4: Electric Field Boundary Value Problems
- Page ID
- 48135
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- 4.1: The Uniqueness Theorem
- Consider a linear dielectric material where the permittivity may vary with position:
- 4.2: Boundary Value Problems in Cartesian Geometries
- For most of the problems treated in Chapters 2 and 3 we restricted ourselves to one-dimensional problems where the electric field points in a single direction and only depends on that coordinate.
- 4.3: Separation of Variables in Cylindrical Geometry
- Product solutions to Laplace's equation in cylindrical coordinates
- 4.4: Product Solutions in Spherical Geometry
- In spherical coordinates, Laplace's equation is
- 4.5: A Successive Method - Numerical Relaxation
- In many cases, the geometry and boundary conditions are irregular so that closed form solutions are not possible. It then becomes necessary to solve Poisson's equation by a computational procedure. In this section we limit ourselves to dependence on only two Cartesian coordinates.
The electric field distribution due to external sources is disturbed by the addition of a conducting or dielectric body because the resulting induced charges also contribute to the field. The complete solution must now also satisfy boundary conditions imposed by the materials.
Thumbnail: Electric field lines due to a point charge in the vicinity of PEC regions (shaded) of various shapes. (CC BY SA 4.0; K. Kikkeri).