Explanation Given information: The vector field is F ( x , y ) = 〈 x 2 x 2 + y 2 , y 2 x 2 + y 2 〉 . Concept used: If curl of F is zero then the vector field has potential function. Consider the function. F 2 = y 2 x 2 + y 2 ..... (1) Differentiate equation (1) with respect to x partially. ∂ F 2 ∂ x = y 2 ∂ ∂ x ( 1 x 2 + y 2 ) = − 2 y 2 x ( x 2 + y 2 ) 2 ..... (2) Consider the function. F 1 = x 2 x 2 + y 2 ..... (3) Differentiate equation (3) with respect to y partially. ∂ F 1 ∂ y = x 2 ∂ ∂ y ( 1 x 2 + y 2 ) = − 2 x 2 y ( x 2 + y 2 ) 2

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ISBN: 9781319055844

Author: FRANZOSA

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Chapter 17.3, Problem 33E

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To find: Whether the vector field has a potential function or not.

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Chapter 17.3, Problem 32E

Chapter 17.3, Problem 34E

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Chapter 17 Solutions

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Whether the vector field has a potential function or not.

Solution Summary: The author evaluates whether the vector field has a potential function. If the curl of F is zero, then it has potential functions.

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To find: Whether the vector field has a potential function or not.

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Chapter 17 Solutions