ad1 Pf.P/EE ,solution (=)=A+BzEquationa-22EE球坐标系中轴对称问题的解Solutionstotheproblemswithaxialsymmetryinsphericalcoordinates:1200asaEquationsineara0sinegeH>(coso)Φ(r,0)=general solutionA求解泊松方程或拉普拉斯方程的边界条件BoundaryconditionstosolvePoisson'sequationorLaplace'sequationOp2ad,Er//=E21l -Φ,=Φ2 D21-D,=0, -E20n1 On象法Methodofimages1.无限柱形体Forlongcylindrical conductors,themethod istofindafictitiouslinecharge to substitute the real surface charges, so that the field outside the conductors is the sameas the real field.For two long cylindrical conductors, the position of the image is at the position p,A(d+pp'=d’-a?. The potential diference between the conductors isV2TEOTa-2.无大接地体板外的点荷Apointchargeqisatadistancedfroman infinitelylargeconducting plate,the image ofthe surface charge on the conducting plate is a -q point chargeat the opposite side ofthe plate.The field in the real space isqgp(x,y,z)4πEVx+y*+(=-d)Vx+y+(=+d)3.接地体球外的点荷Apointchargegisatadistanceafromthecenterofagroundedconducting sphere of radius R, the image is in the sphere at a distance b=R? la from the11
Equation ∂ 2 ∂ z 2 =−f / 0 , solution z=ABz− 1 2 f 0 z 2 . 球坐标系中轴对称问题的解 Solutions to the problems with axial symmetry in spherical coordinates: Equation r 2 ∂ ∂ r 1 sin ∂ ∂ sin ∂ ∂ =0 , general solution r ,=∑ l=0 ∞ Al r l Bl r l1 Pl cos . 求解泊松方程或拉普拉斯方程的边界条件 Boundary conditions to solve Poisson's equation or Laplace's equation: E1||=E2 || 1=2 . D2 ⊥− D1 ⊥= f 2 ∂2 ∂n −1 ∂1 ∂ n =− f . 镜象法 Method of images: 1. 无限柱形体 For long cylindrical conductors, the method is to find a fictitious line charge to substitute the real surface charges, so that the field outside the conductors is the same as the real field. For two long cylindrical conductors, the position of the image is at the position p, p 2=d 2−a 2 . The potential difference between the conductors is V= 20 ln d p d −p . 2. 无大接地体板外的点荷 A point charge q is at a distance d from an infinitely large conducting plate, the image of the surface charge on the conducting plate is a -q point charge at the opposite side of the plate. The field in the real space is x , y , z= 1 4 0 [ q x 2y 2z−d 2 − q x 2 y 2zd 2 ] . 3. 接地体球外的点荷 A point charge q is at a distance a from the center of a grounded conducting sphere of radius R, the image is in the sphere at a distance b=R 2 /a from the 11
center,ofcharge q'=-qRla . The field in the real space is (r)=4元E习题类型求解一维泊松方程或拉普拉斯方程，直接解微分方程，利用边界条件确定积分常数。求解镜象问题，无穷长带电导体，点电荷旁的无穷大导体平板，点电荷旁的导体球。求解具有轴对称的球边界问题，用勒让德级数解，用边界条件确定常数。第四章：稳恒电流和磁场概要1、教学内容4.1电动势和传导4.2磁场4.3磁偶极矩4.4安培定理4.5安培定理的微分形式，比奥一萨筱尔定律4.6作用在线圈上的力和力偶带电粒子在电磁场中的运动2、教学基本要求：掌握电动势、电阻、磁场、洛伦兹力、安培定理的概念和计算，掌握磁场对电流和带电粒子作用的计算3、重点：电流和电阻、磁场和洛伦兹力、安培定理、载流导线和带电粒子在磁场中的运动。难点：电阻的计算、安培定理的运用，安培定理的微分形式、带电粒子在电磁场中的运动。基本概念、定律和公式电流密度Currentdensity:Current densityjis avector.Thedirectionofjis thedirection ofthe drift velocity v.The magnitude of jis the net amount of charge crossing unit areaperpendicular to the drif velocity w.j=-Ney , I=J,j-d s12
center, of charge q'=−qR/a . The field in the real space is r= 1 40 q r q' r' . 习题类型 求解一维泊松方程或拉普拉斯方程，直接解微分方程，利用边界条件确定积分常数。 求解镜象问题，无穷长带电导体，点电荷旁的无穷大导体平板，点电荷旁的导体球。 求解具有轴对称的球边界问题，用勒让德级数解，用边界条件确定常数。 第四章：稳恒电流和磁场 概要 1、 教学内容 4.1 电动势和传导 4.2 磁场 4.3 磁偶极矩 4.4 安培定理 4.5 安培定理的微分 形式，比奥－萨筏尔定律 4.6 作用在线圈上的力和力偶 带电粒子在电磁场中的运动 2、教学基本要求： 掌握电动势、电阻、磁场、洛伦兹力、安培定理的概念和计算，掌握磁场对电流和带电粒子 作用的计算 3、重点：电流和电阻、磁场和洛伦兹力、安培定理、载流导线和带电粒子在磁场中的 运动。 难点：电阻的计算、安培定理的运用，安培定理的微分形式、带电粒子在电磁场中的运动。 基本概念、定律和公式 电流密度 Current density: Current density j is a vector. The direction of j is the direction of the drift velocity v. The magnitude of j is the net amount of charge crossing unit area perpendicular to the drift velocity v. j=−Ne v , I=∫S j⋅d S 12