《电动力学》第3讲§11电荷和电场.PPT

我们的宇宙 恒星间平均距离 1016m 5光年 银河系半径 5x104光年 1020m 银河系恒星数 4x1012个 星系间平均距离 2x106光年 距地球最近的河外星系仙女座 100万光年 人们所认识的最外的星系 1010光年 星系总数 1012个 1024颗恒星，约 1 mol 太阳系 Coulombs law Coulombs law, or Coulombs inverse-square law, is a law of physics describing the electrostatic interaction between electrically charged particles. The law was first published in 1784 by French physicist Charles Augustin de Coulomb and was essential to the development of the theory of electromagnetism. It is analogous to Isaac Newtons inverse-square law of universal gravitation. Coulombs law can be used to derive Gausss law, and vice versa. The law has been tested heavily, and all observations have upheld the laws principle. Coulombs law Coulombs law states that: The magnitude of the electrostatic force of interaction between two point charges is directly proportional to the scalar multiplication of the magnitudes of charges and inversely proportional to the square of the distance between them. The force is along the straight line joining them. If the two charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive. Gausss law In physics, Gausss law, also known as Gausss flux theorem, is a law relating the distribution of electric charge to the resulting electric field. The law was formulated by Carl Friedrich Gauss in 1835, but was not published until 1867. Gausss law Gausss law states that: The net electric flux through any closed surface is equal to 1?ε times the net electric charge enclosed within that closed surface. 谢谢！ 电场的旋度 山东大学物理学院 宗福建 * 静电场的散度和旋度 山东大学物理学院 宗福建 * 例题 例 电荷Q均匀分布于半径为a的球内，求各点的电场强度，并由此直接计算电场的散度。 山东大学物理学院 宗福建 * 例题 解 作半径为r的球（与电荷球体同心）由对称性，在球面上各点的电场强度有相同的数值E，并沿径向。当r a时，球面所围的总电荷位Q，由高斯定理得 山东大学物理学院 宗福建 * 例题 写成矢量式得 山东大学物理学院 宗福建 * 例题 若r a，则球面所围电荷为 山东大学物理学院 宗福建 * 例题 应用高斯定理得 山东大学物理学院 宗福建 * 例题 应用高斯定理得 山东大学物理学院 宗福建 * 例题 现在计算电场的散度。当r a时，在这区域r ≠ 0，由直接计算可得 山东大学物理学院 宗福建 * 例题 当r a时