Poisson's Differential Equation/Examples
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Examples of Poisson's Differential Equation
General Scenario
Let $R$ be a region of ordinary space.
Let $R$ contain a spatial distribution of sources of flux.
Let $\mathbf V$ be the vector field arising from the sources in $R$.
Then $\mathbf V$ satisfies Poisson's differential equation.
Electric Field of Volume Distribution of Charges
Let $R$ be a region of ordinary space.
Let $R$ contain a volume distribution of particles bearing electric charge.
Let $\mathbf V$ be the vector field arising from these electric charge.
Then $\mathbf V$ satisfies Poisson's differential equation.
Gravitational Force inside Mass
Let $B$ be a body situated in ordinary space.
$B$ consists of a volume distribution of particles with mass.
Let $\mathbf V$ be the vector field arising from these electric charge.
Then $\mathbf V$ satisfies Poisson's differential equation.