Curl of Gradient is Zero/Examples/Electrostatic Field
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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 $\curl \grad$