Explanation No work done in displacement from a point A to another point in the field and back to Aand the mechanical energy is conserved. i.e., ∮ F ⋅ d R = 0 , the field is said to be conservative. Every irrotational field is conservative. c u r l F = 0 , then vector field is irrotational. The field is irrotational the vector F can be expressed as the gradient of a scalar potential ϕ i.e., F = g r a d ϕ ⇒ F = ∇ ϕ Given: F = ( x e 2 x , y e 2 z , z e 2 y ) is the vector point function. Formula used: F = F 1 i + F 2 j + F 3 k Curl of a continuously differentiable vector point function F is c u r l F = ∇ × F = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z F 1 F 2 F 3 | Calculation: The components of the vector F are F 1 = x e 2 x , F 2 = y e 2 z , F 3 = z e 2 y c u r l F = ∇ × F = | i j k ∂ ∂ x ∂ ∂ y ∂ ∂ z x e 2 x y e 2 z z e 2 y | , expanding 3 × 3 determinant by 1 st row = i ( ∂ ∂ y ( z e 2 y ) − ∂ ∂ z ( y e 2 z

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

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Chapter 17, Problem 26CRE

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Whether the vector field is conservative, if so find potential function.

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Chapter 17 Solutions

CALCULUS W/SAPLING ACCESS >IC<

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Whether the vector field is conservative, if so find potential function.

Solution Summary: The author explains that if the vector field is conservative, the mechanical energy is conserved. If c u r l F = 0, then it is irrotational.

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Chapter 17 Solutions