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- #1

- Apr 13, 2013

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I am given the following exercise:

"Calculate the work and the flux for the path $C: a \cos{\theta}\hat{i}+a \sin{\theta}\hat{j}, 0 \leq \theta \leq \frac{\pi}{2}$ , knowing that $\overrightarrow{F}=x\hat{i}+y\hat{j}$. "

To solve this I thought that I could use the Green's Theorem,like that:

To calculate the work,I did the following:

$$ \oint_C{\overrightarrow{F}}dR=\int \int_R {\nabla \times \overrightarrow{F} \cdot \hat{n}}dA=\iint_R {\nabla \times \overrightarrow{F} \cdot \hat{k}}dA=\iint_R {0}dA=0$$

Is the result for the work correct?

And,for the flux,I tried this:

$$ \oint_C{\overrightarrow{F} \cdot \hat{n}}ds=\iint_R{\nabla \cdot \overrightarrow{F}}dA=\iint_R{2}dA$$

How can I continue to find the flux?