Phedotikov / 1 / FreeEnergy_27.01.08 / !Информация / Nikolo Tesla / Modern Physics For Engineers - Nikola Tesla

Avogadro’s number

[molecules/mole]

NA = 6.0221367 ×1023

Bohr magneton

μB =

qh

= 9.27407836×10−24

J/T

2me

Boltzmann’s constant

k = 1.380658×10−23 J/K

or

K = 8.62 ×10−5

eV/K

Earth to Moon distance

» 384 ´106 m

Elementary charge

q = 1.60 ×10−19

C

Electron mass

me

= 9.1093897 ×10−31

kg

m = 0.51100 MeV/c2

e

Neutron mass

mneutron = 1.6749×10−27

kg

m

= 939.57 MeV/c2

neutron

Proton mass

mp

= 1.6726231×10−27

kg

m

p

= 938.27 MeV/c2

Permittivity of free space

ε0

= 8.8541878×10−12

F/m

Planck’s constant

h = 6.6260755´10−34

J-s

= 4.14×10−15 eV-s

Rydberg constant

R = 1.097373×107

m-1

kT @ room temperature

kT = 0.0259 eV

Speed of light

c = 2.998×108

m/s

Speed of sound (air 0°C)

vs

= 331.29 m/s

1 Å (angstrom)

10-8 cm = 10-10 M

1 mm (micron)

10-4 cm

1 nm = 10Å = 10-7 cm

273.15K = 0°C

1 eV = 1.6 × 10-19 J

1 W = 1 J/S = 1 VA

1 V = 1 J/C

1 N/C = 1 V/m

1 J = 1 N· m = 1 C· V

UNITS

Energy:

Joules ×

1

= eV

q

Mass:

c2

2

Kg ×

= eV/c

q

Momentum: kg × m ×

c

= eV

q

s

c

For

x

< 1:

(1± x)n

= 1± nx +

n(n −1)

x2 ±

n(n −1)(n − 2)

x3 +L

2!

3!

When x is much less than 1:

(1± x)n

= 1± nx

WAVELENGTH SPECTRUM

BAND

METERS

ANGSTROMS

Longwave radio

1 - 100 km

1013 - 1015

Standard Broadcast

100 - 1000 m

1012 - 1013

Shortwave radio

10 - 100 m

1011 - 1012

TV, FM

0.1 - 10 m

109 - 1011

Microwave

1 - 100 mm

107 - 109

Infrared light

0.8 - 1000 μm

8000 - 107

Visible light

360 - 690 nm

3600 - 6900

violet

360 nm

3600

blue

430 nm

4300

green

490 nm

4900

yellow

560 nm

5600

orange

600 nm

6000

Red

690 nm

6900

Ultraviolet light

10 - 390 nm

100 - 3900

X-rays

5 - 10,000 pm

0.05 - 100

Gamma rays

100 - 5000 fm

0.001 - 0.05

Cosmic rays

< 100 fm

< 0.001

GREEK ALPHABET

Α

α

alpha

Ι

ι

iota

Ρ

ρ

rho

Β

β

beta

Κ

κ

kappa

Σ

σ

sigma

Χ

χ

chi

Λ

λ

lambda

Τ

τ

tau

δ

delta

Μ μ

mu

Υ

υ

upsilon

Ε

ε

epsilon

Ν

ν

nu

Ω

ω

omega

Φ

φ

phi

Ο

ο

omicron

Ξ

ξ

xi

Γ

γ

gamma

Π π

pi

Ψ ψ

psi

Η

η

eta

Θ

θ

theta

Ζ

ζ

zeta

i2sin x = eix - e−ix

2 sinh x = ex - e− x

2 cos x = eix + e−ix

2 cosh x = ex + e− x

eix = cos x + i sin x

sin ( A ± B ) = sin A cos B ± cos A sin B

cos ( A ± B) = cos A cos B m sin A sin B

æ A + B ö

æ A - B ö

sin A + sin B = 2 sin ç

÷ cos ç

÷

2

2

è

ø

è

ø

æ A + B ö

æ A - B ö

cos A + cos B = 2 cos ç

÷ cosç

÷

2

2

è

ø

è

ø

SPHERE

ELLIPSE

Area A = 4πr 2

Area A = πAB

Volume V =

4

πr 3

Circumference

3

L ≈ 2π

a

2

+ b

2

2

COORDINATE SYSTEMS

Cartesian or Rectangular Coordinates:

r(x, y, z) = xxˆ + yyˆ + zzˆ

xˆ is a unit vector

rˆ

ˆ

, and

ˆ

, è

φ are functions of position—their

A =

x 2

+ y 2

rˆ = xˆ cos φ + yˆ sin φ

r

−1

y

ˆ

φ = tan

φ = −xˆ sin φ + yˆ cos

φ

x

z = z

zˆ = zˆ

Cylindrical to Rectangular:

To obtain: r(x, y, z) = xxˆ + yyˆ + zzˆ

x = r cos φ

ˆ

xˆ = rˆ cos φ − φ cos φ

y = r sin φ

ˆ

φ = rˆ sin φ + yˆ cos φ

z = z

zˆ = zˆ

Rectangular to Spherical:

ˆ

ˆ

To obtain: A(r, θ, φ) = rˆAr + èAθ

+ φAφ

A =

x 2

+ y 2 + z 2

r

rˆ = xˆ sin θ cos φ + yˆ sin θ sin φ + zˆ cos θ

θ =

z cos−1

x 2 + y 2 + z 2

ˆ

è = xˆ cosθ cosφ + yˆ cos θsin φ − zˆ sin θ

−1

y

ˆ

φ = tan

φ = −xˆ sin φ + yˆ cos

φ

x

Spherical to Rectangular:

To obtain: r(x, y, z) = xxˆ + yyˆ + zzˆ

x = r sin θ cos φ

ˆ

ˆ

xˆ = rˆ sin θ cos φ − è cos θ cos φ − φsin φ

y = r sin θsin φ

ˆ

ˆ

yˆ = rˆ sin θsin φ + è cos θ sin φ + φ cos φ

z = r cos θ

ˆ

zˆ = rˆ cos θ − è sin θ