Explanation Given: F = 〈 x , y 〉 is a vector field. Formula used: If f is a potential function for the vector field F → then F → = ∇ → f Where, ∇ → = 〈 ∂ ∂ x , ∂ ∂ y 〉 Curl of a vector is given by ∇ → × F → If Curl F → = 0 F → is conservative then potential function exist. If F → = 〈 P , Q 〉 , its scalar curl is given by ∂ P ∂ y − ∂ Q ∂ x If Curl F → ≠ 0 mean F → is not conservative then potential function does not exist. Calculation: F → = 〈 x , y 〉 is conservative as ∂ x ∂ y − ∂ y ∂ x = 0 − 0 = 0 F → = ∇ →

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.1, Problem 39E

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Potential function for the vector field $\vec{F} = 〈 x, y 〉$ by inspection or show that one does not exist.

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Chapter 17.1, Problem 38E

Chapter 17.1, Problem 40E

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Chapter 17 Solutions

CALCULUS (CLOTH)

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Potential function for the vector field F → = 〈 x , y 〉 by inspection or show that one does not exist.

Solution Summary: The author explains that the potential function for F = x, y, is a vector field.

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Potential function for the vector field $\vec{F} = 〈 x, y 〉$ by inspection or show that one does not exist.

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Chapter 17 Solutions

Potential function for the vector field F → = 〈 x , y 〉 by inspection or show that one does not exist.

Solution Summary: The author explains that the potential function for F = x, y, is a vector field.

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Potential function for the vector field F→=〈x,y〉 by inspection or show that one does not exist.

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Chapter 17 Solutions

Potential function for the vector field $\vec{F} = 〈 x, y 〉$ by inspection or show that one does not exist.