PHY 132 - Tables & Formulas
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m
Things you should know from PHY 131 and other prerequisites. (If you don’t, learn them now.)
- Definitions of trig functions
- Pythagorean theorem
- Newton's three laws
- Relationship between weight and mass
- Formula for kinetic energy
- Relationship between frequency and period
- Definition of pressure
- Ideal gas law
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Sec. 1: Gravitational Force:
F
Gm1m2
r2
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: Memorize: Definition of potential (and potential difference).
 

B 

E ds
Potential difference: ΔV = VB - VA =
= E s if E constant
_
A
Potential energy of one charge: U = Σ U for every pair which includes that charge
Total U of a group of charges: Σ U for every pair of charges.
Potential at some point: V = Σ V from all charges at other points
_
- 2 -
Charge per unit length: λ = Q/L
Charge per unit area: σ = Q/A
Charge per unit volume: ρ = Q/V
Sec 4: Memorize: Definition of current, definition of capacitance, and Ohm’s law.
_
Between parallel plates in a vacuum:
E
V
d
and
E
Q
0
A
C = εoA/d
Current density: Magnitude: J = I/A
Direction: direction positive charge is moving
If n = number of free charges per unit volume, q = charge of one of them, and vd = their drift velocity,
J = nqvd
Resistivity, ρ: E = ρJ, ρ = RA/l
Conductivity:
σ = 1/ρ
Series
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 + …
Ceq = C1 + C2 + C3 + …
1/Ceq = 1/C1 + 1/C2 + …
________________________________________________________________________________
Sec 5:
Electric Power: P = VI = I2R = V2/R
(Recall, P = W/t = (energy delivered)/t)
EMF (Electromotive "force", in volts): E = (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.
_
- 3 sec. 6:
Unit vector =
(No other formulas are new.)__________________________________________________________
Sec. 7: Know how ’s direction is defined.

Force on a moving charge: F

q (v

B)
Charge circling in a B field: F centripetal = F magnetic


(Fc=mv2/r)

Force on a wire: F I (  B )


 's magnitude = wire's length,  's direction = direction of current

Lorentz force equation: F

qE

q (v

B)
_
Sec. 8:
(If field or angle vary from point to point,
In a toroidal coil of
circumference 2πr:
Sec. 9:
B = μoIN
2πr
Magnetic flux, ΦB : Replace E with B in ΦE equation, sec. 3
.)
_
- 4 Maxwell’s Equations (If field or angle vary from point to point, replace ∑ with
.):
_____________________________________________________________________________
Sec. 10:
Lenz's Law: Direction of induced current is such that coil's own B field opposes the change in flux.
Permittivity: ε = κεo (ε replaces εo in all equations when a
material medium is present.)
Magnetic permeability: μ replaces μo in all equations when a material medium is present.)
______________________________________________________________________________
Sec. 11:
LR circuits:
Time constant: τ = L/R = time to get about 63% (1-1/e) of the way to the final value.
-t/τ
Current decay: I = I0e
RC circuits:
Time constant: τ = RC
-t/τ)
Discharging: q = Q0e
Charging up:
Find current from I = dq/dt, capacitor’s voltage using C = q/v. (When discharging, Qo/C = Vo.)
Energy stored in a capacitor : U = ½ CV2 = Q2/(2C)
Energy per unit volume in an E field: u = ½ ε E2
Energy stored in an inductor: U = ½ LI2
Energy per unit volume in a B field: u = B2/(2μ)
- 5 -
Find current from I = dq/dt, and voltage using C = q/v. (Qmax/C = Vmax.)
LC circuits total energy: U = ½ CV2 + ½ LI2
_
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 =
Power: PAV = (IRMS)2R = VRMSIRMScos
Transformer: V1/V2 = N1/N2
and
(cos
= "power factor")
V1 I1 = V2 I2
_
Sec. 13: From Phy 131: Heat flow when temperature changes: Q = m c ΔT
Heat flow when state changes: Q = m Lf or Q = m Lv
First Law of Thermo.:
Eint = Q + W
W = Work Done on System.
Eint = Increase in Internal Energy
Q = Heat Added
Molar Heat Capacity: Q = nC T
CP
For any Ideal Gas:
E int
nC v T ,
CP - Cv = R,
CP = constant pressure heat capacity,
Cv
CV = constant volume heat capacity
- 6 For a Monatomic Ideal Gas: CV
3
2
R,
CP
5
2
R
Isobaric Process = No Pressure Change
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SEC. 14: Know 2nd law of Thermodynamics in terms of entropy and in term of heat.
Work Done In A Cycle = Area Enclosed On P-V Diagram.
Qin = W + Qout
Efficiency of Carnot Cycle:
Change in Entropy for a Reversible Process:
Efficiency:
- 7 Geometric Formulas:
(r = radius, h = height)
Circumference of a circle or sphere . . . . . . . . . . .
2πr
Area of circle. . . . . . . . . . . . . . . . . . . . . . . . . . . . .
πr
Area of a circular cylinder (excluding ends) . . . .
2πrh
Area of a sphere . . . . . . . . . . . . . . . . . . . . . . . . .
4πr
Volume of a circular cylinder . . . . . . . . . . . . . . .
πr h
Volume of a sphere . . . . . . . . . . . . . . . . . . . . . . .
(4/3)πr
Quadratic Formula:
2
2
2
3
If ax2 + bx + c = 0 then x
b
b2
4ac
2a
Logarithms:
y
def.: if x = b then logb(x) = y
common log: log = log10
natural log: ln = loge where e = 2.71828
Properties (for log of any base):
log (xy) = log x + log y
log (x/y) = log x - log y
log (xa) = a log x
logb (bx) = x
Short Table of Integrals:
n+1
xn dx = x
n+1
+ c if n =/ -1
dx/x = ln x + c
ax
sin(ax)dx = - 1 cos ax + c
a
cos(ax)dx = 1 sin(ax) + c
a
ax
2
e dx = 1 e + c
a
sec (ax)dx = 1 tan(ax) + c
a
2
sin (ax)dx = x - sin(2ax) + c
2
4a
2
sin(ax)cos(ax)dx = sin (ax) + c
2a
2
cos (ax)dx = x + sin(2ax) +c
2
4a
- 8 Partial Derivatives:
Differentiate with respect to one variable, treating the others as constants.
example:
z = x + x2 y3
z = 1 + (2x)y3
x
z = 0 + x2(3y2)
y
Vector Multiplication:
Determinants:
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Material
Dielectric
Dielectric
Constant, k
Strength (V/m)
Vacuum
Air
Bakelite
Fused quartz
Pyrex glass
Polystyrene
Teflon
Neoprene rubber
Nylon
Paper
Strontium titanate
Water
Silicone oil
1.00000
1.00059
4.9
3.78
5.6
2.56
2.1
6.7
3.4
3.7
233
80
2.5
3 x 106
24 x 106
8 x 106
14 x 106
24 x 106
60 x 106
12 x 106
14 x 106
16 x 106
8 x 106
15 x 106
- 9 Molar Heat Capacities of gasses:
Monatomic:
CP
CV
Diatomic:
CP
CV
(J/mol K) (J/mol K)
He
Ar
Ne
Kr
20.8
20.8
20.8
20.8
12.5
12.5
12.7
12.3
Polyatomic:
CP
CV
(J/mol K) (J/mol K)
1.67
1.67
1.64
1.69
H2
N2
O2
CO
Cl2
28.7
29.1
29.2
29.2
34.7
20.4
20.8
20.9
20.9
25.7
(J/mol K) (J/mol K)
1.41
1.40
1.40
1.40
1.35
CO2
SO2
H2O
CH4
Some physical constants:
Elementary charge: e = 1.602 x 10
-19
C
-12
Permittivity of free space: εo = 8.854 x 10 c2/N m2
1
9
= 8.988 x 10 N m2/c2
4 0
-11
Gravitational constant: G = 6.672 x 10 N m2/kg2
8
Speed of light in a vacuum: c = 2.998 x 10 m/s
Electron mass: me = 9.110 x 10-31 kg
Proton mass: mp = 1.673 x 10-27 kg
Permeability of free space: μo = 4π x 10-7 N/A2
Universal Gas Constant: R = 8.314 J/mole K
SI prefixes:
Power:
-24
10
-21
10
-18
10
-15
10
-12
10
-9
10
-6
10
-3
10
-2
10
-1
10
Prefix:
yocto
zepto
atto
femto
pico
nano
micro
milli
centi
deci
Abbreviation:
y
z
a
f
p
n
μ
m
c
d
Power:
1
10
2
10
3
10
6
10
9
10
12
10
15
10
18
10
21
10
24
10
Prefix:
deka
hecto
kilo
mega
giga
tera
peta
exa
zetta
yotta
Abbreviation:
da
h
k
M
G
T
P
E
Z
Y
36.9
40.4
35.4
35.5
28.5
31.4
27.0
27.1
1.30
1.29
1.30
1.31
- 10 Fundamental 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
1kg=.0685 slug, weighs 2.21 lb in standard gravity
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
FREQUENCY
hertz = Hz
1 Hz = 60 rev/min = 1 cycle/sec
IMPULSE &
MOMENTUM
kg m/s = N S
PRESSURE
pascal = N/m2
CHARGE
coulomb = C
Derived Units
1 atmosphere = 1.013 x 105 Pa = 14.7 lb/in2
ELECTRIC FIELD N/C = V/m
POTENTIAL
volt = V
CAPACITANCE
farad = F
RESISTANCE
REACTANCE&
IMPEDANCE
ohm = Ω
ELECTRIC FLUX
N m2/C = V m
MAGNETIC FLUX weber = Wb
MAGNETIC FIELD Wb/m2 = tesla = T
INDUCTANCE
henry = H
1 T = 104 gauss