Environmental Engineering Reference
In-Depth Information
Table 4.1
Overview of the Most Important Electrical Quantities
Name
Symbol
Unit
Name
Symbol
Unit
ρ
Ω
Electrical energy
W
,
E
W s, J Specific resistance
m
Electrical power
P=V
•
I
W
Electrical field strength
E=-dV/ds
V/m
Voltage
V
V
Inductivity (inductance)
L
H=Vs/A
Current
I
A
Capacity
C
F=As/V
Resistance
R=V/I
Ω
Electrical charge
Q=
Idt
C=As
Conductance
G=1/R
Force in electrical field
F=E
•
Q
N
According to Bohr's atomic model, electrons with rest mass:
m
e
= 9.1093897
•
10
-31
kg
(4.1)
revolve around the atomic nucleus in an orbit with radius
r
n
and angular
frequency
ω
n
. This orbital movement results in a
centrifugal force
:
(4.2)
Electrons, each with the
elementary charge of an electron
(4.3)
are held in obit around the nucleus of an atom (which consists of
Z
positively
charged protons and additional uncharged neutrons) by the attractive
Coulomb force
:
(4.4)
where
(4.5)
and is called the
permittivity
or dielectric constant. The Coulomb and the
centrifugal force are balanced, keeping the electron in its orbit. According to
Planck's theorem, electrons can only remain in orbits where the orbital angular
momentum is an integer multiple of:
(4.6)
which is derived from
Planck's constant
:
(4.7)
The quantization of the orbital angular momentum leads to:
