Explanation Key concept applied: Curl of a gradient vector field is zero. Proof: We can represent the flux of C u r l ( F ) as: ∬ S C u r l ( F ) ⋅ d S But we know that F is a gradient vector field. Thus curl of it must be zero. Hence, we get, ⇒ ∬ S C u r l ...

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ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 18, Problem 17CRE

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To prove:

If F is a gradient vector field, then flux of $C u r l (F)$ through a smooth surface S is equal to zero.

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Chapter 18, Problem 16CRE

Chapter 18, Problem 18CRE

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Chapter 18 Solutions

CALCULUS (CLOTH)

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To prove: If F is a gradient vector field, then flux of C u r l ( F ) through a smooth surface S is equal to zero.

Solution Summary: The author explains that if F is a gradient vector field, then flux of C u r l ( F ) through the smooth surface S is equal to zero.

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To prove:

If F is a gradient vector field, then flux of $C u r l (F)$ through a smooth surface S is equal to zero.

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Chapter 18 Solutions

To prove: If F is a gradient vector field, then flux of C u r l ( F ) through a smooth surface S is equal to zero.

Solution Summary: The author explains that if F is a gradient vector field, then flux of C u r l ( F ) through the smooth surface S is equal to zero.

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To prove: If F is a gradient vector field, then flux of Curl(F) through a smooth surface S is equal to zero.

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Chapter 18 Solutions

To prove:

If F is a gradient vector field, then flux of $C u r l (F)$ through a smooth surface S is equal to zero.