Download 对流(运流)电流(DK Cheng, p. 198)

D. K. Cheng
Field and Wave Electromagnetics
Chapter 5
Steady Electric Currents
Chapter 5
Steady Electric Currents
§5-1 Introduction
由运动电荷导致的电流可分三类：传导电流、电解电流、对流(运流)电流 (D. K. Cheng, p. 198)
Conduction current: Drift motion of conduction electrons and/or
holes in conductors and semiconductors;
Electrolytic current: Migration of positive and negative ions;
Convection current: Motion of electrons and/or ions (positively
or negatively charged particles) in vacuum or in rarefied gas.
Convection current, the result of hydrodynamic motion involving a mass
transport, are not governed by Ohm’s law.
(D. K. Cheng, p. 199)
When an external electric field is applied on a conductor, an organized motion
of the conduction electrons will result, producing an electric current. The
average drift velocity of the electrons is very low (1/1000 m/s) even for very
good conductors because they collide with the atoms, dissipating part of their
kinetic energy as heat.
(D. K. Cheng, p. 199)
§5-2 Current density and Ohm’s law
We’d like to point out…
The explicit expression for the electron mobility in a metallic conductor
The physical meanings of the mobility μ:
The electron mobility μ depends on q/m and τ(relaxation time).
If the electrons are scattered (collided) very frequently by ions,
the τ (relaxation time) is small. The large relaxation time will
lead to large mobility μ.
We have presented the explicit expression for the electron mobility in a
metallic conductor. Now we discuss the relevant concepts in more details:
Count Alessandro Giuseppe
Antonio Anastasio Volta,
1745--1827, Italy
André-Marie Ampère,
1775--1836, France
Georg Simon Ohm,
1789—1854, German
The relation between microscopic and macroscopic Ohm’s laws
Fig. 5-3 Homogeneous conductor
with a constant cross section
(J=σE)
Note: J=σE is the microscopic form of Ohm’s law, and I=U/R
is the macroscopic form of Ohm’s law. They can be related by
Eq. (5-27).
§5-3 Electromotive force and Kirchhoff’s voltage law
Eq. (5-32) tells us that a steady current cannot be maintained in the same
direction in a closed circuit by an electrostatic field. (D. K. Cheng, p. 206)
steady: 稳态的；
static: 静态的
区别：稳态，可以有运动，但运动恒速（x的一阶时间
导数不为零，二阶导数为零）；
静态，没有运动（x的一阶导数也为零）。
例如：一个稳恒的电流可以产生一个静态的磁场
A steady current can lead to a static magnetic
field (magnetostatic field).
Fig. 5-4 Electric fields inside an electric battery
Ei is the impressed electric field
(non-conservative electric field) caused by chemical
action.
Note: The line integral of the impressed field Ei from
the negative to the positive electrode (from electrode
2 to electrode 1 in figure) inside the battery is
“electromotive force” (电动势)。(D. K. Cheng, p. 206)
(voltage rise)
Note:
E is the conservative electrostatic field, and Ei is the impressed electric
field (non-conservative electric field)
§5-4 Equation of continuity and Kirchhoff’s current law
The current leaving the region is the total outward flux of the current density
vector through the surface S (D. K. Cheng, p. 208)
The charge conservation law can also be
given as follows
Thus, ρcan be considered zero in the
interior of a conductor.
(D. K. Cheng, p. 210)
由于静电平衡（导体是
一个等势体），金属内
部不可能有多余的自由
电荷。一旦有多余电荷，
就立即跑到金属表面，
尤其积聚到曲率大的地
方（如尖端处）。
§5-5 Power dissipation and Joule’s law
The power provided by an electric field E in moving a charge q is
This is the (electric) power density (power per unit volume).
§5-6 Boundary conditions for current density
In the absence of non-conservative energy source, we shall have
We can obtain the boundary conditions for J
(as in Fig. 3-23 and in Sec. 3-9):
Eq. (5-59) states that the ratio of the tangential components
of J at two sides of an interface is equal to the ratio of the electric
conductivities.
(D. K. Cheng, p. 212)
§5-7 Resistance calculations
The basic formula for capacitance can be written as
Fig. 5-7 Two conductors in a lossy
dielectric medium
Since the metallic conductors are equipotential media, you can choose anyone of
the integral paths for calculating the
electric potential difference.
Note: The dimension of RC and ε/σ is [time].