Laplace's Equation/Examples/Electric Force in Free Space

Example of Laplace's Equation

Let $R$ be a region of free space.

Let $\mathbf V$ be an electric force in a given electric field over $R$.

Then $\mathbf V$ satisfies Laplace's equation.

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: $\text {(i)}$