Explanation Given information: The given field is F = 〈 x , y , z 〉 . Concept used: We use the concept that a potential function f ( x , y , z ) of the vector field F = 〈 f 1 , f 2 , f 3 〉 exists if it is conservative i.e. c u r l F = 0 and the potential function satisfies f ( x , y , z ) = ∫ f 1 d x , f ( x , y , z ) = ∫ f 2 d y , f ( x , y , z ) = ∫ f 3 d z The curl of the function is given by c u r l F = ∇ × F = ( ∂ f 3 ∂ y − ∂ f 2 ∂ z ) i − ( ∂ f 3 ∂ x − ∂ f 1 ∂ z ) j + ( ∂ f 2 ∂ x − ∂ f 1 ∂ y ) k Calculation: As given F = 〈 x , y , z 〉 , first we check if the potential function exists. Therefore, we find c u r l F = ∇ × F = ( ∂ z ∂ y − ∂ y ∂ z ) i − ( ∂ z ∂ x − ∂ x ∂ z ) j + ( ∂ y ∂ x − ∂ x ∂ y ) k = 0 i + 0 j + 0 k = 0 Thus, c u r l F = 0

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ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17.3, Problem 7E

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To find: The potential function of the given vector field F=〈x,y,z〉 if it exist.

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Chapter 17.3, Problem 6E

Chapter 17.3, Problem 8E

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Chapter 17 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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The potential function of the given vector field F = 〈 x , y , z 〉 if it exist.

Solution Summary: The author uses the concept that a potential function of the given vector field F=langle x,y,zrangle exists if it is conservative.

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To find: The potential function of the given vector field F=〈x,y,z〉 if it exist.

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Chapter 17 Solutions