Poisson's Differential Equation/Examples/Electric Field of Volume Distribution of Charges

Example of Poisson's Differential Equation
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.

An example of such a scenario is a thermionic tube.