Curl of Gradient is Zero/Examples/Electrostatic Field

Example of Use of Curl of Gradient is Zero
Let $R$ be a region of space in which there exists an electric potential field $F$.

From Electric Force is Gradient of Electric Potential Field, the electrostatic force $\mathbf V$ experienced within $R$ is the negative of the gradient of $F$:


 * $\mathbf V = -\grad F$

Hence from Curl of Gradient is Zero, the curl of $\mathbf V$ is zero.