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Stationary Electric Charges & Gauss' Law: Solving Poisson's Equation

Explore examples of electric fields, Gauss' Law, conductors, Poisson's Equation, and uniqueness theorem. Learn how to obtain solutions for charge distributions using mathematical physics.

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Stationary Electric Charges & Gauss' Law: Solving Poisson's Equation

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

  2. Example 1: hollow conductorthe charge on its inner surface is equal to the charge enclosed within the hollow,

  3. Example 2: isolated charged conducting plate

  4. Example 3:pair of parallelconducting plates They carry charges of equal magnitude and opposite signs. E=0, except btwn the plates.

  5. 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.

  6. 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.

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