Poisson’s and Laplace’s Boundary Value Problems: Potential Theory
In this chapter we study the interaction of electrostatic potentials with material media. A typical problem would be to determine the electrostatic field or potential in the vicinity of a conductor or dielectric in the presence of sources. These types of problems are very important for several reasons. First, many important electrical quantities, such as capacitance and resistance, can be determined using the methods developed in this chapter. Also, electrostatic principles are directly utilized in a variety of important technologies, such as photocopying, electrostatic cleaning and purification, and electrostatic protection. Furthermore, slowly varying electrodynamic fields can often be approximated as being electrostatic or quasi-static, greatly simplifying analysis methods.
KeywordsNeumann Problem Eigenfunction Expansion Exterior Problem Interior Problem Homogeneous Dirichlet Condition
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