时谐电磁场：经典教材英文版

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"TIME-HARMONIC ELECTROMAGNETIC FIELDS" 是一本关于时谐电磁场的经典教材，由Roger F. Harrington撰写。该书涵盖了电磁波理论的基础概念、波动介绍、若干定理与概念、平面波函数、柱面波函数、球面波函数、扰动与变分技术以及微波网络等内容。附录部分包括向量分析、复介电常数、傅里叶级数和积分、贝塞尔函数以及勒让德函数。书目和索引的提供进一步增强了参考价值。在时谐电磁场这一领域，我们讨论的是电磁场随时间按照正弦或余弦规律变化的情况，这在许多实际应用中至关重要，例如无线通信、雷达系统、光学设备和微波技术等。Harrington的教材深入浅出地讲解了这一主题，是学习和研究电磁场理论的重要参考资料。书中"Fundamental Concepts"章节可能涉及电磁场的基本定律，如库仑定律、法拉第电磁感应定律和安培环路定理。"Introduction to Waves"则会涵盖电磁波的性质，如波速、频率、波长以及不同类型的电磁波（如横波和纵波）。 "Plane Wave Functions"、"Cylindrical Wave Functions" 和 "Spherical Wave Functions" 这三章详细讨论了各种几何形状下的波函数，这是理解电磁场在空间传播的关键。平面波通常用于描述无约束的电磁场传播；柱面波适用于描述沿着圆柱轴线传播的波；而球面波则在描述点源产生的辐射时特别有用。 "Perturbational and Variational Techniques"章节可能涉及到解决复杂电磁问题的方法，如利用摄动理论处理小扰动问题，以及使用变分方法求解近似解。这些技术在工程计算中非常实用。 "Microwave Networks"一章则专注于微波频段的电路和系统，包括传输线理论、滤波器设计和微波器件分析，这些都是微波工程中的核心内容。附录部分提供了相关数学工具，如向量分析用于理解和描述电磁场的方向和强度，复介电常数在处理介质性质时必不可少，傅里叶级数和积分在频域分析中常用，而贝塞尔函数和勒让德函数则是解决特定电磁问题的特殊函数。这本书是电磁学领域的宝贵资源，不仅适合学生学习，也对从事相关科研和工程工作的专业人士具有极高的参考价值。通过深入阅读和理解，读者可以掌握时谐电磁场的理论基础，以及解决实际问题的分析技巧。

FUNDAMENTAL

CONCEPTS

(1-10)

can

neither

created

nor

destroyed, merely

transported.

Lines

cur-

rent

must

begin

and

end

points

of increasing or decreasing

charge

density.

1-3.

Constitutive

Relationships.

addition

the

equations

Sec.

1-2 we

need

equations

specifying

the

characteristics of

the

medium

in which

the

field exists. We shall consider

the

domain

of g

and

:JC

the

electromagnetic field

and

express n,

<8,

and

S in

terms

Sand

:IC.

Equations

the

general

form

n = 9)(8,3C)

= <8(8,X)

= S(8,3C)

are

called constitutive relationships. Explicit forms for

these

can

found

experimentation

deduced

from

atomic

considerations.

The

term

free space will be

used

denote

vacuum

any

other

medium

having

essentially

the

same

characteristics as

vacuum

(such as

air).

The

constitutive

relationships

assume

the

particularly

simple forms

9) =

E08

}

(IS =

po:JC

~=o

in free space

(1-11)

where

the

capacitivity or permittivity of vacuum,

and

Po is

the

indue-

tivity or permeability of

vacuum.

is a

mathematical

consequence

the

field

equations

that

(EOPO)-J-i is

the

velocity of

propagation

electromagnetic

disturbance

in free space. Light is

electromagnetic

nature,

and

this

velocity is called

the

velocity of light c.

Measurements

have

established

that

c =

= 2.99790 X 10

3 X 10

meters

per

second (1-12)

EO!J.O

The

choice of

either

or Po

determines

system

electromagnetic

units

according

our

equations.

international

agreement,

the

value

P.O

has

been chosen as

P.o

41r

10-

henry

per

meter

(1-13)

(1-14)

for

the

mksc

system

units.

then

follows from

Eq.

(1-12)

that

Eo = 8.854 X

10-

3&n-

10-

farad

per

meter

for

the

mksc

system

units.

Under

certain

conditions,

the

constitutive

relationships

become

simple

proportionalities

for

many

materials. We

say

that

such

matter

linear

TIME-HARMONIC

ELECTROMAGN~TIC

FIELDS

the

simple sense,

and

call

simple matter for

short.

Thus

n = E8 }

(B =

/ol:JC

0"8

in simple

matter

(1-15;

where, as in

the

free-space case, E is called

the

capacitivity

the

medium

and

p. is called

the

inductivity

the

medium.

The

parameter

0" is called

the

conductivity of

the

medium. We originally

made

the

qualifying

state-

ment

that

Eqs. (1-15) hold

"under

certain

conditions."

They

may

not

hold

8 or X are

very

large, or

time

derivatives of B or

are

very

large.

Matter

is often classified according

its

values of

0",

and

Mate-

rials

having

large values of 0" are called conductors

and

those

having

small

values

of 0" are called insulators or dielectrics.

For

analyses,

is often

convenient

approximate good conductors

perfect conductors, charac-

terized

a =

ex>

and

approximate

good dielectrics

perfect dielec-

trics, characterized by 0" =

The

capacitivity

E of

any

material

never

less

than

that

vacuum

Eo.

The

ratio

EO is called

the

dielectric

constant

or relative capacitivity.

The

dielectric

constant

of a good con-

ductor

hard

to measure

but

appears

to be

unity.

For

most

linear

matter,

the

inductivity

p. is

approximately

that

of free space p.o.

There

is a class of materials, called diamagnetic, for which p. is slightly less

than

P.O

(of

the

order of 0.01

per

cent).

There

is a class of materials, called

paramagnetic, for which p, is slightly

greater

than

P.O

(again of

the

order of

0.01

per

cent). A

third

class of materials, called ferromagnetic,

has

values

much

larger

than

/olo,

but

these

materials are

often

nonlinear.

For

our

purposes, we shall call all

materials

except

the

ferromagnetic ones

nonmagnetic

and

take

p. =

/olo

for

them.

The

ratio

P.r =

p.1

P.O

is called

the

relative inductivity or relative permeability

and

is, of course, essentially

unity

for nonmagnetic

matter.

Quite often the restriction on

the

time

rate

of change of

the

field,

made

the

validity of Eqs. (1-15),

can

be overcome

extending

the

definition of linearity. We

say

that

matter

is linear in

the

general sense,

and

call

linear matter, when

the

constitutive

relationships

are

the

following linear differential

equations:

in linear

matter

(1-16)

Even

more complicated formulas for

the

constitutive

relationships

may

FUNDAMENTAL

CONCEPTS

(1-17)

be necessary in some cases,

but

Eqs. (1-16)

are

the

most

general

that

shall consider.

Note

that

Eqs.

(1-16) reduce to Eqs. (1-15) when

the

time

derivatives

of 8

and

become sufficiently small.

The

physical

significance of

the

extended

definition of

linearity

foilows.

The

atomic

particles of

matter

have

mass as well as

charge,

so when

the

field changes

rapidly

the

particles

cannot

"follow"

the

field.

For

example, suppose

electron

has

been accelerated

the

field,

and

then

the

direction

of 8 changes.

There

will be a

time

lag before

the

electron

can

change

direction, because of

its

momentum.

Such

picture

holds for

the

electron

is a free electron.

holds for

the

electron

is a

bound

electron. A similar

picture

holds for dl

except

that

the

mag-

netic

moment

the

electron is

the

contributing

quantity.

shall

not

attempt

give significance

each

term

Eqs.

(1-16).

will be

shown

in Sec. 1-9

that

all

terms

of Eqs. (1-16)

contribute

"admittivity"

and

"impedivity"

of a

material

the

time-harmonic case.

1-4.

The

Generalized

Current

Concept.

was Maxwell

who

first

noted

that

Ampere's

law

for statics, V X

:JC

was incomplete

for

time-varying

fields. He

amended

the

law

include

electric displace-

ment

current

a~/

at in

addition

the

conduction

current.

visualized

this

displacement

current

in free space as a motion of

bound

charge

"ether,"

ideal weightless fluid

permeating

all space. We

have

since

discarded

the

concept

ether,

for

has

proved

undetectable

and

even

somewhat

illogical in view of

the

theory

relativity.

dielectrics,

part

the

term

a~/at

is a motion of

the

bound

particles

and

thus

current

the

true

sense of

the

word. However,

con-

venient

consider

the

entire

a~/at

term

as a

current.

view of

the

symmetry

of Maxwell's equations,

also is convenient

consider

the

term

adl/at

as a magnetic displacement current.

Finally,

represent

sources, we

amend

the

field

equations

include impressed currents, elec-

tric

and

magnetic.

These

are

the

currents

we view as

the

cause of

the

field. We

shall

see in

the

section

that

the

impressed

currents

repre-

sent

energy

sources.

The

symbols

and

91l will be used

denote electric

and

magnetic

currents

in general,

with

superscripts indicating

the

type

current.

discussed above, we define

total

currents

mt'

= as + 91l'

where

the

superscripts

t, c,

and

denote

total,

conduction,

and

impressed

currents.

The

symbols i

and

k will be used

denote

net

electric

and

magnetic

currents,

and

the

same

superscripts will indicate

the

type.

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