# Difference between revisions of "Dictionary:Poisson’s equation"

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(pwa sonz’) In a space where the source density is ρ, the Laplacian of a potential ''U'' is | (pwa sonz’) In a space where the source density is ρ, the Laplacian of a potential ''U'' is | ||

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{\nabla}^2 U = 4 \pi \rho K, | {\nabla}^2 U = 4 \pi \rho K, | ||

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where <math>\nabla</math> is the operator del and ''K'' is a constant (the gravitational constant in the case of mass and gravitational potential). The constant 4π is deleted in some systems. In empty space where ρ=0, this becomes Laplace’s equation. Named for Simeon Denis Poisson (1781–1840), French mathematician. | where <math>\nabla</math> is the operator del and ''K'' is a constant (the gravitational constant in the case of mass and gravitational potential). The constant 4π is deleted in some systems. In empty space where ρ=0, this becomes Laplace’s equation. Named for Simeon Denis Poisson (1781–1840), French mathematician. | ||

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## Latest revision as of 16:24, 14 February 2019

(pwa sonz’) In a space where the source density is ρ, the Laplacian of a potential *U* is

where is the operator del and *K* is a constant (the gravitational constant in the case of mass and gravitational potential). The constant 4π is deleted in some systems. In empty space where ρ=0, this becomes Laplace’s equation. Named for Simeon Denis Poisson (1781–1840), French mathematician.