Equations · equation
Poisson's Equation
Electrostatics · 1813
- Equation
- ∇²φ = −ρ/ε₀
- Field
- Electrostatics
- Named After
- Siméon Denis Poisson
- Year
- 1813
Symbols
φ the electric potential (voltage landscape) · ∇² Laplacian, its curvature · ρ charge density · ε₀ permittivity of free space · with ρ = 0 it is Laplace's equation
Significance
Given where the charge is, find the voltage everywhere — Gauss's law rewritten for the potential, and the workhorse behind capacitor design, semiconductor junctions, and molecular electrostatics. Swap ε₀ for G and it's Newtonian gravity's potential too.
Referenced by
constant
equation
theory
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