电磁场与电磁波课件(英文版)
电磁场与电磁波第4讲梯度散度散度定理yPPT课件
P
6
3) 在广义坐标系中V的梯度为：
dV ( V)dl
dV
V l1
dl1
V l2
dl2
V l3
dl3
dl aˆu1dl1 aˆu2dl2 aˆu3dl3 aˆu1 (h1du1)aˆu2 (h2du2)aˆu3 (h3du3)
dV
V (
l1
aˆu1
V
l2
aˆu2
V
l3
aˆu3
)(aˆu1dl1
5
即：
dV GradV dn an
于是
沿着 dl 的方向导数为：
dV dV dn dV cos
dl dn dl dn
V n
aˆn aˆl
V
aˆl
该式表示V沿着al方向的空间增长 率等于V的梯度在该方向上的投影 （分量），也可写成：
dV ( V)dl
V
dV dn
an
l
nˆ
dn cos dl
直角坐标系
divAA=Ax Ay Az x y z
15
柱坐标系
divA
A=1 r
(rrAr
)
A
(rAz z
)
1 (rAr) 1 A Az
r r r z
球坐标系
divAA=R2s1in(ARR R 2sin)(A Rsin)(RA) =R 12(R 2 RAR)Rs1in(Asin)Rs1inA
aˆu2dl2
aˆu3dl3)
(V l1
aˆu1
V l2
aˆu2
V l3
aˆu3
)dl
V
V l1
aˆu1
V l2
aˆu2
电磁场与电磁波英文教学课件-Ch4 Steady Electric Currents
Electric current, Electromotive force Principle of current continuity, Energy dissipation.
1. Current & Current Density 2. Electromotive Force 3. Principle of Current Continuity 4. Boundary Conditions for Steady Electric Currents 5. Energy Dissipation in Steady Electric Current Fields 6. Electrostatic Simulation
when the impressed electric field is equal but opposite to the electric field produced by the charges on the plates, and the charges will be at rest.
If the conducting medium is connected, the positive charges on the positive electric plate will be moved to the negative electric plate through the conducting medium, while the negative charges on the negative electric plate to the positive electric plate. In this way, the charges on the plates will be decreased, and E < E' . The charges in the source will be moved againthe conductivity, and its unit is S/m. A large
华工电磁场与电磁波全英课Lecture 12
Field and Wave ElectromagneticsField and Wave ElectromagneticsLecture 12李融林R.L. Li4.5Magnetic Fields in Materials and MagneticCircuitsBehavior of Magnetic MaterialsNonmagnetic if(Vacuum)Diamagnetic,if(Silver,Lead,Copper,Water)Paramagnetic, if(Air, Aluminum)Ferromagnetic, if(Cobalt, Nickel, Iron, Silicon iron, Mumetal)The orbiting electrons cause circulating currents and form microscopic magnetic dipoles.In the absence of an external magnetic field the magnetic dipoles of the atoms of most materials have random orientations,resulting in no net magnetic moment.The application of an external magnetic field causes both an alignment of the magnetic moments of the spinning electrons and an induced magnetic moment due to a change in the orbital motion of electrons.4.5.1 Magnetization and Equivalent Current DensitiesWe define a magnetization vector,M ,aswhich is the volume density of magnetic dipole moment. The magnetic dipole moment d m = M dv’will produce a vector magnetic potential(Note thatfor a magnetic dipole of moment .)Usingwe can rewrite d A aswhere V’is the volume of the magnetized material. We now use the vector identityto rewriteThe following vector identity enables us to change the volume integral of the curl of a vector into a surface integral:where F is any vector with continuous first derivatives.Proof: Applying divergence theorem to (F x C), where C is a constant vector, we haveSinceandwe haveWe havewhere is the unit outward normal vector from ds’and S’is the surface bounding the volume V’.The effect of the magnetization vector isequivalent to both a volume current densityand a surface current densityThe problem of finding the magnetic flux density B caused by a given volume density of magnetic dipole moment M is then reduced to finding the equivalent magnetization current densities J m and J ms .Figure 4.5.1The cross-sectionof a magneticmaterial.Example4.5.1Determine the magnetic flux density on the axis of a uniformly magnetized circular cylinder of a magnetic material.The cylinder has a radius b, length L,and axial magnetization .Figure4.5.2A uniform magnetized circular cylinder.SolutionSince Mis a constant,The equivalent magnetization surface current density on the side wallisThe magnet is then like a cylindrical sheet with a surface current density of M(A/m).To find B at P(0,0,z),we consider a differential length dz’with a current andobtain4.5.2 Equivalent Magnetization Charge DensitiesIn a current-free region we may define a scalar magnetic potential V m , from which the magnetic flux density B can be found as . In terms of magnetization vector Mwe may write the scalar magnetic potentialIntegrating this equation over a magnetized body carrying no current, we have We know the gradient of 1/Rwith respect to the primed coordinates isHence(Note thatfor a magnetic dipole of moment.)Recalling the vector identityWe obtainwhere is the outward normal to the surface element ds’.We can conclude that, for field calculation,a magnetized body may be replaced by an equivalentmagnetization surface charge densityρms and an equivalent magnetizationvolume charge densityρmsuch that4.5.3 Boundary Conditions for Magnetostatic FieldsBoundary Condition for BApplying to a small pillbox: the normal component of B is continuous across an interface;For linear media, B 1= µ1H 1 and B 2= µ2H 2Boundary Condition for HSimilarly, applying to a small rectangular closed path, we have orWhere is the outward unit normal from medium 2at the interface .Thus the tangential component of the H field is discontinuous across an interface where a free surface current exists.When the conductivities of both media are finite,current are defined by volume current densities and free surface currents do not exist on the interface.Hence J s =0,and the tangential component of H is continuous across the boundary of almost all physical media;it is discontinuous only when an interface with an ideal perfect conductor or a superconductor is assumed.Figure 4.5.3Boundary condition for H .Example 4.5.2Two magnetic media with permeabilities µ1and µ2have a common boundary,as shown in Figure 4.5.4.Determine the magnitude and the direction of the magnetic field intensity at point P 2in medium 2.SolutionFigure 4.5.4Boundary conditions for Hand B.The desired unknown quantities are H 2andα2.Continuity of the normal component of BfieldrequiresThe tangential component of H field is continuous.WehaveDivision of the second equation by the first equation giveswhich describes the refraction property of the magnetic field.If medium 1is nonmagnetic and medium 2is ferromagnetic,then µ2>>µ1and,α2will be nearly 90degrees.If medium 1is ferromagnetic medium and medium 2is air,then α2will be nearly zero.We obtainThe magnitude of H 2isExample4.5.3Find the image currents of a long straight line current I above an interface between two magnetic media with permeabilitiesµ1andµ2SolutionFigure4.5.5A long straight line current I above an interface between two magnetic media(a);Image current for medium1(b)and image current for medium2(c).Since there is no surface current at the interface which leads toUsing yieldsororSolving the equations givesForForFigure4.5.6Magnetic field lines of a long straight line current in two media.Example 4.5.4Sketch the magnetic flux lines both inside and outside a cylindrical bar magnet having a uniform axial magnetization.Figure 4.5.2A uniform magnetizedcircular cylinder.SolutionWe know that the problem of a cylindrical barmagnet could be replaced by that of amagnetization current sheet having a surfacecurrent density J ms =M 0(J m =0).It is obvious from above equations that the magnetic flux density along the axis at the end faces of the magnet is less than that at the center.Fromwe getOn the side of the magnet there is a surface current given byHence according tothe axial component of B changes by anamount equal to µ0M 0.It must be remarked that while H =B/µ0outside the magnet,H and B inside themagnet are far from being proportionalvectors in the same direction.From H =B /µ0–M ,and the fact that B/µ0along theaxis inside is less than M 0,we observe thatH and B are in opposite directions alongthe axis inside.For a long,thin magnet,L>>b,B p0~µ0M 0.From H =B/µ0–M,weobtain H p0~0.Figure 4.5.7Magnetic flux linesaround a cylindrical bar magnet.4.5.4 Magnetic CircuitsThe curl equation for magnetic fields in materials iswhere J(A/m2) is the volume density of free current.The corresponding integral form is obtained asorwhich is the Ampere’s circuital law in materials,where C is the contour bounding the surface S and I is the total free current passing through S. Ampere’s circuital law states that the circulation of the magnetic field intensity around any closed path is equal to the free current flowing through the surface bounded by the path.Ampere’s circuital law is useful on determining the magnetic field in magnetic circuits.The quantity V mmf (=NI )is called a magnetomotive force (mmf).We define reluctance R as the ratio of the magnetic voltage to the flux ;thusAmpere’s Law for an N-turn magnetic circuit becomesSimilar to Kirchhoff’s voltage law,we may write,for any closed path in a magneticcircuit,Around a closed path in a magnetic circuit the algebraic sum of ampere-turns is equal to the algebraic sum of the products of the reluctances andfluxes.Kirchhoff’s current law for a junction is consequence of. Similarly leads to. Thus we havewhich states that the algebraic sum of all the magnetic fluxes flowing out of a junction in a magnetic circuit is zero.Example 4.5.5N turns of wire are wound around a toroidal core of aferromagnetic material with permeabilityµ.Determine Bf ,in the ferromagneticcore;Hf in the core;and Hgin the airgap.Figure4.5.8Coil on ferromagnetictoroid with air gap.Applying Ampere’s circuital lawSolutionIf flux leakage is neglected,the same totalflux will flow in both the ferromagnetic coreand in the air gap.If the fringing effect ofthe flux in the air gap is also neglected,themagnetic flux density B in both the core andthe air gap will also be the same.However,because of the different permeabilities,themagnetic field intensities in both parts willbe different.Wehavewhere the f and g denote ferromagnetic and gap, respectively.In the ferromagnetic core,and, in the air gap,Ampere’s law yieldsWe haveSimilarlyIf the radius of the cross section of the core is much smaller than the mean radius of the toroid,the magnetic flux density B in the core is approximately constant,and the magnetic flux in the circuitiswhere S is the cross-sectional area of the core.where R f and R g are the reluctances of the ferromagnetic core and the air gap, respectively .Figure 4.5.9Equivalent magneticcircuit and analogous electric circuitfor toroidal coil with air gap.Therefore,or,mfmfThe reluctances are:The two loop equations areSolving these simultaneous equations, we haveExample 4.5.6Find the flux linked with coil N 1in a magnetic circuit shown in Figure 4.5.10.Figure 4.5.10A magnetic circuit.Solution.HomeworkProblems P.6-26 and P.6-27References &Acknowledgements1.M.J.Rhee’s Lectures on Electromagnetic Theory,2005.2.W.H.Hayt,J.A.Buck,Engineering Electromagnetics,7th Ed.,McGraw-Hill,2006.3.U.S.Inan,A.S.Inan,Engineering Electromagnetics,AddisonWesley Longman,2000.4. D.Cheng,Field and Wave Electromagnetics,Second Edition,Addison Wesley,1992.。
电磁场与电磁波：4 Steady Electric Current_zmh(英文)
dUe e E Ue Relaxation-time Approximation
dt
m
:第一项为驱动项，第二项为耗散项。
Under steady conditions, we have:
eE Ue 0
m
e
Ue m E
Mobility:
e
e
m
4.2.2 Conduction Current Density
1
4.1 Introduction
Electrostatics: dv/dt=0 I=0
Steady Electric Current（自 由电荷产生的电流）: dv/dt=0 I≠0
2
4.2 Nature of Current and Current Density
4.2.1 Conduction (传导）Current 4.2.2 Conduction Current Density 4.2.3 Convection （运流）Current 4.2.4 Convection Current Density
V 0
( Ne)
0
8
9
10
4.3 Resistance of a Conductor
R U l E dl I sJ ds
(1) Parallel-plate resistor R l
S
(2) A spherical resistor R b a
4ab
(3) Concentric cylindrical conductors resistor
G-R (Depletion Region) D-R
(Quasi-neutral region)
Jn 0, J p 0, but (Jn J p ) 0
电磁场与电磁波英文教学课件-Ch
A loop coil with N turns the magnetic flux linkage with the current
is = N , and the inductance of the loop coil with N turns is
z
L N
II
l1
I1
l2
I2 Suppose we have two loop currents,
S
(
E)
B t
dS
0
Since the equation holds for any area S, the integrand must be
zero, so that
E B t
E B t
which is called the differential form of law of electromagnetic induction, and it means that the negative time rate of change of the magnetic flux density at a point is equal to the curl of the timevariable electric field intensity at that point.
flux linkage with the current I, and it is denoted as . The ratio of
to I is denoted by L, hence L
I
It is called the inductance of the circuit, with the unit henry (H), and the inductance can be also considered as the magnetic flux linkage per unit current.
电磁场与电磁波课件第2章1教学提纲
方S法D 。d在S已 知q电提荷供或了电一荷个分计布算的电情场况的下简，便
求E。
适用于场形规则、场强均匀的情况
D d S D co d S s
选取一高斯面S
S
S
使dS与D垂直或平行
或直接使用
S
EdS q
求解
E q
S
D q S
DSq
0
S
D
dS
如
果
D 为
常
数
D
dS
S
例题
例1：计算均匀电荷密度为σ的无限大平面 的电场强度E
B两点，则场强E沿此曲线的线积分为
lE •dl4q0(R1AR1B)
当积分路径是闭合回路时，有
E•dl 0
l
静电场的一个重要性质——保守性
静电场环流定理的积分形式
E•dl 0
l
说明在静电场中场强沿任意闭合路径的线 积分为零，即单位正电荷沿静电场中的任 一个闭合路径移动一周，电场力不做功。
静电场是一个保守场
lBdl 0 I
SBdS 0
左式称为安培环路定律，式中 0 为真空磁导率，04π107 (H/m)，
I 为闭合曲线包围的电流。
安培环路定律表明，真空中恒定磁场的磁感应强度沿任一闭合曲 线的环量等于曲线包围的电流与真空磁导率的乘积。
右式表明，真空中恒定磁场通过任一闭合面的磁通为零。
由此可见，磁场线是处处闭合的，没有起点与终点，这种特性称 为磁通连续性原理。
此，一切介质的介电常数均大于真空的介电常数。
实际中经常使用介电常数的相对值，这种相对值称为相对介电常
数，以 r 表示，其定义为
r
0
1 e
可见，任何介质的相对介电常数总是大于1。下表给出了几种介质的 相对介电常数的近似值。
电磁场与电磁波课件
V
S (r ) R
dS C dl C
S
Line charge：
l ( r ) R C
C
Point charge： (r )
电磁场与电磁波
第3章 静态电磁场及其边值问题的解
dl
8
3. Potential Difference Multiplying to the both side of
1 2
介质1 介质2
E2
1
1
2
2
BC on the face of conductor In the case of balance of static E field, the field inside conductor is zero, the BC on surface will be:
Criteria of reference
两点间电位差有定值
Expression meaningful
Expression simplicity, the reference is always at infinite if charge on finite space One reference point for one problem
0
2
电磁场与电磁波
第3章 静态电磁场及其边值问题的解
11
6. Static Potential’s BC P1 and P2 are two point near the interface of two dielectric, one on each side, the potential are 1 and 2 respectively. If the distance between the two point is ⊿l→0
华工电磁场与电磁波全英课Lecture 13
conductor. The second term comes from the linkage of the flux that exists
between the inner and the outer conductors; this term is known as the external
Therefore the inductance per unit length is
1
Example 4.6.3 An air coaxial transmission line has a solid inner conductor of radius a and a very thin outer conductor of inner radius b. Determine the inductance per unit length of the line.
where the proportionality constant L12 is called the mutual inductance between loops C1 and C2, with unit (H). In case C2 has N2 turns, the flux linkage Λ12 due to Φ12 is Λ12 = N2 Φ12 and
Before we present some examples showing how to determine the mutual inductance between two circuits, we pose the following about Figure 4.6.1 and
.
Is the flux linkage with loop C2 caused by a unit current in loop C1 equal to the flux linkage with C1 caused by a unit current in C2? That is, is it true that
华工电磁场与电磁波全英课Lecture 14
Noting that, for linear media, we obtain .
A single current-carrying loop can be considered as consisting of a large number, N, of contiguous filamentary current elements of closed paths Ck, each with a current ∆Ik flowing in an infinitesimal cross-sectional area ∆ak’ and linking with magnetic flux Φk.
At the same time a work W22 must be done in loop C2 in order to counteract the induced emf and increase i2 to I2
The total amount of work done in raising the currents in loops C1 and C2 from 0 to I1 and I2, respectively, is then the sum of W1, W21, and W22:
where Sk is the surface bounded by Ck. Substituting this Equatin in
电磁波英文原版ch02
F(ζ) ζ F(ζ) E+ = = F(z ct)= z ζ ζ z z F(ζ) ζ F(ζ) E+ = = c F(z ct)= t t t ζ ζ
E+ 1 E+ = z c t
2 E 1 1 2 E (ηH × )= 2 z = c t2 z2 c t z
1 2 2 2 z2 c t2 E(z, t)= 0
Vectorially, F must have only x, y components, F = xFx + yFy , that is, it must be transverse to the propagation direction, F = 0. z Similarly, we nd from the second of Eqs. (2.1.10) that E (z, t) must depend on z, t through the combination z + ct, so that E (z, t)= G(z + ct), where G(ξ) is an arbitrary (transverse) function of ξ = z + ct. In conclusion, the most general solutions for the forward and backward elds of Eqs. (2.1.10) are: E+ (z, t) = F(z ct) E (z, t) = G(z + ct)
E t
Ez =0 z Hz =0 z
(2.1.1)
An immediate consequence of uniformity is that E and H do not have components along the z-direction, that is, Ez = Hz = 0. Taking the dot-product of Amp`re’s law e with the unit vector , and using the identity ( × A)= 0, we have: z z z × z z
电磁场与电磁波英文教学课件-Contents
in Rectangular Coordinates 4. Method of Separation of Variables
in Cylindrical Coordinates 5. Method of Separation of Variables
in Spherical Coordinates
Preface Chapter 1 Vector Analysis
1. Directional Derivative and Gradient of Scalar Fields 2. Flux and Divergence of Vector Fields 3. Circulation and Curl of Vector Fields 4. Solenoidal and Irrotational Fields 5. Green’s Theorems 6. Uniqueness Theorem for Vector Fields 7. Helmholtz’s Theorem 8. Orthogonal Curvilinear Coordinates
6. Principle of Duality 7. Principle of Image 8. Principle of Reciprocity 9. Huygens’ Principle 10. Radiation by Aperture Antennas
电磁场与电磁波(英文版)ppt课件
The magnetic fields unchanging with time are called steady magnetic
fields. 不随时间变化的磁场称为恒定磁场。
4
Electromagnetic Wave电磁波
If the charge and the current vary with time, the electric field and magnetic field they produce will be functions of time.如果电荷及电流均随时间改变，它 们产生的电场及磁场也是随时变化的
为了研究方便起见，我们先介绍真空中的电磁场，然后再讨论媒质中的电 磁场。
7
Field & Source 场与源
Electric charges and currents are the only sources for producing electromagnetic fields. Up to now, no magnetic charge or magnetic current has been found to exist in nature.电荷及电流是产生电磁场惟一的源。至今，人们 尚未发现自然界中存在磁荷及磁流。
Investigation on and its source is a fundamental subject. We will introduce a number of mathematical equations to describe the relationship between the field and the source, as well as between the field and the media.研究场与源的关系是电磁理论的基本问题之一。我们将 要详述场与源，以及场与媒质之间的关系，并且给予严格的数学描述。 8
电磁场与电磁波课件
P ( r , , )
ˆ r rr
z
r
上页 下页 首页
P y
x
1、位置矢量表示空间位置： Rectangular-to –Spherical coordinates:
x cos y sin zz
x2 y2 1 y tg x zz
空间位置的坐标表示和矢量的坐标表示
A vector field is a vector function of a position vector and time;
A scalar field is a scalar function of a position vector and time. 上页 下页 首页
( x , y, z ), ( , , z ), ( r , , )
方位角：azimuthal angle； 俯仰角：polar angle
x
z
r
P y
Chapter one： Vector Field
1-1 Vector algebra(矢量运算)
一、 矢量的数学表示： • Rectangular Coordinate：
ˆ A Aa
ˆ 1 a
AA
ˆ cosx ˆ cos y ˆ cosz ˆ a
ˆ cos y ˆ cosz ˆ) ˆ Ay y ˆ Az z ˆ A(cosx A Ax x (cos , cos , cos ) • 定义其方向余弦为：
• 矢量的几何表示，用有 向线段表示，长度为模， 指向为大小。 • Magnitude of A
A // B A B AB
华工电磁场与电磁波全英课Lecture 10
Introduction
Maxwell’s Equations for Static Magnetic Fields:
with
Constitutive relations:
Boundary conditions:
4.1 Ampere’s Circuital Law in Free Space
The curl equation for static magnetic fields in free space is where µ0 is the permeability of free space
Field and Wave Electromagnetics
Field and Wave Electromagnetics
Lecture 10
李融林 R.L. Li
Field and Wave Electromagnetics
Chapter 4
Static Magnetic Fields
李融林 R.L. Li
Setting the reference on the y-z plane, i.e., the vector potential becomes
The vector potential is reduced to
Therefore, we have the following boundaryvalue problem
Figure 4.2.2 A current-carrying infinitely-long cylindrical wire.
In cylindrical coordinates,
becomes
Integrating the equation yields
电磁场与电磁波1
– Suppose at ωt=0, the traveling wave equation becomes A cos( β z ) f ( z , t ) = A cos(ω t − β z ) – Distance zo for one period can be determined by zo
The Shanghai Transrapid Maglev Line: speed up to 430 km/hr.
Japanese Bullet Train
What are Fields?
• Gravitational Field
• Magnetic Field
• Electric Field
1.4 Orthogonal Coordinate Systems
1.4 Orthogonal Coordinate Systems
1.4 Orthogonal Coordinate Systems
1.5 Vector Differential Operators
1.5 Vector Differential Operators
A cos( β z )
– Suppose at ωt=π/4 , the traveling equation The wave moved a distance of π /4β becomes in π /4ω seond. What is the velocity?
A cos(π / 4 − β z )
1.5 Vector Differential Operators
1.5 Vector Differential Operators
1.5 Vector Differential Operators
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In 1831, British scientist Michael Faraday (1791-1867)
discovered the
phenomenon of electromagnetic induction and put forth the law of electromagnetic induction, which states that a time-varying magnetic field must give rise to an electric field. 1831 年英国科学家法拉第（ 1791 － 1867 ）发现电磁感应现象，创建了电
Investigation on the relation between the field and its source is a fundamental subject. We will introduce a number of mathematical equations to describe the relationship between the field and the source, as well as between the field and the media.研究场与源的关系是电磁理论的基本问题之一。我们
Class hour distribution
（Class hours 64：Lecture 60，Spare:4）
Vector analysis 4 Electrostatic fields 7 Boundary-value problems 4
EM induction 3 Time-varying EM fields 7 Plane EM waves 10 Guided EM waves 8
which will modify the original field distribution.
between the field and matters.
This is the interaction
当空间存在媒质时，在电磁场的作用下媒质中会发生极化与磁化现象，
结果在媒质中又产生二次电场及磁场，从而改变了媒质中原先的场分布，这
电磁场。
Field & Source 场与源
Electric charges and currents are the only sources for producing electromagnetic fields. Up to now, no magnetic charge or magnetic current has been found to exist in nature.电荷及电流是产生电磁场惟一的源。至今，人们 尚未发现自然界中存在磁荷及磁流。 Nevertheless, the introduction of magnetic charges and currents in the analysis of electromagnetic fields can prove to be beneficial sometimes, although these must be treated as fictitious entities.然而，有时引入磁荷及磁 流的概念是十分有益的，但是，它们仅是假想的。
In 1820, Danish scientist Hans Christian Oersted (1777—1851) discovered the magnetic field produced by an electric current. In the same year, French scientist Andre Marie Ampere安德烈.玛丽.安培(1775—1836) determined the force between two electric currents. 1820 年丹麦人奥斯特（ 1777 － 1851 ）发现了电流产生的磁场，同年法国 科学家安培（1775－1836）计算了两个电流之间的作用力。
磁感应定律，说明时变磁场可以产生时变电场。
A Great Innovation 重大突破
In 1873, British scientist James Clerk Maxwell (1831—1879) postulated the displacement current, which provided the link between a time-varying electric field and a magnetic field. He put on a firm mathematical foundation the laws governing an electromagnetic field. They are known today as the famous Maxwell’s equations. 1873年英国科学家麦克斯韦（1831－1879）提出了位移 电流的假设，认为时变电场可以产生时变磁场，并以严格数学方程描述了电 磁场与波应该遵循的统一规律，这就是著名的麦克斯韦方程。
Forces and energy are the most important.
The existence and transmission of electromagnetic waves need not rely on any medium. Specifically, when an electromagnetic wave travels through a vacuum, it is said to propagate in “free space”. 电磁场与电磁波是一种物质，它的存在和传播无需依赖于任何媒质。在 没有物质存在的真空环境中，电磁场与电磁波的存在和传播会感到更加“自
Electromagnetic Fields and Waves
Rugui Yang
Higher Education Press
Higher Education Electronic and Video Press
The physical understanding is emphasized instead of the mathematical derivation.
Steady current fields 3
Steady magnetic fields 6
Principles of EM radiation 8
Preface 前言
Electric Field & Magnetic Field 电场和磁场
The fields produced by the static charges behaves as the function of the force acting on the charge, and it is called the electric fields. 静止电荷产生的场表现为对于带电体有力的作用，这种场称为电场 The electricfields unchanging with time are called electrostatic fields. 不随 时间变化的电场称为静电场 The fields produced by the moving charges or the electric currents behaves as the function of the force acting on the magnet and the conductor carrying currents are called magnetic fields. 运动电荷或电流产生的场表现为对于磁铁和载流导体有力的作用，这种物质 称为磁场 The magnetic fields unchanging with time are called steady magnetic fields. 不随时间变化的磁场称为恒定磁场。
and may be investigated separately.静电场与恒定磁场相互无关、彼此独立， 可以分别进行研究EnFra bibliotekity 物质属性
Electromagnetic fields and waves are invisible (except for visible light), their existence can be inferred from the energy and momentum they carry. 电磁场与电磁波虽然不能亲眼所见，但是客观存在的一种物质，因为它 具有物质的两种重要属性：能量和质量。但是，电磁场与电磁波的质量极其 微小，因此，通常仅研究电磁场与电磁波的能量特性。
就是场与媒质的相互作用现象。 For the convenience of study, we first introduce electro-magnetic fields in free space, after which the electromagnetic field in matter will be discussed. 为了研究方便起见，我们先介绍真空中的电磁场，然后再讨论媒质中的
将要详述场与源，以及场与媒质之间的关系，并且给予严格的数学描述。
History 历史的回顾
The ability of a piece of amber琥珀 to attract small items after it had been rubbed was discovered by the Greeks in 600 B.C. The attractive force between a magnet and iron铁 was noted by the Chinese in 300 B.C. 公元前600年希腊人发 现了摩擦后的琥珀能够吸引微小物体；公元前 300年我国发现了磁石吸铁的现 象； Early in the first century, the compass was invented and it was among the four great inventions in ancient China. Thereafter, the magnetic field of the earth was discovered. In 1785, French scientist Charles Augustin de Coulomb (1736—1806) discovered Coulomb’s law (1785年法国科学家库仑（1736－1806）通过实验 创建了著名的库仑定律 ), and it gives the relationship between the force experienced by two small charged objects and the distance between them.