Prove that if (mathbf{F}) is a gradient vector field, then the flux of (operatorname{curl}(mathbf{F})) through a smooth

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Prove that if $\mathbf{F}$ is a gradient vector field, then the flux of $\operatorname{curl}(\mathbf{F})$ through a smooth surface $\mathcal{S}$ (whether closed or not) is equal to zero.

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Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

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Question Posted: Jan 28, 2024 12:03 AM

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Prove that if (mathbf{F}) is a gradient vector field, then the flux of (operatorname{curl}(mathbf{F})) through a smooth

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This proof can be completed through a couple steps using the properties of vector calculus specifica...View the full answer

Calculus

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