物理与光电工程学院：《大学物理》课程PPT教学课件（讲稿，英文第三版）Chapter 20 Gauss's Law

Chapter 20 Gauss s law 第八章静电场 Chapter 20 Gauss's Law A statement of the relationship between electric charge and electric field 1 Electric flux 2 Gauss's law 3 Application of Gausss Law

Chapter 20 Gauss’s Law 第八章静电场 Chapter 20 Gauss’s Law A statement of the relationship between electric charge and electric field. 1 Electric Flux 2 Gauss’s Law 3 Application of Gauss’s Law

Chapter 20 Gauss s law 第八章静电场 New Words and Expressions 通量 Gauss's law 高斯定理 gaussion surface 高斯面 spherical 球面的 cylindrical 柱面的 planar 平面的

Chapter 20 Gauss’s Law 第八章静电场 New Words and Expressions flux 通量 Gauss’s Law 高斯定理 gaussion surface 高斯面 spherical 球面的 cylindrical 柱面的 planar 平面的

Chapter 20 Gauss s law 第八章静电场 1. Electric flux(通量)p487-489 1)The cases that planes are in the uniform E and the electric field direction is perpendicular to the surface Φn=ES E electric flux-The product of electric field and area of surface

Chapter 20 Gauss’s Law 第八章静电场 1. Electric Flux (通量) p487-489 E  S electric flux —The product of electric field and area of surface. ES E  1) The cases that planes are in the uniform and the electric field direction is perpendicular to the surface E 

Chapter 20 Gauss s law 第八章静电场 2)The cases that planes are in the uniform e but the area s in not perpendicular to e The number of electric field line through both area ofs and s are equal, so ◆均匀电场,E与平面夹角O ①= ES COS 6 Φe=E·S E

Chapter 20 Gauss’s Law 第八章静电场 2) The cases that planes are in the uniform but the area S in not perpendicular to E  The number of electric field line through both area of S and are equal, so  S E  S Φe  ES cos  均匀电场 ，E与平面夹角    n e   Φ E S     e E 

Chapter 20 Gauss s law 第八章静电场 3)For nonuniform fields and curved surfaces we rewrite this definition of electric flux in differential form. ◆非均匀电场强度电通量 dS=dS·en Eds E d④=EdS ④=|d④ E cos edS ①=E.dS (electric flux through a Gaussian surface)

Chapter 20 Gauss’s Law 第八章静电场 3) For nonuniform fields and curved surfaces we rewrite this definition of electric flux in differential form: E 非均匀电场强度电通量      s Φ dΦ E cos dS e e     s Φ E S   d e Φ E S   d d e   d d n S S e     S  d E   n e  (electric flux through a Gaussian surface)

Chapter 20 Gauss s law 第八章静电场 3)For the surfaces which is closed ◆S为封闭曲面 E 规定:取闭合面外法线方 向为正向。 We define of E s or of ds, to point E outward from the enclosed volume。 d s d④ el 0 Flux leaving the volume is positive. 几 d④<0 2 Whereas flux entering the volume is negative

Chapter 20 Gauss’s Law 第八章静电场 规定：取闭合面外法线方 向为正向。We define of S or of dS, to point o u t w a r d f r o m t h e enclosed volume. E  , d 0 2 π  2  Φe2  , d 0 2 π  1  Φe1  S 为封闭曲面 dS1 d S 2   2 E2  1 E1  3) For the surfaces which is closed Flux leaving the volume is positive. Whereas flux entering the volume is negative

Chapter 20 Gauss s law 第八章静电场 ◆闭合曲面的电场强度通量 E dφ=EdS Φ=E.dS= Ecos edS 例:如图所示,有一个 y 三棱柱体放置在电场强 E 度E=200N.C-1的 匀强电场中.求通过此三 棱柱体的电场强度通量

Chapter 20 Gauss’s Law 第八章静电场      S S Φ E dS E cos dS e    闭合曲面的电场强度通量 Φ E S   d e  d E  S  d  E  S x y z E  o 例: 如图所示 ，有一个 三棱柱体放置在电场强 度 E  200i N C 1 的   匀强电场中. 求通过此三 棱柱体的电场强度通量

Chapter 20 Gauss s law 第八章静电场 解④=④ e刖 + e后 P +④,++ n E e前 e后 RX E·dS=0 M e左Js左 E·dS= ES coS兀=-ES 左 右 E·dS=ES S右 右Cosb=ES 左 ④=④+④+④+6 e下 0

Chapter 20 Gauss’s Law 第八章静电场 x y z E  o P Q R N M 解 左 右 下 前 后 e e e e e e Φ Φ Φ Φ Φ Φ      Φ e前 Φe后 Φe下  d  0 s E S   Φe左  s左 E dS  ES左 cosπ  ES左   n e  n e  n e   Φe右  s右 E dS  ES右 cos  ES左   e 0 Φe Φ e前 Φe后 Φe左 Φe右 Φ 下 

Chapter 20 Gauss s law 第八章静电场 3. Gauss'Law(P489-491) Karl Friedrich Gauss(1777-1835), German mathematician and physicist He made a lot of contributions in the fields of experimental physics, theoretical physics and mathematics. He made major contributions to the theory of electromagnetism

Chapter 20 Gauss’s Law 第八章静电场 Karl Friedrich Gauss (1777-1835), German mathematician and physicist. He made a lot of contributions in the fields of experimental physics, theoretical physics and mathematics. He made major contributions to the theory of electromagnetism. 3. Gauss’ Law (P489-491)

Chapter 20 Gauss s law 第八章静电场 高斯( Carl friedrich gauss 1777-1855)德国数学家和物理学家 1777年4月30日生于德国布伦瑞克, 幼时家境贫困,聪敏异常,受一贵族 资助才进学校受教育。1795-1799年 在哥廷根大学学习,1799年获博士学 位。1833年和物理学家WE.韦伯共同 建立地磁观测台,组织磁学学会以联 系全世界的地磁台站网。1855年2月 23日在哥廷根逝世。 高斯长期从事于数学并将数学应用于物理学、天文学 和大地测量学等领域的研究,著述丰富,成就甚多。他 生中共发表323篇(种)著作,提出404项科学创见(发表 178项),在各领域的主要成就有:

Chapter 20 Gauss’s Law 第八章静电场