Solution Found!
Rotation fields are usually not conservativea. Prove that
Chapter 13, Problem 55AE(choose chapter or problem)
Rotation fields are usually not conservative
a. Prove that the rotation field \(\mathbf{F}=\frac{\langle-y, x\rangle}{|\mathbf{r}|^{p}}\), where \(\mathbf{r}=\langle x, y\rangle\) is not conservative for \(p \neq 2\).
b. For \(p=2\), show that F is conservative on any region not containing the origin.
c. Find a potential function for F when \(p=2\).
Questions & Answers
QUESTION:
Rotation fields are usually not conservative
a. Prove that the rotation field \(\mathbf{F}=\frac{\langle-y, x\rangle}{|\mathbf{r}|^{p}}\), where \(\mathbf{r}=\langle x, y\rangle\) is not conservative for \(p \neq 2\).
b. For \(p=2\), show that F is conservative on any region not containing the origin.
c. Find a potential function for F when \(p=2\).
ANSWER: