kilogram kg electric ohm Ω *time second s resistance *current ampere A electric siemens S conductance *temperature kelvin K electric farad F *amount of mole mol capacitance substance magnetic flux weber Wb *luminous candela cd intensity magnetic henry H inductance plane angle radian rad † magnetic tesla T solid angle steradian sr intensity † frequency hertz Hz luminous flux lumen lm energy joule J illuminance lux lx force newton N activity (of a becquerel Bq radioactive pressure pascal Pa source) power watt W absorbed dose gray Gy (of ionizing electric charge coulomb C radiation) *SI base unit Supplementary unit † METRIC PREFIXES Multiple Prefix Symbol Multiple Prefix Symbol 1 10− deci d 10 deca da 2 2 10− centi c 10 hecto h 3 3 10− milli m 10 kilo k 6 6 10− micro µ 10 mega M 9 9 10− nano n 10 giga G 12 12 10− pico p 10 tera T 15 15 10− femto f 10 peta P 18 18 10− atto a 10 exa E 13 PHYSICAL CONSTANTS (SI)7 Physical Quantity Symbol Value Units 23 1 Boltzmann constant k 1.3807 10− JK− × 19 Elementary charge e 1.6022 10− C × 31 Electron mass m 9.1094 10− kg e × 27 Proton mass m 1.6726 10− kg p × 11 3 2 1 Gravitational constant G 6.6726 10− m s− kg− × 34 Planck constant h 6.6261 10− J s × 34 h¯ = h/2π 1.0546 10− J s × 8 1 Speed of light in vacuum c 2.9979 10 m s− × 12 1 Permittivity of ǫ 8.8542 10− F m− 0 × free space 7 1 Permeability of µ 4π 10− H m− 0 × free space Proton/electron mass m /m 1.8362 103 p e × ratio 11 1 Electron charge/mass e/m 1.7588 10 C kg− e × ratio 4 me 7 1 Rydberg constant R = 1.0974 10 m− 2 3 ∞ 8ǫ0 ch × 2 2 11 Bohr radius a = ǫ h /πme 5.2918 10− m 0 0 × 2 21 2 Atomic cross section πa 8.7974 10− m 0 × 2 2 15 Classical electron radius r = e /4πǫ mc 2.8179 10− m e 0 × 2 29 2 Thomson cross section (8π/3)r 6.6525 10− m e × 12 Compton wavelength of h/mec 2.4263 10− m × 13 electron h/m¯ c 3.8616 10− m e × 2 3 Fine-structure constant α = e /2ǫ0hc 7.2974 10− 1 × α− 137.04 2 16 2 First radiation constant c = 2πhc 3.7418 10− W m 1 × 2 Second radiation c = hc/k 1.4388 10− mK 2 × constant 8 2 4 Stefan-Boltzmann σ 5.6705 10− W m− K− × constant 14 Physical Quantity Symbol Value Units 6 Wavelength associated λ = hc/e 1.2398 10− m 0 × with 1 eV Frequency associated ν = e/h 2.4180 1014 Hz 0 × with 1 eV 5 1 Wave number associated k = e/hc 8.0655 10 m− 0 × with 1 eV 19 Energy associated with hν 1.6022 10− J 0 × 1 eV 25 Energy associated with hc 1.9864 10− J 1 × 1 m− 3 2 2 Energy associated with me /8ǫ0 h 13.606 eV 1 Rydberg 5 Energy associated with k/e 8.6174 10− eV × 1 Kelvin Temperature associated e/k 1.1604 104 K × with 1 eV 23 1 Avogadro number N 6.0221 10 mol− A × 4 1 Faraday constant F = N e 9.6485 10 C mol− A × 1 1 Gas constant R = NAk 8.3145 JK− mol− 25 3 Loschmidt’s number n 2.6868 10 m− 0 × (no. density at STP) 27 Atomic mass unit m 1.6605 10− kg u × Standard temperature T0 273.15 K Atmospheric pressure p = n kT 1.0133 105 Pa 0 0 0 × Pressure of 1 mm Hg 1.3332 102 Pa × (1 torr) 2 3 Molar volume at STP V = RT /p 2.2414 10− m 0 0 0 × 2 Molar weight of air M 2.8971 10− kg air × calorie (cal) 4.1868 J 2 Gravitational g 9.8067 m s− acceleration 15 PHYSICAL CONSTANTS (cgs)7 Physical Quantity Symbol Value Units 16 Boltzmann constant k 1.3807 10− erg/deg (K) × 10 Elementary charge e 4.8032 10− statcoulomb × (statcoul) 28 Electron mass m 9.1094 10− g e × 24 Proton mass m 1.6726 10− g p × 8 2 2 Gravitational constant G 6.6726 10− dyne-cm /g × 27 Planck constant h 6.6261 10− erg-sec × 27 h¯ = h/2π 1.0546 10− erg-sec × Speed of light in vacuum c 2.9979 1010 cm/sec × Proton/electron mass m /m 1.8362 103 p e × ratio Electron charge/mass e/m 5.2728 1017 statcoul/g e × ratio 2 4 2π me 5 1 Rydberg constant R = 1.0974 10 cm− ∞ ch3 × 2 2 9 Bohr radius a =h ¯ /me 5.2918 10− cm 0 × 2 17 2 Atomic cross section πa 8.7974 10− cm 0 × 2 2 13 Classical electron radius r = e /mc 2.8179 10− cm e × 2 25 2 Thomson cross section (8π/3)r 6.6525 10− cm e × 10 Compton wavelength of h/mec 2.4263 10− cm × 11 electron h/m¯ c 3.8616 10− cm e × 2 3 Fine-structure constant α = e /hc¯ 7.2974 10− 1 × α− 137.04 2 5 2 First radiation constant c = 2πhc 3.7418 10− erg-cm /sec 1 × Second radiation c2 = hc/k 1.4388 cm-deg (K) constant 5 2 Stefan-Boltzmann σ 5.6705 10− erg/cm - × constant sec-deg4 4 Wavelength associated λ 1.2398 10− cm 0 × with 1 eV 16 Physical Quantity Symbol Value Units Frequency associated ν 2.4180 1014 Hz 0 × with 1 eV 3 1 Wave number associated k 8.0655 10 cm− 0 × with 1 eV 12 Energy associated with 1.6022 10− erg × 1 eV 16 Energy associated with 1.9864 10− erg 1 × 1 cm− Energy associated with 13.606 eV 1 Rydberg 5 Energy associated with 8.6174 10− eV × 1 deg Kelvin Temperature associated 1.1604 104 deg (K) × with 1 eV 23 1 Avogadro number N 6.0221 10 mol− A × Faraday constant F = N e 2.8925 1014 statcoul/mol A × Gas constant R = N k 8.3145 107 erg/deg-mol A × 19 3 Loschmidt’s number n 2.6868 10 cm− 0 × (no.