E●ds Qr·d 4兀6 Discussion: Left side is scalar. That means, for no-point charge, left Side should be total charges enclosed inside S, therefore, for any surface, E●ds= The flux of the electrostatic field intensity through an enclosed surface equals the total charges divided by a Apply the definition of divergence in the above V●E= Discussion: Remember ? VXE=0 The divergence of electrostatic field intensity at any point equal the local charges' density divided by co
2 0 4 0 r Q r ds E ds • • = • = s v dv E ds 0 Discussion: Left side is scalar. That means, for no-point charge, left Side should be total charges enclosed inside s, therefore, for any surface, The flux of the electrostatic field intensity through an enclosed surface equals the total charges divided by 0 Apply the definition of divergence in the above, 0 • E = The divergence of electrostatic field intensity at any point equal the local charges’ density divided by 0 Discussion: Remember ? E = 0
Conclusion electrostatic field is a field with source and without curl 1.4.4 Poisson equation △=_D Special case: Laplace equation AV=0 1.4.5 EXamples of application D Electric field of an infinitive straight wire You may make a cylindrical Qauss surface to enclose part of the ine. then consider )the symmetrical property of the field 2) the flux of field go through the top and bottom plans must be zero E 2m60
1.4.4 Poisson equation 0 V = − Conclusion electrostatic field is a field with source and without curl. 1.4.5 Examples of application 1) Electric field of an infinitive straight wire You may make a cylindrical Qauss surface to enclose part of the line, then consider 1)the symmetrical property of the field; 2) the flux of field go through the top and bottom plans must be zero. 0 2 0 r r E = Special case: Laplace equation V = 0
2)Infinitive flat ion beam Question Pls. derive inside nside 0 2b p 2at/ X outside outside Z a)Using Poisson equation to derive E and v inside the ion beam
2) Infinitive flat ion beam x y z 2b ρ 2a Question Pls. derive Einside Vinside Eoutside Voutside V0 V0 a) Using Poisson equation to derive E and v inside the ion beam
Lecture break we need a drill class 1)to enhance the understanding of Electrostatic field and Electric potential 2)Also at the same time, we need some practice for problem solving, particularly using the Gauss theorem 3)Thinking problem: If the inverse square law is not correct think whether the electric imaginary line is still valid Chapter 2: Gauss theorem in Conductor and dielectrics (conductor, insulator, capacitor, resistor, etc
Lecture break we need a drill class 1) to enhance the understanding of Electrostatic field and Electric potential. 2)Also at the same time, we need some practice for problem solving, particularly using the Gauss theorem. 3) Thinking problem: If the inverse square law is not correct, think whether the electric imaginary line is still valid. Chapter 2: Gauss theorem in Conductor and Dielectrics (conductor, insulator, capacitor, resistor, etc.)
Terminology of the day Electrostatic equilibriun静电平衡 nduced charge感应电荷 Conductor导体 insulator绝缘体 dielectric电介质 Equal- potential surface等势面 Ceramics陶瓷 Electrical generator电机 Electrostatic shielding电屏蔽 Thunder lighting Arrester Photo- conductor光导体 Xerography复印术 Capacitance电容 Capacitor电容器 Parallel平行/并联 serles竖行/伟联
Terminology of the day Electrostatic equilibrium静电平衡 Induced charge 感应电荷 Conductor 导体 insulator 绝缘体 dielectric电介质 Equal-potential surface 等势面 Ceramics陶瓷 Electrical Generator电机 Electrostatic shielding电屏蔽 Thunder lighting Arrester Photo-conductor 光导体 Xerography 复印术 Capacitance 电容 Capacitor 电容器 Parallel 平行/并联 series 竖行/串联