Units of measurement

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Unit Systems for Electro­dynamics

For electrodynamics exist two different unit systems, the SI - System and the CGS System.

The SI-System uses Meter (m), Kilogram (Kilogramme)(kg) and Second (s) as basic units.
It is also named MKS - System (or the MKSA-System).

The CGS System uses Centimeter, Gram, Second as basic units.

The attached physical units for both systems are lengthmass and time.

Further basic units for the SI System are Ampère (A), with the attached physical unit electric current,
the Lichtstärke (light strength) Candela (cd), the Temperature Kelvin (K)
and the Stoffmenge (quantity of material) Mol (mol).


SI-Units

Basic SI - Units

Unit name Unit symbol attached physical unit
Kilogram (Kilogramme) kg mass (m)
Meter m length (l)
Second s time (t)
Ampère  A current
Candela cd candela
Kelvin K temperature
Mol mol mole (quantity of material)

Derived SI-Units

Derived SI-Units are

Unit name description attached physical unit
Coulomb (C) C = A * s Charge
Newton (N) N = kg * m / s2 Force (F)

F stands for "force"

Joule (J) J = N * m Energy
Watt (W) W = J/s Power
Volt (V) V = W/A Voltage (electric potential)

Coulomb Law in SI units

between two point like charges Q1 and Q2 with the space localizations r1 and r2
expressed in SI Units (K is used instead of F):



Note: "point like" means the charge is concentrated at a single point in space

From SI Units derived units


Physical Unit Symbol of the Unit description of the unit
Newton [N] N N = kg * m /s2
force
Joule [J] J = N * m = W * s = W s J = kg * m2 / s2
energy
Watt [W] W = J / s W = kg * m2 / s3
power
Pascal [Pa] Pa = N / m2 Pa = kg * m-1 / s2
kg / (s2 * m)
pressure
Weber [Wb] Wb = V * s = V s Wb = kg * m2 / (s2 * A)
magnetic flux
Tesla [T] T = Wb / m2 T = V * s / m2 = kg / (s2 * A)
magnetic flux density
Leuchtdichte [L] cd / m2 light density
luminance
Lumen [] Lumen, lm = cd * sr The solid angle sr is defined as the quotient (A/r2) by the spherical area A and it's radius r
luminous flux
Lux Lux, lx = lm / m2 illumination

Some physical units expressed in SI Units

Description in SI Units Notation
H = A / m magnetic field strength
M = A / m magne­tization
B = T  inductance
m = A * m2 = A m2 magnetic area moment

CGS - System

Gauß System

Basic units: Centimeter (centimetre) (C), Gram (G), Second (S)

cgs - Basic units


Name of the unit symbol of the unit physical name
gram g mass
centimeter cm length
second s time
...

The Coulomb Law expressed in cgs Units

The Coulomb Law expressed in cgs units:


Note: dimensionslos = without dimensions, dimensions are cm, s, m, g ...

[F] = g * cm / s2 = [Q2] = g * cm3 / s2 => [Q] = g1/2 * cm3/2 / s, the charge is a derived unit

Further examples

Maxwell Equations

Maxwell­gleichungen

Further differences between SI and CGS Units

related to http://www.physik.uni-bielefeld.de/~hempel/diplom/node7.html
(Link does not work anymore - 22.06.08)

and www.ita.uni-heidelberg.de/~wjd/AA-1.html
(contents of the web representation changed - 22.06.08)

with extensions


SI - System Trans­formations cgs - System
[Q] = C
Q: charge
  esu = cm3/2 g1/2 s-1
esu: electro static unit
D = 0E + P   D = E + 4P
B = 0H + M
B: inductance
  B = H + 4M
[E] = V / m
E: electric field strength
  [E] = dyn/esu =
cm-1/2 g1/2 s-1
[M] = A / m 79,577 A / m = 1 Oe
1 Oe = (1000/(4 pi)) A/m
[M] = emu / cm3
[B] = T = V * s / m2
B: inductance
1 T = 104 G [B] = Gauss (Gs)
Gs = cm-1/2 * g1/2 * s-1
[H] = A / m
H: magnetic field strength
  [H] = Oe (Oersted)
Oe = cm-1/2 * g1/2 * s-1
[m] = A * m2 = A m2
m: magnetic area moment
  [m] = emu
... 0 = 4 * 10-7 Tm / A
permeability (of the vacuum)
  ... 0 = 1
    |E| = |H| = |B|
the same units for E, H und B
    E in electro­static units, B in Oe, H in Gauss
all units in
cm-1/2 g1/2 s-1

Electro­static unit

(esu)

After Walter Greiner Bd. III, Klassische Elektrodynamik, Verlag Harry Deutsch, 1991,
it follows for the charge in cgs units: cm3/2 g1/2 s-1 , this quantity is also called electrostatic unit

from cgs units derived units

regarding
www.unics.uni-hannover.de/ntr/russisch/(access not allowed - 22.06.08)
and Kuchling, Taschenbuch der Physik, Fachbuchverlag Leipzig, 1991

Table of Units

Unit Names trans­formation from cgs units to SI Units
[cm]

centimeter
basic unit
10-2 m
[g]

gram

10-3 kg


second
basic unit
s
K = cm-1 Kayser [K]
wave number
 
Gal = cm / s2 acceleration (galileo) 10-2 m / s2
dyn = g * cm / s2 dyne 10-5 N
dyn / cm2 pressure (barye) 10-1 Pa
dyn * cm = g * cm2 / s2 energy 10-7 J
erg / s power 10-7 W
erg / Gs magnetic area moment 10-3 A * m2
P = dyn * s / cm2
(g * cm / s2) * 
s / cm2 =
g / (cm * s)
Poise [P]
dynamic viscosity
1 P = 0.1 Pa * s
(Pa = Pascal)
Gb = Oe * cm =
cm1/2 * g1/2 * s-1
Gilbert [Gb]
magneto­motive force
(10 / 4)A
dyn/esu =
cm-1/2 * g1/2 * s-1
electric field strength  
Oe = Gb / cm =
cm-1/2 * g1/2 * s-1
Oersted [Oe]
magnetic field strength
H in SI Units
(103 / 4) A/m
Mx = Gs * cm2 =
cm3/2 * g1/2 * s-1
Maxwell [Mx]
magnetic flux
10-8 Wb
Wb: Weber
Gs = Mx / cm2

cm-1/2 * g1/2 * s-1
Gauss [Gs]
magnetic flux density
B in SI Units
10-4 T
T: Tesla
ph, Lb
illumination
(phot, lambert)
104 lx (lx = lm / cm2)
[cal]
heat energy (calorie) 4.1868 J
[Bi]
electric current (biot) 10 A
[D]
electric dipole moment (debye) 3.33564 * 10-30 C m
[St]
kinematic viscosity (Stokes) 10-4 m2 s-1
darcy
permeability 0.98692 * 10-12 m2
4 micro-oersteds =
1.256 637 * 10-5 Oe
magnetic dipole moment 0.001 A m2
dyn1/2 * cm electric charge (Franklin) 3.3356 * 10-10 C
langley
heat trans­mission 41.84 kJ m-2
sb
luminance (stilb) 104 lx
unit pole
magnetic flux 1.256 637 * 10-7 Wb

see http://www.unc.edu/~rowlett/units/
a dictionary of units of measurement that works (22.06.08)
parts of the entries are referenced from this site

Some physical units expressed in cgs units


[H] = Oe = Gb / cm =
cm-1/2 * g1/2 * s-1
  magnetic field strength
[M] = emu / cm3   magnetization
[B] = G (Gauss) 1 G = 10-4 T inductance
[m] = emu 1 emu = 0,001 A m2 magnetic dipole moment