课程名称：电磁场与电磁波授课学院：国际学院学生班级： 07 级，电信工程及管理专业

课程名称：电磁场与电磁波授课学院：国际学院学生班级：07级，电信工程及管理专业课程名称：电磁场与电磁波授课学院：国际学院学生班级：07级，电信工程及管理专业教师姓名：乔耀军所在学院：信息与通信工程学院

课程简介 • 主要内容：课程首先通过基本的实验定律结合矢量分析的方法，建立静电场、静磁场和稳恒电流电场的基本方程；然后讲述更普遍的时变电磁场，麦克斯韦在总结基本实验定律的基础上，结合自己提出的位移电流假说，给出了麦克斯韦方程组。麦克斯韦方程组是解决所有电磁问题的理论依据。课程的最后利用麦克斯韦方程组分析电磁波的产生和传播的问题，对应后续课程的光波导、传输线、天线等课程。 • 重要性：因为麦克斯韦方程组是解决所有电磁问题的理论基础，而通信中发射机和接收机之间要靠电磁波传输，所以这门课程对北邮的学生十分重要。 • 学习方法：同时这又是很难学的一门课，学生原来学习的知识都是基于“路”的课程，利用标量和微分方程可以求解；本门课要建立“场”的概念，需要利用矢量分析的方法和求解偏微分方程，需要学生有较好的数学基础。

Guass’s lawandDivergence Equations of Electrostatics Yaojun Qiao April 1，2009

The main contents ___ ___ ___ ___ ('v') ('v') ('v') ('v') (( )) (( )) (( )) (( )) -/-"--"----/-"--"----/-"--"----/-"--"-- Review Coulomb’s law, superpositionprinciple，and Electric field intensity Gauss’s law and its application Divergence equation and its application Summary

1. ☆Coulomb’s Law C. A. Coulomb, France source Observation point e0refers to the Dielectric Constant in free space erefers tothe Dielectric Constant of medium

1. ☆Superposition principle（叠加原理） • For scattered charges • For chargers distribution

1. ☆ Electric Field Intensity（电场强度） Unit: Electric Field Intensity is actually the electro-static force per unit charge. Why q test0 ? Electric field intensity for point charge: Electric field intensity satisfies superposition principle ___ ___ ___ ___ ('v') ('v') ('v') ('v') (( )) (( )) (( )) (( )) -/-"--"----/-"--"----/-"--"----/-"--"--

Tangent S  line 1. ☆ Electric Field lines（电力线） Definition of Electric field lines: • From positive charge, end at negative charge; • The tangent direction of electric field line is the direction of electric field intensity; • The density of electric field line is the magnitude of electric field intensity; • From high potential to lower potential. M. Faraday ,England

？ How to studyElectric Field Intensity Helmholtz Theorem: ——亥姆霍兹公理 In limited region, any vector field can be uniquely determined by its divergence,curl and the boundary conditions. Boundary conditions

S 2. ☆ Electrostatic Gauss’s Law（高斯定理） Electric flux（电通量）

q内 S 2. ☆ Electrostatic Gauss’s Law（高斯定理） J. C. F. Gauss, Germany Gauss’s law: The net electric flux emanating from a closed surface is numerically equals to the sum of charge inside the closed surface over

+ Coulomb’s law Superposition principle θ S r q 2. ☆ Electrostatic Gauss’s Law（高斯定理） How to get Gauss’s law？ Guass’s law

2. ☆ Electrostatic Gauss’s Law P  S P P   S S • Discuss Gauss’s law: • The charge is the source of electrostatics; • The line of electrostatic is from positive charge, end at negative charge, continually at W/O charge point; • Although E are generated by all charge in space, electric flux only relates with the charges inside the enclosed surface.

2. ☆ Solve the electrostatics problem with Guass’s law It is significantly useful for ——solution to E Intensity in symmetrical cases. Symmetrical system: • Spherical symmetrical • Cylindrical symmetrical • Surface symmetrical

2. ☆ Solve the electrostatics problem with Guass’s law The tip of E-Gauss’s Law: (1) Find a closed surface (2) The quantity of on the surface is constant. When the charge distribution is symmetrical, ——Try E-Gauss’s Law! (^_^) Example --->>> in next page

S 2 r S 1 S 3 Example : Infinite Line Charges Solution via Gauss’s Law • Axial Symmetry——construct a cylindrical surface, in unit height, with line charges as the axis, and r as the radius. Since the E field has only radial component,

3. ☆ Divergence equation （散度方程） Gauss’s Law Integral form Please note: r here refers to volume density of free charge.

z z y y x x Guass’s law,macroscopic Surface for Integration Surface for Integration E

z Surface for Integration E y x Divergence equation, microscopic Argh!! I am shrinking!!!

3. ☆ Solve the charge distribution with divergence eq. • E-intensity in space is known as follows. Please determine the charge distribution. • Analysis: • Due to spherical symmetry, E has only radial component; • Apply div equ in differential form; (^_^) --------------->>> in next page

4. ☆ Summary Guass‘ law Div Equ: Integral form Differential form

Review Guass’s Law and the Div Equation • Physical Meaning: • describing the scattering character of static E field • For integral equation: • E-flux through any closed surface S = charges within S • Flux Source of Static E Field is Charges. • For differential equation: • Electrostatics Div = Volume density of Q at that point • Div Source of Static E Field is Volume density of Charges. Integral form Differential form

Kernel of E-Gauss’s Law: (1) Find a closed surface (2) The quantity of on the surface is constant. Please note this tip. When the charge distribution is symmetrical, ——Try E-Gauss’s Law!

Homework • Exercises: 3.4，3.8， • Problem：3.23(optional)

课程名称：电磁场与电磁波 授课学院：国际学院 学生班级： 07 级，电信工程及管理专业