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Phy 122 – Tables and Formulas f' You may refer to this handout during quizzes and exams. Do not add additional information. Sec. 1: q = charge _ Field lines show direction of the force on a positive test charge. Superposition: Force: Vector sum of forces from all charges at other points. E: Vector sum of fields from all charges at other points. Sec. 2: _ (Energy = stored up work.) Potential: V = PE/q PE = electric potential energy, q = charge (Assuming a uniform field. E = electric field, V = potential, d = distance.) Capacitance: C = q/V Charge stored per volt. Parallel-plate capacitor: Series & parallel combinations: See table under section 4.____________________________________ Sec. 3: Electric current: I = q/t Charge per unit time Ohm's Law: V = IR R = Resistance Power: P = ΔPE/t The rate work is done, or the rate energy is delivered 2 2 P = VI = I R = V /R Sec. 4: EMF (Electromotive "force", in volts): (energy form source)/q Loop rule: Σ potential changes around a closed loop = 0 (increase = pos, decrease = neg, where + side is higher V) Point rule: Total current into a point = total current out _ --22Series Parallel Vtot = V1 + V2 + V3 + … Vtot = V1 = V2 = V3 = … Itot = I1 = I2 = I3 = … Itot = I1 + I2 + I3 + … Req = R1 + R2 + R3 +... 1/Req = 1/R1 + 1/R2 + ... Qtot = Q1 = Q2 = Q3 = … Qtot = Q1 + Q2 + Q3 + … 1/Ceq = 1/C1 + 1/C2 + … Ceq = C1 + C2 + C3 + … __________________________________________________________________________________ Sec. 5: Force on a moving charge: _________________________________________________________________________________ Sce. 6: Transformer: V2/V1 = N2/N1 __________________________________________________________________________________ Sec. 7: LR circuits: Time constant: = L/R = time to get about 63% (1-1/e) of the way to the final value. -t/ Current decay: I = I0 e -t/ Current building up: I = (E /R)(1 - e --33RC circuits: Time constant: = RC -t/ Discharging: q = Q0 e -t/ Charging up: q = CE (1 - e (Voltage from C = q/V, current from loop rule & Ohm’s law.) Period & frequency: T = 1/f __________________________________________________________________________________ Sec. 8: General forms: i = Imax cos (ωt) v = Vmax cos (ωt + ) where ω = 2πf, = phase angle Resistor: V = IR (That is, VRMS= IRMSR and vmax= imaxR), v & i in phase. Capacitor: V = IXc, capacitive reactance = Xc = 1/(ωC), ELI ICE Inductor: V = IXL, inductive reactance = XL = ωL Circuit as a whole: V = IZ, impedance = Z = __________________________________________________________________________________ Sec. 9: kx Hooke's law: F Period & frequency: T = 1/f k Frequency of a harmonic oscillator: m where Speed, frequency and wavelength: F = string tension (force), Speed of sound in air: = mass per unit length T= kelvin temperature (Celsius + 273) Superposition Principle: Displacement of medium due to several waves at once is the vector sum of the individual displacements. _ --44sec. 10: Intensity: I = Power /area Standing waves: String: Node at a fixed end Air column: Node at closed end, antinode at free end. Harmonic sequence: f2 = 2f1 , f3 = 3f1 , etc. _ Sec. 11: Index of Refraction: n = c / v c = speed of light in a vacuum, v = speed of light in the material Snell's Law: Law of Reflection: Magnification: ________________________________________________________________________________ Sec. 12: If no reflection or refraction along the paths, Constructive interference if path difference = m = 0,1,2… Destructive interference if path difference = Double-slit: Bright at Dark at d = slit separation Diffraction grating: Bright at Complete darkness at all other θ's d = slit separation, m = 0,1,2, --55- Thin film interference: n higher or lower than what's on either side: destructive: constructive: (t = thickness) n between what's on either side: destructive: constructive: Single slit: Dark at Bright at a = slit width, m = 1,2,3, Angular separation of barely resolved sources ( in radians): _ Sec.13: Energy of a photon: E = hf h = Planck's constant, f = frequency Bohr model of the hydrogen atom: electron's orbit circumference = multiple of its wavelength 2 Energy levels: En = - (13.6 eV) /n ’s in H (Emission) Spectrum: 1 R 1 n F2 1 n02 n = 1, 2, 3, ... R = Rydberg Constant = 1.097 x 107m-1 ________________________________________________________________________________ Sec. 14: Binding energy: Eb (in MeV) = (ZmH + Nmn - matom)(931.5) mH = mass of 11H = 1.007825 u mn = mass of neutron = 1.008665 u Radioactive decay: Number of nuclei present: Decay rate, or “activity” (R = N/ t): or Disintegration energy/ reaction energy: Q = (total m before - total m after)(931.5 MeV/u) _ --66Some physical constants: Elementary charge: e = 1.602 x 10-19 C Coulomb's law constant: k = 8.988 x 109 N·m2/c2 Speed of light in a vacuum: c = 2.998 x 108 m/s Speed of sound in air at 19°C: 343 m/s Electron mass: me = 9.110 x 10-31 kg Proton mass: mp = 1.673 x 10-27 kg Permeability of free space: = 4 x 10 -7 T·m/A Planck’s constant: h = 6.626 x 10-34 J·s _________________________________________________________________________________________________________________ Material Dielectric Constant, Dielectric Strength (V/m) Vacuum 1.00000 Air 1.00059 3 x 106 Bakelite 4.9 24 x 106 Fused quartz 3.78 8 x 106 Pyrex glass 5.6 14 x 106 Polystyrene 2.56 24 x 106 Teflon 2.1 60 x 106 Neoprene rubber 6.7 12 x 106 Nylon 3.4 14 x 106 Paper 3.7 16 x 106 Strontium titanate 233 8 x 106 Water 80 Silicone oil 2.5 15 x 106 _____________________________________________________________________________ Substance: Index of refraction: Solids: Diamond. . . . . . 2.419 Fluorite . . . . . . . 1.434 Fused quartz . . . 1.458 Glass, crown . . . 1.52 Glass, flint . . . . . 1.66 Ice. . . . . . . . . . . 1.309 Polystyrene. . . . 1.49 Sodium chloride 1.544 Zircon . . . . . . . . 1.923 Substance: Index of refraction: Liquids: Benzene. . . . . . . . . . . 1.501 Carbon disulfide . . . . 1.628 Carbon tetrachloride . 1.461 Ethyl alcohol. . . . . . . 1.361 Glycerin. . . . . . . . . . 1.473 Water. . . . . . . . . . . . . 1.333 Gases (0 C, 1 atm): Air. . . . . . . . . . . . . . . 1.000293 Carbon dioxide . . . . . 1.00045 --77Mathematical Background: Circumference of a circle or sphere . . . . . 2 r Area of circle. . . . . . . . . . . . . . . . . . . . . . . r2 Surface area of a sphere: 4 r2 Definition of a logarithm: if x = by then logb x = y common log: log = log10 natural log: ln = loge where e = 2.71828 log (xy) = log x + log y log (x/y) = log x - log y log (xa) = a log x logb (bx) = x _________________________________________________________________________________________________________________________ SI prefixes: Power: 10-24 10-21 10-18 10-15 10-12 10-9 10-6 10-3 10-2 10-1 Prefix: yocto zepto atto femto pico nano micro milli centi deci Abbreviation: y z a f p n Power: 101 102 103 106 109 1012 m c d 1018 1021 1024 Prefix: deka hecto kilo mega giga tera peta exa zetta yotta Abbreviation: da h k M G T P E Z Y -8Fundamental Units: Standard SI Unit and Abbreviation: Conversion Factors LENGTH meter = m 1 m = 3.28 ft, 1 mile = 1609 m = 5280 ft 1 Angstrom = 10-10 m, 1 inch = 2.54 cm 1 hour = 3600 s, 1 day = 86,400 s 1 year = 3.16 x 107 s 1 unified mass unit = 1 u = 1.66 x 10-27 kg TIME second = s MASS kilogram = kg CURRENT ampere = C/s = A TEMPERATURE kelvin = k T (in kelvins) = T (in Celsius) + 273.15 VOLUME m3 1 Liter = 10-3 m3 = 10+3 cm3 SPEED m/s 1 mi/hr = 0.447 m/s = 1.47 ft/sec FORCE newton = N 1 N = 0.225 pound ENERGY & WORK joule = J 1 calorie = 4.186 J 1 J = 0.738 ft lb 1 electronvolt = 1.602 x 10-19 J, 1 BTU =252 cal POWER watt = W 1 horsepower = 746 W = 550 ft·lb/sec ANGLE radian = rad 1 revolution = 360° = 2π rad Derived Units FREQUENCY hertz = Hz CHARGE coulomb = C ELECTRIC FIELD N/C = V/m POTENTIAL volt = V CAPACITANCE farad = F RESISTANCE REACTANCE& IMPEDANCE ohm = Ω MAGNETIC FLUX weber = Wb MAGNETIC FIELD Wb/m2 = tesla = T INDUCTANCE henry = H 1 Hz = 60 rev/min = 1 cycle/sec 1 T = 104 gauss