   Chapter 16, Problem 6RCC

Chapter
Section
Textbook Problem

(a) What does it mean to say that ∫C F · dr is independent of path?(b) If you know that ∫C F · dr is independent of path, what you say about F?

(a)

To determine

To explain: The independent of path of CFdr.

Explanation

Calculation:

Consider a smooth curve C which is given by vector r(t) in a region D={atb}.

Consider function f is differentiable and the gradient of f (f) is continuous on curve C.

The line integral over the curve C is,

CFdr=f(r(b))f

(b)

To determine

To explain: The field vector F, if the CFdr  is independent of path.

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