Explanation Given: Curl and Divergence of a vector field are given as: C u r l ( F ) ( 0 , 0 , 0 ) = 〈 2 , − 1 , 4 〉 D i v ( F ) ( 0 , 0 , 0 ) = − 2 Formula used: As per vector form of Green’s Theorem: ∮ C F . d r = ∬ S C u r l ( F ) ⋅ d S Calculation: We can rewrite the given line integral using Green’s Theorem: ∮ C F . d r = ∬ S C u r l ( F ) ⋅ d S We have been given the value of curl at origin to be: C u r l ( F ) ( 0 , 0 , 0 ) = 〈 2 , − 1 , 4 〉 For the xy plane, we can set up, d S = 〈 0 , 0 , 1 〉 d A Thus, the surface integral gets converted to: ∮ C F . d r = ∬ S C u r l ( F ) ⋅ d S ∮ C F ...

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 18, Problem 29CRE

To determine

To estimate:

The value of $\oint_{C} F . d r$ where C is the circle of radius $0.03$ in xy-plane centered at origin.

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Chapter 18, Problem 28CRE

Chapter 18, Problem 30CRE

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Chapter 18 Solutions

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To estimate: The value of ∮ C F . d r where C is the circle of radius 0.03 in xy -plane centered at origin.

Solution Summary: The solution is to estimate the value of C F. d r is the circle of radius 0.03 in xy -plane centered at origin.

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To estimate:

The value of $\oint_{C} F . d r$ where C is the circle of radius $0.03$ in xy-plane centered at origin.

Want to see the full answer?

Chapter 18 Solutions

To estimate: The value of ∮ C F . d r where C is the circle of radius 0.03 in xy -plane centered at origin.

Solution Summary: The solution is to estimate the value of C F. d r is the circle of radius 0.03 in xy -plane centered at origin.

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To estimate: The value of ∮CF.dr where C is the circle of radius 0.03 in xy-plane centered at origin.

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Chapter 18 Solutions

To estimate:

The value of $\oint_{C} F . d r$ where C is the circle of radius $0.03$ in xy-plane centered at origin.