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Poisson's & Laplace's Equations — Boundary-Value Problems
Inside this lesson
- Derive Poisson's equation by substituting E = −∇V into the differential form of Gauss's law
- Identify Laplace's equation as the charge-free special case
- State the uniqueness theorem and explain its practical significance for boundary-value problems
- Solve the parallel-plate boundary-value problem V(x) = V₀x/d and extract the uniform electric field
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Educational content covering topics typical of a first- and second-year electrical engineering curriculum. Not a substitute for accredited coursework, and not suitable for real antenna, transmission-line, or signal-processing system design without review by a licensed professional engineer.