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Chapter 14: Q. 36 (page 1096)

Show that the vector fields in Exercises 33鈥�40 are not conservative.

G(x,y)=yi-xj

Short Answer

Expert verified

The vector fields is not conservative because 鈭�G1鈭�y鈮�鈭�G2鈭�x.

Step by step solution

01

Step 1. Given Information

We have to show that the vector fields in the given exercise is not conservative.
G(x,y)=yi-xj

02

Step 2. A vector field G(x,y)=(G1(x,y),G2(x,y)) is not conservative if and only if ∂G1∂y≠∂G2∂x.

For the vector field

鈭�F1鈭�y=鈭�鈭�yy鈭�F1鈭�y=1

03

Step 3. Now finding ∂F2∂y

鈭�F2鈭�x=鈭�鈭�x(鈭�x)鈭�F2鈭�x=-1

Hence, 鈭�G1鈭�y鈮�鈭�G2鈭�x.

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