Laplace's Equation/Examples

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Examples of Laplace's Equation

Electric Force in Free Space

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.


Irrotational Motion of Incompressible Fluid

Let $B$ be a body of incompressible fluid.

Let $\mathbf V$ be the vector field which describes the irrotational motion of $B$.

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