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

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(pwa sonz&#x2019;) In a space where the source density is &#x03C1;, the Laplacian of a potential ''U'' is  
 
(pwa sonz&#x2019;) In a space where the source density is &#x03C1;, 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 4&#x03C0; is deleted in some systems. In empty space where &#x03C1;=0, this becomes Laplace&#x2019;s equation. Named for Simeon Denis Poisson (1781&#x2013;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 4&#x03C0; is deleted in some systems. In empty space where &#x03C1;=0, this becomes Laplace&#x2019;s equation. Named for Simeon Denis Poisson (1781&#x2013;1840), French mathematician.
 
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Revision as of 16:24, 14 February 2019

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(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.