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.

Sources

• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {V}$: Further Applications of the Operator $\nabla$: $2$. The Operator $\curl \grad$