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The fundamental units are the meter, second, kilogram, and Coulomb. They were originally defined in 1793 as the "Standard International" (SI) units, or "MKS" units.
Quantity Unit Definition
Length Meter The Earth's circumference is 40 million meters
Time Second There are 86400 seconds in one Earth day
Mass Kilogram The mass of a cube of water 10 cm on a side is 1 kilogram
Charge Coulomb The force between two charges of one Coulomb each and
separated by 1 meter is 9 billion Newtons
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Density of water = 1000 kg/meter = 1 g/cm Density of air = 1.2 kg/meter = .0012 g/cm
The fundamental units are length, mass, time, and charge, and all other units are derived from these.
Quanity Composition Units Length meters Mass kg Time seconds Charge Coulomb Speed = Length / Time meters/second Momentum = Mass * Speed kg meters/second Acceleration = Velocity / Time meters/second2 Force = Mass * Acceleration Newtons = kg meters/second2 Energy = Force * Distance Joules = kg meters2/second2 Power = Energy / Time Watts = kg meters2/second3 Area = Length meters Volume = Length meters Density = Mass / Volume kg / meters2 Pressure = Force / Area Pascals = Newtons/meter = Joules/meter Angular momentum = Momentum * Length kg meters/second Torque = Force * Length kg meters/second Frequency = 1 / Time Hertz = 1/second
Meter = 39.37 inches
= 1.0936 yards
= 3.281 feet
= 1/1609 miles
Mile = 1609 meters
= 1760 yards (exact)
Yard = 3 feet (exact)
= .9144 meters
Foot = 12 inches (exact)
= .3048 meters
Inch = 25.4 mm (exact)
Minute = 60 seconds
Hour = 60 minutes
Day = 24 hours
Year = 365.25 days
Ton = 1000 kg (exact)
Kilogram = 1000 grams (exact)
= 2.205 pounds (pounds interpreted as mass)
Newton = .2248 pounds (For Earth gravity at the surface)
(pounds interpreted as force)
Pound = 16 ounces (exact) (interpreted as mass)
= .4535 kg
4.448 Newtons (interpreted as force)
Ounce = 28.35 grams (interpreted as mass)
Meter/second = 2.24 miles/hour
Km/hour = .6214 miles/hour
Miles/hour = 1.609 km/hour
Pascal = .0001450 pounds/inch2 (pounds interpreted as force)
Pound/inch2 = 6895 Pascals
Bar = 101325 Pascals (Atmosphere pressure at sea level)
= 14.50 pounds/inch2 (pounds interpreted as force)
Earth gravity= 9.807 meters/second2
= 32.2 feet/second2
Standard sheet of paper = 11 x 8.5 inches = 27.94 x 21.59 cm
PoundAsMass = Pound interpreted as mass, with units of kg
= .4535 kg
PoundAsForce = Pound interpreted as force, with units of Newtons
= The force exerted by .4535 kg in Earth's gravity
= .4535 kg * 9.8 m/s2
= 4.448 Newtons
EarthGravity = 9.8 m/s2
Force = Mass * Acceleration
PoundAsForce = PoundAsMass * EarthGravity
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Meters Earth Earth Light travel
radii orbits time
(AU)
Nucleus 2⋅10
Atom 2⋅10
Green light 5.5⋅10
Neuron .00002
Dime thickness .00135
Dime diameter .0178
Quarter diameter .024
Tennis ball diameter .067
Soccer ball diameter .22
Average person 1.78
Central Park width 800
Mount Everest 8848
Moon radius .273
Mars radius .532
Earth radius 6371000 1.0
Jupiter radius 10.9
Moon distance 60.3 .00257 1.5 seconds
Sun radius 109 .00474
Earth orbit 1.496⋅1011 1.0 8 minutes
Jupiter orbit 5.2 40 minutes
Neptune orbit 30.1 3 days
Light year 9.461⋅1015 63241 1 year
Alpha Centauri 4.4 years Nearest star
Galaxy thickness 1000 years
Galaxy center 27200 years
Galaxy diameter 100000 years
Andromeda distance 2.54 million years
Virgo cluster distance 54 million years
Size of universe 14 billion years
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meters/second Mach
Walk 1.5
Running sprint 10
Cycling sprint 20
Cheetah 30 Fastest land animal
70 miles/hour 31
Baseball pitch 45 100 miles/hour
Human neuron 100
747 airplane 300 .9
Sound 340 1.0
F-16 Falcon 590 2.0
Concorde 605 1.7
F-22 Raptor 670 2.0
F-15 Eagle 740 2.2
SR-71 Blackbird 980 2.9
Orbit speed 7800 22.9 Minimum speed to orbit the Earth (Mach 23)
Ion rocket 100000 Fastest spacecraft we can build
Fission rocket 107
Fusion rocket 107
Light 3⋅108 880000
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kg Earth Solar
masses masses
Electron 9.109e-31
Proton 1.673e-27
Neutron 1.675e-27
1 ounce .0283
Tennis ball .058
Soccer ball .44
1 pound .454
Typical human 67
Sumo wrestler 230
Ton 1000
Honda Civic 1200
Elephant 5000
Bradley tank 27000
Argentinosaurus 70000 Largest dinosaur
Blue whale 200000
Moon 7.35⋅1022 .0123
Mars 6.42⋅1023 .107
Earth 5.92⋅1024 1
Jupiter 1.90⋅1027 318 .00096
Sun 1.99⋅1030 330000 1.0
White dwarf max 2.9⋅1030 1.44
Milky Way black hole7.4⋅1036 4.2 million
Milky Way 2.5⋅1042 1.2 trillion
Andromeda 2.5⋅1042 1.2 trillion
M87 galaxy 10 trillion
Virgo galaxy cluster 1200 trillion
Meters/second2
Ceres gravity .27
Europa gravity 1.31
Titan gravity 1.35
Moon gravity 1.62
Mars gravity 3.8
Venus gravity 8.87
Earth gravity 9.8
Bugatti Veyron 15.2 0 to 100 km/h in 2.4 seconds
Red out 30 Max long-term acceleration in the direction of blood rushing to your head
Blackout 50 Max long-term acceleration while sitting
Formula-1 car 50 High-speed breaking and cornering with a downforce wing
Blackout with g suit 90 Max long-term acceleration while sitting with a g-suit
Max long-term (front) 120 Max long-term acceleration while lying on one's front
Max long-term (back) 170 Max long-term acceleration while lying on one's back
Max short-term 500 Max short-term acceleration
Bullet 310000 9x19 Parabellum handgun, average acceleration along the barrel
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Mass Diameter Height Density Density Copper Nickel Zinc Manganese
(g) (mm) (mm) (g/cm3) ($/kg) frac frac frac frac
Penny 2.5 19.05 1.52 5.77 4.0 .025 .975
Nickel 5.000 21.21 1.95 7.26 10.0 .75 .25
Dime 2.268 17.91 1.35 4.62 44.1 .9167 .0833
Quarter 5.670 24.26 1.75 6.29 44.1 .9167 .0833
Half dollar 11.340 30.61 2.15 7.90 44.1 .9167 .0833
Dollar 8.100 26.5 2.00 7.53 123.5 .885 .02 .06 .035
Dollar bill 1.0 .11 .88 1000
Silver 10.49 640
Gold 19.30 43000
Platinum 21.45 37000
The above objects are all to scale. The dimensions of a dollar bill are
155.956 mm * 66.294 mm * .11 mm
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Ball Ball Court Court Ball
diameter Mass length width density
(mm) (g) (m) (m) (g/cm2)
Ping pong 40 2.7 2.74 1.525 .081
Squash 40 24 9.75 6.4 .716
Golf 43 46 1.10
Badminton 54 5.1 13.4 5.18 .062
Racquetball 57 40 12.22 6.10 .413
Billiards 59 163 2.84 1.42 1.52
Tennis 67 58 23.77 8.23 .368
Baseball 74.5 146 .675 Pitcher-batter dist. = 19.4 m
Whiffle 76 45 .196
Football 178 420 91.44 48.76 .142
Rugby 191 435 100 70 .119
Bowling 217 7260 18.29 1.05 1.36
Soccer 220 432 105 68 .078
Basketball 239 624 28 15 .087
Cannonball 220 14000 7.9 For an iron cannonball
The distance from the back of the court to the ball is the
characteristic distance the ball travels before losing half its speed to
air drag.
The following data is a five-year average of results from the NFL Combine, from 2008-2013.
Pounds Reps 40 20 Broad Vertical
Wide receiver 202.3 15.4 4.55 4.25 120 35
Cornerback 193.2 15.5 4.55 4.17 121 35
Running back 213.3 20.5 4.59 4.28 117 34.5
Safety 208.9 18.1 4.62 4.24 114 34.5
Outside linebacker 238.1 22.7 4.74 4.34 117 33.5
Tight end 251.6 21.5 4.77 4.37 116 33.5
Fullback 242.6 24.1 4.80 4.39 120 33.5
Inside linebacker 241.5 22.7 4.80 4.31 115 33
Quarterback 223.1 17.8 4.87 4.34 110 31
Defensive end 266.3 25.6 4.88 4.46 113 32.5
Defensive tackle 304.8 28.3 5.13 4.66 105 29
Offensive center 303.1 27.3 5.30 4.66 100 27
Offensive tackle 314.7 25.3 5.32 4.80 101 27
Offensive guard 314 26.2 5.36 4.85 99 27
Pounds: Weight of the player
Reps: Bench press repetitions at 225 pounds.
40: Time for the 40 yard dash. Reaction time is not counted.
20: 20 yard shuttle. 5 yards to the right, 10 yards to the left, and 5 yards to the right.
Broad: Broad jump in inches
Vertical: Vertical leap in inches
grams/cm2
Air on Mars .00002
Air at Everest .0004 10 km altitude
Air at Denver .001 1 Mile altitude
Air at sea level .00127
Ice .92
Water 1.0
Rock 2.5
Magnesium 1.7
Aluminum 2.7
Titanium 4.5
Iron 7.9
Silver 10.5
Lead 11.3
Gold 19.3
Tungsten 19.3
Osmium 22.6 Densest element
Earth 5.52
Moon 3.35
Mars 3.95
Europa 3.103
Ganymede 1.94
Callisto 1.83
Titan 1.88
Balsa .12
Corkwood .21
Cedar .32
Pine .37
Spruce, red .41
Oak, red .66
Hickory .81
Bamboo .85
Oak, live .98
Ironwood 1.1
Lignum Vitae 1.26
Energies in MJoules = 106 Joules
Raise 1 kg of water by 1 Kelvin = .00419 = 1 Food Calorie = 1000 calories Sprinting person = .004 (80 kg moving at 10 m/s) Phone battery = .018 (5 Watt hours) Laptop battery = .180 (50 Watt hours) 1 kg of supercapacitors = .04 1 kg of Lithium battery = 1.3 1 kg of TNT = 4.2 1 kg of sugar = 20 = 5000 Food Calories 1 kg of protein = 20 = 5000 Food Calories 1 kg of alcohol = 25 = 6000 Food Calories 1 kg of fat = 38 = 10000 Food Calories 1 kg of gasoline = 48 = 13000 Food Calories Uranium fission bomb (Little boy) = 7⋅107 = 16 kilotons of TNT Plutonium fission bomb (Trinity) = 8⋅107 = 20 kilotons of TNT Uranium fission bomb (Fat man) = 9⋅107 = 22 kilotons of TNT Fusion bomb = 4⋅1010 = 10 megatons of TNT 1 kg of antimatter = 9⋅1010 = 20 megatons of TNT Krakatoa volcano, 1883 = 8⋅1011 World energy production in 1 year = 6⋅1014 Dinosaur-extinction asteroid = 5⋅1017 Typical energy of a supernova = 1⋅1038 Intense gamma ray burst = 1⋅1041
Watts
Human cell 10-12
Laptop computer 10
Human brain 20
Incandescent Light bulb 60
Human at rest 100
1 horsepower 746
Strenuous exercise 1000
Maximum human power 1600
World power per person 2500
Tesla S Ludicrous 397000 532 horsepower
Wind turbine 1⋅106
Blue whale 2.5⋅106
Boeing 747 1.4⋅108
Hoover Dam 2.1⋅109
U.S. power consumption 3.4⋅1012
World power consumption 1.5⋅1013
Earth geologic heat 4.4⋅1013
World photosynthesis 7.5⋅1013
Hurricane 1.0⋅1014
Earth solar power 1.7⋅1017 Total solar power falling on the Earth
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A typical bottle of beer has a volume of 12 ounces, is 5% alcohol, and contains
.6 ounces of alcohol. We use this amount as a reference unit and define
.6 ounces of alcohol to be one "Bond".
Volume of the drink = V
Fraction of alcohol = F
Volume of alcohol = Valc = F V
Volume of one beer = Vbeer = 12 ounces
Fraction of alcohol in beer = Fbeer = .05
Volume of alcohol in one beer = VBond = .6 ounces
One ounce = 29.6 mL
One "Bond" of alcohol = .6 ounces
One wine or Scotch bottle = 25.4 ounces = 750 ml
Alcohol Volume Alcohol Alcohol $ $/Bond
fraction (oz) (oz) (Bonds)
Beer (12 oz) .05 12 .6 1 .67 .67 Budweiser
Wine glass .13 4.6 .6 1 8 8.0 Napa Valley
Scotch shot .40 1.5 .6 1 8 8.0 Laphroaig
Beer pitcher .05 64 3.2 5.3 16 3.0 Budweiser
Beer keg .05 1984 99.2 165.3 100 .60 Budweiser
Wine bottle .13 25.4 3.3 5.5 3 .55 Charles Shaw
Vodka bottle .40 25.4 10.1 16.9 15 .89 Smirnoff
Distilled ethanol .95 25.4 24.1 40.2 15 .37 Everclear
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Kelvin Celsius Fahrenheit
Absolute zero 0 -273.2 -459.7
Water freezing point 273.2 0 32
Room temperature 294 21 70
Water boiling point 373.2 100 212
Kelvin Celsius Fahrenheit
Absolute zero 0
Helium boiling point 4.2
Hydrogen boiling point 20.3
Triton 38
Pluto 44
Titania 70
Nitrogen boiling point 77.4
Oxygen boiling point 90.2
Titan 94
Europa 102
Hottest superconductor 135 HgBaCaCuO
Ceres 168
Mars 210
H2O melting point 273.15 0 32
Earth average 288 15 59
Room temperature 293 20 68
H2O boiling point 373.15 100 212
Venus 740
Wood fire 1170
Copper melting point 1358
Iron melting point 1811
Bunsen burner 1830
Tungsten melting point 3683 Highest melting point among metals
Earth's core 5650 Inner-core boundary
Sun's surface 5780
Solar core 13.6 million
Helium-4 fusion 200 million
Carbon-12 fusion 230 million
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Pressure in bars
Air on Mars .0063
Air at Everest .30 10 km altitude
Air at Denver .8 1.6 km altitude
Air at sea level 1.0 15 pounds per square inch
Air on Titan 1.46
Inside a football 1.9 15 + 13 pounds per square inch
10 meters underwater 2.0
Air on Venus 92.1
Seawolf nuclear sub 50 Maximum depth of 490 meters
11 km underwater 1100 Mariana trench, deepest part of the ocean
1 bar = 101300 Pascals
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Energy density
(MegaJoules/kg)
Antimatter 90 billion
Hydrogen bomb 25,000,000 theoretical maximum yield
Hydrogen bomb 21,700,000 highest achieved yield
Uranium 20,000,000 nuclear fuel
Hydrogen 143
Natural gas 53.6
Gasoline 47
Jet fuel 43
Fat 37
Coal 24
Carbohydrates & sugar 17
Protein 16.8
Wood 16
Lithium-air battery 9
TNT 4.6
Gunpowder 3
Lithium battery 1.3
Lithium-ion battery .72
Alkaline battery .59
Compressed air .5 300 atmospheres
Supercapacitor .1
Capacitor .00036
The energy cost to convert water to hydrogen and oxygen is
13.16 MJ/kg. If hydrogen and oxygen are reacted to produce one kg of
water, the energy produced is equivalent to a 1 kg mass moving at
5.13 km/s.
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Frequency
(Hertz)
Whale songs 10
Human ear lower limit 20
Bass lowest note 41
Bass guitar lowest note 41
Cello lowest note 65
Bass singer lowest note 82
Viola lowest note 131
Tenor lowest note 131
Alto lowest note 196
Soprano lowest note 262
Violin A string 440
Human ear upper limit 20000
Speed of light 2.9979e8 m/s
Gravitational constant 6.6738e-11 m3/kg/s2
Planck constant 6.6261e-34 J s
Earth surface gravity 9.8067 m/s
Electric force constant 8.9876e9 N m2 / C2
Magnetic constant 4 Pi e-7 N/A2
Proton mass 1.6726e-27 kg = 938.272 GeV
Neutron mass 1.6749e-27 kg = 939.565 GeV
Electron mass 9.1094e-31 kg
Electron charge 1.6022e-19 C
Atomic mass unit 1.6605e-27 kg
Bohr radius 5.2918e-11 m = hbar2 / (ElectronMass*ElectronCharge2*Ke)
Boltzmann constant 1.3806e-23 J/K
Avogadro number 6.0221e23 particles/mole
Gas constant 8.3145 J/K/mole
Stefan-Boltzmann constant 5.6704e-8 Watts/m2/K4
Wein constant 2.8978e-3 m K
Mole of Carbon-12 .012 kg Exact
Planck length 1.6162e-35 m
Planck mass 2.1765e-8 kg
Planck time 5.3911e-44 s
Planck charge 1.8755e-18 C
Planck temperature 1.4168e32 K
Water heat capacity 4200 J/kg/K
Steam heat capacity 2080 J/kg/K At 100 Celsius
Ice heat capacity 2110 J/kg/K At -10 Celsius
Air heat capacity 1004 J/kg/K
Stefan-Boltzmann 5.67e-8 Watts/meter2/Kelvin4
= (2π5/15) Boltzmann4 / SpeedOfLight2 / PlanckConstant3
Wein 2.898e-3 Kelvin meters
Electron spin 5.2729e-35 Joule seconds = PlanckConstant / (4 Pi)
Pi 3.14159
Euler number 2.71828
System Units Best suited for
SI (MKS) Meters, Kilograms, Seconds Newtonian mechanics, EM forces between currents
Gaussian (CGS) Centimeters, Grams, Seconds EM forces between particles, plasma physics, astrophysics
Particle Meters, Electron Volts, Seconds Particle physics
Planck Planck length, Planck mass, Planck time General relativity, quantum gravity
1 gram = .001 kg
1 cm = .01 meters
1 electron Volt (eV) = 1.602e-19 Joules
= The energy gained by an electron upon descending a potential of 1 Volt
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In this plot, the diameter of each particle proportional to CubeRoot(Mass). This is what the particles would look like if they were uniform-density spheres.
The electron is exaggerated otherwise it would be invisible.
The blue particles represent the heaviest particle that can be produced by each accelerator.
At this scale, a Big Bang particle has a diameter of 10 km.
Photons, Gluons, and Gravitons are massless.
Electron neutrino < 1 eV Muon neutrino < 2 eV Red photon 1.8 eV Green photon 2.3 eV Blue photon 3.1 eV Electron .51 MeV Up quark 1.9 MeV Down quark 4.4 MeV Strange quark 87 MeV Muon 105.7 MeV Neutral pion 135 MeV Charged pion 140 MeV Proton 938.27 MeV Neutron 939.57 MeV Charm quark 1.32 GeV Discovered at SLAC Tau 1.78 GeV Discovered at SLAC Bottom quark 4.24 GeV Discovered at Fermilab SLAC limit 45 GeV Highest-energy particle that SLAC can produce W boson 80 GeV Discovered at the Super Proton Synchrotron Z boson 91 GeV Discovered at the Super Proton Synchrotron Fermilab limti 125 GeV Highest-energy particle that Fermilab can produce Higgs Boson 125 GeV Discovered at the LHC Top quark 173 GeV Discovered at Fermilab LHC limit 1000 GeV Highest-energy particle that the LHC can produce Cosmic rays 10^12 GeV Highest-energy events observed Planck energy 10^19 GeV Quantum gravity. Planck energy = 1.22e28 eV = 1.956e9 Joules 1 electron Volt (eV) = 1.602e-19 Joules ~ kT at 11,000 Kelvin
Quantity MKS units CGS units Conversion factor Mass M kg gram .001 Wire length Z meter cm .01 Radial distance from wire R meter cm .01 Time T second second 1 Force F Newton dyne 100000 Charge Q Coulomb Franklin 3.336e-10 Velocity of a charge V meter/second cm/s .01 Speed of light C 2.999e8 meter/second cm/s 100 Energy E Joule erg e-7 Electric current I Ampere = Coulomb/s Franklin/s 3.336e-10 Electric potential V Volt Statvolt 299.79 Electric field E Volt/meter StatVolt/cm 29979 Magnetic field B Tesla Gauss 10000 Capacitance C Farad cm 1.11e-12 Inductance L Henry s2/cm 9e-11 Electric force constant Ke = 8.988e9 N m2/C2 Ke = 1 dyne cm2 / Franklin2 Magnetic force constant Km = 2e-7 = Ke/C2 Km = 1/C2 Vacuum permittivity ε = 8.854e-12 F/m =1/4/π/Ke Vacuum permeability μ = 4 π e-7 Vs/A/m =2 π Km Proton charge Qpro = 1.602e-19 Coulomb Qpro= 4.803e-10 Franklin Electric field from a charge E = Ke Q / R2 E = Q / R2 Electric force on a charge F = Q E F = Q E Electric force between charges F = Ke Q Q / R2 F = Q Q / R2 Magnetic field of moving charge B = Km V Q / R2 B = (V/C) Q / R2 Magnetic field around a wire B = Km I / R B = (V/C) I / R Magnetic force on a charge F = Q V B F = (V/C) Q B Magnetic force on a wire F = Km B Z F = I B z Magnetic force between charges F = Km V2 Q1 Q2 / R2 F = (V/C)2 Q Q / R2 Magnetic force between wires F = Km I1 I2 Z / R F = I1 I2 Z / R Energy of a capacitor E = .5 C V2 Field energy per volume Z = (8 π Ke)-1 (E2 + B2/C2) Z = .5 (E2 + B2/C2)
Speed of light C Electric field E Electric field, time derivative Et Magnetic field B Magnetic field, time derivative Bt Charge Q Charge density q Current density J MKS CGS Ke=8.988e9 Ke=1 Km=2e-7 Km=2/C ∇˙E = 4 π Ke q ∇˙E = 4 π q ∇˙B = 0 ∇˙B = 0 ∇×E = -Bt ∇×E = -Bt / C ∇×B = 2 π Km J + Et / C2 ∇×B = 4 π J / C + Et / C
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Charges of the same sign repel and charges of opposite sign attract.
Charge 1 Charge 2 Electric Force + + Repel - - Repel + - Attract - + Attract Charge = Q (Coulombs) 1 Proton = 1.602e-19 Coulombs Distance between charges = R Mass of the charges = M Gravity constant = G = 6.67e-11 Newton m2 / kg2 Electric constant = K = 8.99e9 Newton m2 / Coulomb2 Gravity force = F = -G M1 M2 / R2 = M2 g Electric force = F = -K Q1 Q2 / R2 = Q2 E Gravity field from M1 = g = G M1 / R2 Electric field from Q1 = E = K Q1 / R2 Gravity voltage = H g (H = Height, g = Gravitational acceleration) Electric voltage = H E (H = Distance parallel to the electric field) Gravity energy = -G M1 M2 / R Electric energy = -K Q1 Q2 / R
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A charge generates an electric field. The electric field points away from positive charges and toward negative charges.
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A moving charge is an "electric current". In an electric circuit, a battery moves electrons through a wire.
Charge = Q Time = T Electric current = I = Q / T (Coulombs/second)The current from a positive charge moving to the right is equivalent to that from a negative charge moving to the left.
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Moving charges and currents exert forces on each other. Parallel currents attract and antiparallel currents repel.
Charge = Q Velocity of the charges = V Current = I Length of a wire = L Distance between the charges = R Electric force constant = Ke = 8.988e9 N m2/C2 Magnetic force constant = Km = 2e-7 = Ke/C2 Electric force between charges = Fe = Ke Q1 Q2 / R2 Magnetic force between charges = Fm = Km V2 Q1 Q2 / R2 = (V2/C2) Fe Magnetic force between currents = Fm = Km I1 I2 Z / R Magnetic force / Electric force = V2 / C2The magnetic force is always less than the electric force.
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The electric force can be interpreted as an electric field, and the magnetic force can be interpreted as a magnetic field. Both interpretations produce the same force.
Radial distance = R (Distance perpendicular to the velocity of the charge) Magnetic field from charge Q1 = B = Km V Q1 / R2 Magnetic field from current I1 = B = Km I1 / R Magnetic force on charge Q2 = Fm = Q2 V B = Km V2 Q1 Q2 / R2 Magnetic force on current I2 = Fm = I2 Z B = Km I1 I2 Z / R
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The direction of the magnetic force on a positive charge is given by the right hand rule. The force on a negative charge is in the opposite direction (the left hand rule).
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We use the above symbols to depict vectors in the Z direction. The vector on the left points into the plane and the vector on the right points out of the plane.
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The direction of the force is the cross product "×" of V and B. The direction is given by the "right hand rule".
Magnetic field = B Magnetic force on a charge = F = Q V × B Magnetic force on a current = F = 2e-7 I × B
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Voltage = V = I R Charge = Q Energy of a charge at voltage "V" = E = Q V Current = I Power = P = Q V / T = I V Resistance = R Ohm's law: V = I R Power: P = I V = I2 R = V2 / R
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In a superconductor, electrons move without interference.
In a resistor, electrons collide with atoms and lose energy.
Resistance (Ohms)
Copper wire .02 1 meter long and 1 mm in diameter
1 km power line .03
AA battery .1 Internal resistance
Light bulb 200
Human 10000
Typical values for battery energies are:
Energy Energy Time Power
(kJoule) (WattHour) (hour) (Watt)
Smartphone 28.7 8 10 .80
Tablet 57.6 16 10 1.60
Macbook air 129 36 5 7.2
Small external battery 42 11 - -
Large external battery 160 44 - -
All lithium batteries have a voltage of 3.7 Volts. If a lithium battery
delivers 1 Amp of current for 1 hour,
Voltage of a lithium battery = V = 3.7 Volts Energy of a lithium battery = E = 13320 Joules Current = I = 1 Amp Time the battery lasts = T = 3600 seconds Power = P = E / T = V I = 3.7 WattsBattery energy is often quoted in WattHours.
1 WattHour = 1 Watt * 3600 seconds = 3600 Joules
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