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