Chapter 20 Gauss s law 第八章静电场 (1)物理学和地磁学中,关于静电学、温差电和摩擦电 的研究、利用绝对单位(长度、质量和时间)法则量度非 力学量以及地磁分布的理论研究。 (2)利用几何学知识研究光学系统近轴光线行为和成像, 建立高斯光学。 (3)天文学和大地测量学中,如小行星轨道的计算,地球 大小和形状的理论研究等。 (4)结合试验数据的测算,发展了概率统计理论和误差理 论,发明了最小二乘法,引入高斯误差曲线。此外,在纯 数学方面,对数论、代数、几何学的若干基本定理作出严 格证明。 在CGS电磁系单位制(emu)中磁感应强度的单位定为 高斯(1932年以前曾经用高斯作为磁场强度单位),便是 为了纪念高斯在电磁学上的卓越贡献
Chapter 20 Gauss’s Law 第八章静电场
Chapter 20 Gauss s law 第八章静电场 1) Gauss'law for vacuum. 定理:在真空中,通过任一闭合曲面的电场强度通 量,等于该曲面所包围的所有电荷的代数和除以 0 (与面外电荷无关,闭合曲面称为高斯面) Φ=pE·dS= q Fo. permittivity of free space 0i=1 The flux of the electric field through a closed surface of any shape equals to 1/En times of the algebraic sum of charges enclosed within the surface
Chapter 20 Gauss’s Law 第八章静电场 1) Gauss’law for vacuum. The flux of the electric field through a closed surface of any shape equals to 1/ 0 times of the algebraic sum of charges enclosed within the surface. n i i S Φ E S q 0 1 e 1 d 定理：在真空中,通过任一闭合曲面的电场强度通 量,等于该曲面所包围的所有电荷的代数和除以 . 0 （与面外电荷无关，闭合曲面称为高斯面） 0: permittivity of free space
Chapter 20 Gauss s law 第八章静电场 =∮Ed5=∑ Discussion I)The relation of the source of electric filed and the field(反映场和源的关系) 2)Where 2a, is the algebraic sum of all interior charges enclosed in the gaussian surface. g is not related to the way of distribution and outside charges 电通量只与面内电荷有关,与面外电荷无关
Chapter 20 Gauss’s Law 第八章静电场 1) The relation of the source of electric filed and the field (反映场和源 的关系). n i i S Φ E S q 0 1 e 1 d Discussion 2) Where is the algebraic sum of all interior charges enclosed in the Gaussian surface. is not related to the way of distribution and outside charges. qi 电通量只与面内电荷有关，与面外电荷无关
Chapter 20 Gauss s law 第八章静电场 3)The quantity E on the left side of above equation is the electric field resulting from all charges, both those inside and those outside the gaussian surface E为高斯面上某点的场强,是由空间所有电荷产生 的,与面内面外电荷都有关。 4)Gausss law and coulomb's law are equivalent(see P496). However, Gauss's law is hold for the eproduced by moving charges; Coulomb's law is only true for electrostatic field 5It give a simple way to calculate the distribution of electric field for a given charge distribution with sufficient symmetry
Chapter 20 Gauss’s Law 第八章静电场 3) The quantity on the left side of above equation is the electric field resulting from all charges, both those inside and those outside the Gaussian surface. E 为高斯面上某点的场强，是由空间所有电荷产生 的，与面内面外电荷都有关。 E 5) It give a simpl e way to cal culate the distribution of electric field for a given charge distribution with sufficient symmetry. 4) Gauss’s Law and Coulomb’s law are equivalent (see P496). However, Gauss’s Law is hold for the produced by moving charges; Coulomb’s law is only true for electrostatic field. E
Chapter 20 Gauss s law 第八章静电场 2) TThe derivation of gausss law(高斯定理的导出) 库仑定律 高斯 电场强度叠加原理 定理 ◆点电荷位于球面中心( a spherical surface enclosing a point charge at its center) E q ds 4 8 0 =E·dS= ds S4兀Ear
Chapter 20 Gauss’s Law 第八章静电场 2) The derivation of Gauss’s Law(高斯定理的导出) 高斯 定理 库仑定律 电场强度叠加原理 + S d 点电荷位于球面中心 (a spherical surface enclosing a point charge at its center) 2 π 0 4 r q E S S S r q Φ E S d 4π d 2 0 e 0 e q Φ r