Chapter 3 Fields of Stationary Electric Charges : II Solid Angles Gauss ’ Law Conductors Poisson ’ s Equation Laplace ’ s Equation Uniqueness Theorem Images

Example 1: hollow conductor the 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.

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.