大学英文版电磁学讲义1-8
大学物理-电磁学(英文授课)
大学物理-电磁学（英文授课）IntroductionElectromagnetism is a field of physics that concerns itself with the study of electromagnetic forces and fields. It is a branch of physics that focuses on the interaction between electrically charged particles, including charged particles at rest and moving charges. This course is designed to help students understand the basic principles of electromagnetism, including electric and magnetic fields, electromagnetic radiation, and electromagnetic waves.Electric FieldsElectric fields are created by electric charges, which are either positive or negative. The electric field is said to be the space surrounding a charged particle. If another charged particle is placed in the electric field, it will experience a force. The direction of the force depends on the charge of the particle and the direction of the electric field.Magnetic FieldsMagnetic fields are created by moving charges. A magnetic field is said to be the space surrounding a magnetic object. If a charged particle is placed in a magnetic field, it will move in a circular path. The direction of the circular path depends on the charge of the particle and the direction of the magnetic field. Electromagnetic FieldsAn electromagnetic field is created by the interaction of an electric field and a magnetic field. Electromagnetic fields have both electric and magnetic components, and they travel through space at the speed of light. Electromagnetic waves are a form of electromagnetic radiation that carries energy. Electromagnetic radiation includes radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays, and gamma rays.Maxwell's EquationsMaxwell's equations describe the behavior of electric and magnetic fields. They are a set of partial differential equations that relate the electric and magnetic fields to the electric charges and currents that are present. The equations describe how an electric field can produce a magnetic field, and a magnetic field can produce an electric field. They also describe how the electromagnetic fields propagate through space.Electromagnetic WavesElectromagnetic waves are waves of energy that are propagated through space by the interaction of electric and magnetic fields. Electromagnetic waves do not require any medium to propagate through. They can travel through a vacuum, which is why they are also known as vacuum waves.Electromagnetic waves are classified based on their frequency and wavelength. Radio waves have the lowest frequency, and gamma rays have the highest frequency. Radio waves have the longest wavelength, and gamma rays have the shortest wavelength.Applications of ElectromagnetismElectromagnetism has many practical applications in our daily lives. Some of the most common applications include electric motors, generators, transformers, telecommunication devices, medical imaging devices, and microwave ovens. Electromagnetism has also played a significant role in the development of modern technology, including computers, television, radio, and mobile phones.ConclusionElectromagnetism is a fascinating field of physics that has wide-ranging applications in our daily lives. This course provides students with a comprehensive understanding of electric and magnetic fields, electromagnetic radiation, and electromagnetic waves. By studying electromagnetism, students can gain a deeper appreciation for the fundamental principles that govern the behavior of the universe around us.Electromagnetism is one of the four fundamental forces of nature, along with gravity, strong nuclear force, and weak nuclear force. It is a field of physics with numerous applications in our modern society. Without the understanding of electromagnetism, we would not have the modern comforts that we have today, including electricity, the internet, cell phones, and many other devices.One of the most significant contributions of electromagnetism to modern society is the use of electric motors. Electric motors are devices that convert electrical energy into mechanical energy.They are used in a wide range of applications, from household appliances to transportation systems. The underlying principle of electric motors is electromagnetic induction, which is the process of inducing an electric current in a conductor by varying the magnetic field around it.Another important application of electromagnetism is in generators. Generators are devices that convert mechanical energy into electrical energy. They are often used in power plants to generate electricity that is distributed to homes and businesses. The principle of electromagnetic induction is also used in generators. When a conductor moves through a magnetic field, an electric current is induced in the conductor.Electromagnetism also plays a central role in the functioning of transformers. A transformer is a device that changes the voltage of an alternating current (AC) power supply. Transformers are used to step up or step down the voltage of an AC power supply. They are used in power grids to maintain a constant voltage throughout the grid. The principle used in transformers is electromagnetic induction, with the primary and secondary coils of wire interacting with the magnetic field to produce the desired voltage change. Telecommunication devices, including radios, televisions, and cell phones, also rely on the principles of electromagnetism. The radio waves used for communication are a form of electromagnetic radiation. Radio waves are used to transmit and receive signals between devices. The workings of these devices depend on the principles of electromagnetic induction and electromagnetic radiation.In addition to powering devices, electromagnetism is used in medical imaging devices. Magnetic resonance imaging (MRI) machines use magnetic fields and radio waves to produce images of the body's internal structures. The patient is placed in a powerful magnetic field, which causes the protons in their body to align with the field. A radio wave is then sent through the body, causing the protons to produce a signal. The signal is detected, and an image is produced based on the strength and location of the signal.Microwave ovens are another example of electromagnetism in action. These appliances use microwaves to cook food. Microwaves are a type of electromagnetic radiation with a frequency of around 2.4 GHz. The microwaves cause the water molecules in the food to vibrate rapidly, producing heat. This heats the food quickly and evenly, making it a popular method for cooking.The study of electromagnetism has also led to the development of modern technology. Computers, televisions, radios, and cell phones all rely on the principles of electromagnetism. The development of these technologies has revolutionized the way we live and communicate. The internet, for example, would not exist without the principles of electromagnetism.In conclusion, electromagnetism is a fascinating field of physics with numerous practical applications in our daily lives. It is the foundation of modern technology, and our society would not be the same without it. By studying electromagnetism, we can gain a deeper understanding of the world around us and appreciate thefundamental principles that govern our universe. As technology advances, we can expect even more exciting and innovative applications of electromagnetism in the years to come.。
电磁(大学英文版)
Electricity and MagnetismExperiments reveal a property of matter called electric charge that can result in the attraction or repulsion of objects. There are two types of electric charge, positive and negative. Most things around us are neutral. They contain an equal number of positive and negative charges. Rubbing one substance against another can transfer charges such that one object acquires a net or total positive charge and the other acquires a net or total negative charge. Two objects that both possess net positive or net negative charge repel one another. There is an attraction between two objects if one has net positive and the other net negative charge. The simplest expression for the electric force between objects with net charges Q and q separated by a distance R is F=kQq/R 2, where k is a constant. Charles Coulomb (1736-1806) proposed this law and it has the same form as Newton’s Law of Gravitation. The net charge can be a positive or a negative number.Michael Faraday (1791-1867) envisioned that the electric force between charged objects is mediated by an electric field. The electric field is a quantity defined at each point in space. It can be used to determine the force F on an object with charge q according to F=qE, where E is the electric field at the position of the object. One way of representing an electric field is to draw field lines. For example, the electric field lines surrounding an isolated object with net positive or negative charge areSome objects are called permanent magnets. They are able to attract or repel other materials even though they are electrically neutral. They have a north (N) and a south (S) pole. It is seen that if the north poles or the south poles of two magnets are brought close to one another, they repel. The magnets exhibit an attraction if the north pole of one and the south pole of the other are in close proximity. The magnetic force between these objects is due to a magnetic field. As with electric fields, magnetic fields can be represented by field lines. Here are some of the field lines for a bar magnet.Suppose an object with charge q and velocity v is exposed to a magnetic field B. The magnetic force on the object due to B depends on the product of q, v, B, and the directions of v and B. The magnetic force on a charged object is more complicated than the electric force on a charged object due to its dependence on the directions of v and B.andMaterials are made of atoms. The evidence for this statement will be examined later. Atoms consist of nuclei surrounded by electrons. The nuclei contain protons and neutrons. An electron, proton, and neutron possess one negative, one positive, and zero units of electric charge, respectively. Applying an electric field to a wire made of copper results in some of the electrons in the wire travelling on average in one direction. The motion of charged objects constitutes an electric current.Many experiments have uncovered connections between electric and magnetic phenomena. A steady electric current in a copper wire causes magnets located near the wire to deflect from their original orientations when the electric current is zero. This shows that electric currents or moving charged objects produce magnetic fields.As a bar magnet is moved towards a closed loop of copper wire, an electric current is generated in the wire. If the bar magnet is held fixed, then the electric current is zero. This demonstrates that a changing magnetic field creates a static electric field. A changing magnetic field means that the magnitude and/or the direction of the magnetic field vary with time.The electric field that is induced in the wire is the cause of the electric current. Much of the electricity we need to run our stereos, computers, lights, and so on is created by employing the above effect that was discovered by Faraday.James Clerk Maxwell (1831-1879) presented four equations that summarized and extended the above mathematics and observations. The first equation is Coulomb’s Law expressed in terms of the electric field. The second equation says that magnetic field lines form closed loops. Another way of expressing this is to note that there are no magnetic monopoles or objects with a single north or south pole. Experimenters have not discovered monopoles. The third equation states that a changing magnetic field generates a static electric field. The fourth equation indicates that steady electric currents produce static magnetic fields and that a changing electric field also generates a static magnetic field. The latter part of the fourth equation had not been observed experimentally when Maxwell proposed it. However, he felt that if a changing magnetic field results in an electric field, as Faraday had observed, then by symmetry it should be possible for a changing electric field to yield a magnetic field. This effect has been confirmed.electric currentS N current meterWavesWaves are moving patterns or oscillations in a medium. A periodic wave consists of a pattern that repeats in time. Periodic waves can be characterized by their wavelength, amplitude, frequency, and speed. Here is a profile of a periodic wave in a medium consisting of horizontal rods that are connected to one another.The wavelength is denoted by the Greek letter lambda, λ, and is the distance over which one complete cycle of the wave occurs. The amplitude A is the height of the wave above the zero line. Waves transport energy. The energy of a wave is proportional to its amplitude squared, A 2. The frequency is denoted by the Greek letter nu, ν, and is the number of wave cycles that pass through a point in the medium in one second. It is measured in cycles/second or hertz, Hz. The wave travels at a constant speed v that is determined by the properties of the medium. The wavelength, frequency, and speed are related asv=(distance travelled by the wave in one cycle)/(time for one cycle) [definition of speed] v=λx(1/(time for one cycle))= λ νUsing his equations, Maxwell predicted the existence of electromagnetic (EM) waves or radiation. In some systems, a changing E field gives rise to a B field that is itself varying with time. This time dependent B will generate a new changing E. There will be a self-sustaining configuration of E and B fields that propagate by themselves without any further connection with their source. EM waves can be produced by accelerating electric charges. Maxwell found that EM waves travel at a constant speed for a given medium. He calculated that EM waves move at a speed of about c=3x108 m/s in empty space, in agreement with measurements for the speed of visible light. Examples of EM radiation include radio waves, ultraviolet radiation, visible light, and X-rays.Superposition of WavesAn important property of waves is that they can be added together or superposed to produce new waves. A superposition that results in an increase of the amplitude is called constructive interference. A superposition that results in a reduction of the amplitude is called destructive interference.+ = =+。
大学英文版电磁学讲义1-4
55
4.2 Electrostatic Problems with Rectangular Symmetry
. V x =V z and E x = E z z z
In the gap, the potential satisfies Laplace's equation: ∇ 2 V =d 2 V / dz 2=0 => V z =C 1 z C 2 The boundary conditions: V(0) = 0, V(d) = V0. => C 2= 0 , C 1=V 0 / d . So, The potential in the gap is V z =V 0 z / d . The field in the gap E =−∇ V =−dV / dz =−V 0 / d . The surface charge density: From the boundary condition E n 2− E n 1= /0 , or from equation (4.1) the upper surface of conductor 1 (z = 0, V = 0), 1 u=−0 V 0 / d . the lower surface of conductor 2 (z = d, V = V0), 2 l =0 V 0 / d . The total charges on the conductors: on the conductor 1, Q1=−0 V 0 A / d . on the conductor 2, Q 2=0 V 0 A / d .
E n=/0
(4.1)
Laplace's Equation, Boundary, and the Uniqueness Theorem 拉普拉斯方程, 边界和唯一性定理
大学英文版电磁学讲义1-7
Example What is the resistance for a radial current between concentric conducting spheres with radii a and b. if there is a material with conductivity between the spheres? Divide the conducting volume into spherical shells(球壳) of radius r and thickness dr. The surface area of the shell is the cross-section 2 area(截面积) of the current. A= 4 r . The resistance of the shell at r is d R= dr 4 r2
I= dQ dt
(7.1)
Charge carrier(载流子): Charges q moving with mean velocity v, and linear density(线密度) nL , I = qn L v nL: number of charge carriers per unit length. (7.2)
∫A J 2 n− J 1 n dA
.
87
7.2 Current density and the continuity equation The surface charge enclosed by Σ is The boundary condition on J(x) is J 2 n− J 1 n=− ∂ ∂t (7.8)
7.5 Joule's Law 焦尔定律
电磁场教学大纲(英文)
《Electromagnetic Field Theory》Course Teaching Programme（Electromagnetic Field Theory）Course number：Course nature：the fundamental courseSuit speciality：Electronic information engineering、Communication engineeringAttended course：Higher mathematicsⅠ、College physicsⅠSucceed course：Microwave technology、Antenna technologyTotal credit：3.5 credit①、The purpose and requirements of teaching1．The purpose of teachingElectromagnetic Field Theory course is the fundamental course of engineer course electronic category ；By way of learning this course，students must have a good grasp of basic concept and basic theory of electromagnetic field and electromagneticwave，In order to lay a foundation of studying succeed course.2．The requirements of teachingDuring teaching，teacher must pay attention to basic theory as well as take note of suiting the needs of the development of modern science and technology，pay attention to developing the students’ ability to analyse and solve problems.②、Class hour plan③、Content of courses1．Vector analysis（6 class hour）（1）The basic requirements of teachingUnderstand：The ordinary specific property of scalar and vector fieldsComprehend：The nature and analysis of scalar and vector fieldsMaster：The solution of divergence、curl、gradient（2）Content of courses①Vector opertions②Divergence of a vector field(emphasis、difficulty)③The curl of a vector field（emphasis、difficulty）④The gradient of a scalar function（emphasis）2．Electrostatics（8 class hour）（1）The basic requirements of teachingUnderstand：The expressing method of electrostaticsComprehend：In common use physical quantity and experiment law of electrostaticsMaster：Use experiment law to do simply calculation（2）Content of courses①Coulomb’ law（emphasis）②Electric filed intensity③Electric flux and flux density（emphasis、difficulty）④The electric potential（emphasis）⑤Energy stored in an electric field⑥Boundary conditions（emphasis、difficulty）⑦Capacitor and capacitance⑧Poisson’s and Laplace’s Equations（emphasis、difficulty）3．Steady electric currents（8 class hour）（1）The basic requirements of teachingUnderstand：The equation of continuityComprehend：Totally specific property of steady electrostaticsMaster：Can calculate current density、boundary conditions for current density and the electromotive force（2）Content of courses①Nature of current and current density（emphasis）②The equation of continuity③Joule’s law（emphasis）④Boundary conditions for current density（emphasis、difficulty）⑤The electromotive force4．Magnetostatics（6 class hour）（1）The basic requirements of teachingUnderstand：The expressing method of magnetostaticComprehend：In common use physical quantity and experiment law of magnetostatic Master：Can calculate potential 、energy（2）Content of courses①The Biot-Savart Law（emphasis、difficulty）②Ampere’s force law③Magnetic flux and Gauss’s law for magnetic fields（emphasis、difficulty）④Magnetic vector potential（difficulty）⑤Magnetic field intensity and Ampere’s circuital law⑥Magnetic scalar potential（emphasis）⑦Boundary conditions for magnetic fields（emphasis、difficulty）⑧Energy in magnetic field（emphasis）5．Time-varying electromagnetic fields（14 class hour）（1）The basic requirements of teachingUnderstand：Faraday’ s law of inductionComprehend：Maxwell’s equatio nMaster：Maxwell’s equation.Can calculate self-inductance、mutual indctance and enengy in a magnetic field（2）Content of courses①Motionnal electromotive force②Faraday’ s law of induction（emphasis、difficulty）③Maxwell’s equation （emphasis、difficulty）④Self-inductance（emphasis）⑤Mutual indctance（emphasis）⑥Enengy in a magnetic field（emphasis）⑦Maxwell’s equation from Ampere’s law⑧Maxwell’s equation from Gauss’s law⑨Maxwell’s equation and boundary conditions6． Plane wave propagation（14 class hour）（1）The basic requirements of teachingUnderstand：General wave equationsComprehend：Polarization of a wave、Normal incidence of uniform plane waves、Oblique incidence on a plane boundaryMaster：Plane wave in all kinds of medium（2）Content of courses①General wave equations（emphasis、difficulty）②Plane wave in a dielectric medium（emphasis）③Plane wave in free space（emphasis）④Plane wave in a conducting medium（emphasis）⑤Plane wave in a good conductor（emphasis）⑥Plane wave in a good dielectric（emphasis）⑦Polarization of a wave（difficulty）⑧Normal incidence of uniform plane waves⑨Oblique incidence on a plane boundary④、Teaching and check ways1．Teaching waysMultimedia teaching、English and the Chinese language teaching2．Check waysUse open-book examination，course result is made up of examination result（70%）with result at ordinary times（30%）⑤、Teaching material and a list of reference books1．B. S. Gurn. Electromagnetic Field Theory Fundamentals.China Machine Press. 2002 2．Kraus.Fleisch.Electromagnetics with Applications.Fifth Edition. Mc Graw-Hill.1999。
大学物理：电磁学PPT
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2 电流元的磁场
dB
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Idl
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——毕奥-萨伐尔定律
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B Bi
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例 1： 判断下列各点磁感强度的方向和大小.
1 8 2Βιβλιοθήκη dB 0 1、 5 点 ：
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例 5：
一半径为R，均匀带电Q的薄球壳。 求球壳内外任意点的电场强 度。
0 r R 如图，过P点做球面S1 E dS E dS 0 E 0
S1 S1
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+ + +
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如图，过P点做球面S2 rR E dS E dS Q / 0
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点电荷电场 中的电势:
V
Q 40 r
电势的叠加 原理:
V Vi
i
点电荷电场中常取 无穷远处为电势零点
点电荷的电场线和等势面：
两平行带电平板的电场线和等势面：
+ + + + + + + + + + + +
大学英文版电磁学讲义1-9
9.2 Magnetization and Bound Currents 磁化和束缚电流
The volume density of bound current(束缚电流体密度): J x =∇ ×M x . The surface density of bound current(束缚电流面密度): K b x = M x × n . (9.13) (9.12)
J by =−∂ M z /∂ x .
. => J b =∇× M For M = M k Fig. 9.8.
K =M × n M= n m k
increasing in the Fig. 9.9 M z x k +x direction. The bound current is ∂M z J b =∇ × M=− j ∂x
9.4 Problems Involving Free Currents and Magnetic Materials 包含自由电流和磁介质的问题
Using Ampere's law of H, we can solve some problems in magnetic material with symmetry. Example 5: An infinite slab of a conducting material(无穷大导体平板) with magnetic susceptibility m carries a certain current distribution. The slab is parallel to the x y plane, between z = −a and z = a. It carries a free i . Above the x y plane the current volume current density J f z = J 0 z / a is out of the page, below it is into the page.
大学英文版电磁学讲义1-2
Chapter 1 History and Perspective 历史与前景
The electromagnetic interaction(电磁相互作用) is one of the fundamental interactions(基本相互作用) of the physical world. Interaction: atoms and molecules. Phenomenon: sunshine, lightning, rainbows. Technology: communication with NASA's planetary probes(行星探测器), electromagnetic medical imaging(医学成象), computer electronics.
Additi i A y B y j A z B z k
Multiplication: 乘法
Chapter 1 History and Perspective 历史与前景 Modern theory of gravity: Einstein's general relativity(广义相对论).
Elementary Charges, Photons, and QED 基本电荷, 光子和量子电动力学
1.1 Brief history of the science of electromagnetism 电磁科学简史
Electric and magnetic phenomena have been known for millenia. Ancient Greece. Amber(琥珀) rubbed with animal fur can attract small bits of matter. The force between natural magnets(磁铁), ferromagnetism(铁磁性). Early part of the scientific revolution in 1600. Gilbert. an important book.
大学英文版电磁学讲义1-3
3.1.1 The Superposition Principle 叠加原理
The force on a charge q due to a set of charges{ q 1 , q 2 , q3 , ⋯ ,q N } is the vector sum of the individual Coulomb forces. F q= ∑
2. What is the field on the x axis? The field on the x axis E x x , 0 = E y x , 0 =
电磁学讲义
SI中库仑定律的常用形式 （有理化）
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Permittivity of free space
r12
真空介电常数
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e12 + q1
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2. Principle of Superposition 电力叠加原理
两个点电荷的之间的作用力并不因第三
个点电荷的存在而改变。
多个点电荷对一个点电荷的作用力等于
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力的矢量和。vector sum
− Q3
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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
英文PPT电磁学Electric_Change
Conductors and Insulators（导体和绝缘体） Semiconductors (半导体)
Electrons are free to move in a perfect conductor.
Electrons stay with their atom in an perfect insulator.
F12
k
q1q2 r122
e12
F21
SI制 k 8.98755 109 N m2 C2
k is a proportionality constant.
令 k 1
4π 0
（ 0 为真空电容率 permittivity of free space ）
F12
New Words and Expressions
static charge
quantized
elementary charge conductor insulator induce Coulomb point charge permittivity of free space electric field test charge
q1
F21
q1
F21
r12
r12
q2
F12 d
q2
F12
The force between two point charges at rest was inversely proportional to the square of the distance between them and proportional to the product of the charges.
电磁场与电磁波课件(英文版)
Electrostatic field and steady magnetic field are independent of each other, 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
Entity 物质属性
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。
Steady magnetic fields 6
Principles of EM radiation 8
Preface 前言
Electric Field & Magnetic Field 电场和磁场
8 电磁 I
Electromagnetic Predators
電 磁 掠 食 者
The torpedo ray and electric eel
Electroplaques
Electric Precipitator
影 印 機
The copying process
Laser Printer
A RAM Chip
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2 qP qP 1.60 × 10 −19 C 9 N ⋅m Fe = = 8.99 ×10 = 14 N ~ 316lb 2 2 2 −15 4πε 0 r C 4 × 10 m
電雙極的電場
2d 2d = [(1 + + ...) − (1 − + ...)] 2 4πε 0 z 2 z (1! ) 2 z (1! ) d d = [(1 + + ...) − (1 − + ...)] 2 4πε 0 z z z 2d 1 qd = = 2 4πε 0 z z 2πε 0 z 3 p E= (electric dipole) 3 2πε 0 z 1 q q q
Charge is quantized
• The electric charge (e) is discrete (quantized)
q = ne , n = ± 1, ± 2, ± 3,... e = 1 . 6 × 10
− 19
C
• SI unit: coulomb (C), defined in term of ampere
大学英文版电磁学讲义1-6
*6.1 The Atom as an Electric dipole 原子作为电偶极子 6.1.1 Induced dipole 诱导偶极子
In equilibrium, an isolated atom in an electric field E has a dipole moment p proportional to the field.
Bound charge density(束缚电荷密度):
In equilibrium, without an applied field(外场) the mean charge density(平均 电荷密度) is 0 throughout the dielectric. When there is polarization, the displacement of charge may create a nonzero net charge density(非零静电荷密度) at some points in the material. Boundary charge density(束缚电荷密度) b x b x =−∇⋅P (6.12)
Chapter 6 Electrostatics and Dielectrics 静电学与电介质
Chapter 6 Electrostatics and Dielectrics 静电学与电介质
Dielectrics(电介质): insulators(绝缘体). Dielectric: The effects of an insulator on a capacitor. In a dielectric the electrons are not free, but bound(约束) to their atoms or molecules. When an external electric field(外电场) is applied to a dielectric, the electrons and nuclei become displaced by small distances.
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(8.3)
93
8.1 The Magnetic Force and the Magnetic Field
8.1.2 Force on a Current -Carrying Wire
作用在载流导线上的力
Electric current is motion of charges. Suppose the current consists of particles with charge q and linear density n L , moving with mean velocity v. The net force on a small segment d l of the wire is
The solution of this inhomogeneous linear equation (非齐次线性方程)(8.12) is v x t = E c 1 cos t c2 sin t B (8.13)
Substitute (8.13) into (8.9), we get
The Biot-Savart law is an empirical law(经验定律). It is a law for steady current. Permeability of vacuum(真空磁导率), 0=4 ×10−7 Tm/A . Example 1 Determine the magnetic field due to a current I in a long straight wire. (Fig, 8.8) , The field point x The direction of I is k in cylindrical coordinates is dz ' ( R , , z ), the line element d l is k z' . , the source point is x ' =k
E t − sin t B
With the integral of v x t and v y t , the trajectory(轨迹) of q is
x t =
(8.16) (8.17)
y t =
E 1 −cos t B
96
Chapter 8 Magnetostatics 静磁学 These are parametric equation(参数方程) for a cycloid curve(旋轮线). The motion of q is a combination of harmonic oscillations(简谐振动) in x and y, and a constant drift in the x direction. The drift velocity(飘移速度) is
Mass Spectrometer 质谱仪
A mass spectrometer is a device to separate charged particles by mass. In the velocity selector(速度选择器) there are crossed E and B fields, E= E j and B = B k . The particle with velocity v = E / B i can pass through the field undeflected. In the magnetic deflector(偏转器), the orbit of a particle is proportional to the ratio m/q, so different particle species travel on different circular path, separate in space.
dW =F⋅d x = F⋅v dt =0
(8.2)
The magnetic force affects the direction of motion of q, but not its kinetic energy(动能). Lorentz force(洛伦兹力) F =q E v × B
d F = n L d l q v × B = I d l × B
(8.4) (8.5)
The total force on the wire is F =∫wire Id l ×B
8.2 Application of the magnetic force 磁力的应用 8.2.1 Helical or Circular Motion of q in Uniform B 运动电荷在均匀磁场中的螺旋或圆运动
v y t =−c 1 sin t c 2 cos t
(8.14) (8.15)
With the initial values v x 0 =v y 0 = 0 , the constants are c1 =− E / B , c2 = 0 Then v x t = E E 1 −cos t , v y t = sin t . B B
The Biot-Savart law is an inverse-square law(平反比定律). The direction of the 97
8.3 Electric Current as a Source of Magnetic Field magnetic field is azimuthal, around the axis of I d l . (Fig. 8.7) For a macroscopic wire, the magnetic field B(x) is B x = I d l× r 0 I d l× x − x ' 0 = ∫ ∫ 2 4 wire 4 wire r ∣x − x '∣3 (8.21)
v D= E i B
(8.18)
The drift velocity does not depend on q. The positive and negative charges drift together.
8.2.3 Electric Motors 电动机
In a simple DC(直流电) motor the current is driven by a constant EMF(电动势). The current exists in a coil of wire, which is free to rotate on an axle. The magnetic force acts in opposite direction on opposite side of the coil, creating a torque(力矩) on the coil. To keep the direction of the torque constant as the coil rotates, the current in the coil must reverse every half cycle. The switch that reverses the current direction is called commutator(交换器).
mv 2 =− F r = qvB R
(8.6)
The angular speed of the particle is
94
Chapter 8 Magnetostatics 静磁学 v qB = = R m
(8.7)
is called cyclotron frequency(回旋频率). The period of revolution is 2 / .
. Suppose B = B k The equation of motion of the charge is dp =q v ×B dt F z = 0 => v z = constant . If v z = 0 , v is in x y plane and F ⊥ v , the charge is in uniform circular motion(匀 速圆周运动). If v z ≠ 0 , the motion is helical(螺旋的). the general trajectory is helix. In circular motion with radius R,
Chapter 8 Magnetostatics 静磁学
Chapter 8 Magnetostatics 静磁学
8.1 The Magnetic Force and the Magnetic Field 磁力和磁场 8.1.1 Force on a Moving Charge 作用在运动电荷上的力
The force on a charge q moving with velocity v, exerted by a magnetic field B, is (磁场作用在以速度 v 运动的电荷上的力)
F =q v ×B
(8.1)
Equation (8.1) is the definition of magnetic field. (从测量的角度定义磁场) SI unit of magnetic field: tesla(特斯拉)(T): 1 newton per ampere-meter (C m/v). The force on 1 C moving 1 m/s perpendicular to a field of 1 T is 1 N. Magnetic force does no work on q. (磁场对电荷不做功)
8.3 Electric Current as a Source of Magnetic Field 电流作为磁场的源 8.3.1 The Biot-Savart Law 毕奥-萨伐尔定律