Poisson's Differential Equation/Examples

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.