电磁学ch3.ppt

Chapter 3 Fields of Stationary Electric Charges : II Solid Angles Gauss’ Law Conductors Poisson’s Equation Laplace’s Equation Uniqueness Theorem Images Example: solve the Poisson equation for flat ion beam (see P75--P78 youself) This example tells us how to actually obtain V and E by solving the Poisson equation, ---a very typical exercise of mathematical  physics. 3.6 The uniqueness theorem According to the uniqueness theorem, the Poisson equation has a unique solution , V(r), for a given charge density and for a given boundary conditions. Mathematicians elaborate very much on proving this kind of theorems. We take this theorem as granted. * * Example 1: hollow conductorthe charge on its inner surface is equal to the charge enclosed within the hollow, Example 2: isolated charged conducting plate Example 3:pair of parallel conducting plates They carry charges of equal magnitude and opposite signs. E=0, except btwn the plates.