Electromotive Force in Closed Path in Electric Field is Zero

Theorem

Let $\mathbf E$ be an electric field acting over a region of space $R$.

Let $\Gamma$ be a closed contour in $R$.

Then the electromotive force in $\Gamma$ is zero.

Proof

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Sources

• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text {II}$: The Products of Vectors: $3$. Line and Surface Integrals