Poisson's Differential Equation/Examples/Electric Field of Volume Distribution of Charges
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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.
Sources
- 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {V}$: Further Applications of the Operator $\nabla$: $7$. The Classification of Vector Fields: $\text {(ii)}$