Radial fields and spheres Consider the radial field F = r/

Chapter 11, Problem 60E

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QUESTION:

Consider the radial field \(\mathbf{F}=\mathbf{r} /|\mathbf{r}|^{P}\), where \(\mathbf{r}=\langle x, y, z\rangle\) and p is a real number. Let S be the sphere of radius a centered at the origin. Show that the outward flux of F across the sphere \(4 \pi / a^{p-3}\). It is instructive to do the calculation using both an explicit and parametric description of the sphere.

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QUESTION:

Consider the radial field \(\mathbf{F}=\mathbf{r} /|\mathbf{r}|^{P}\), where \(\mathbf{r}=\langle x, y, z\rangle\) and p is a real number. Let S be the sphere of radius a centered at the origin. Show that the outward flux of F across the sphere \(4 \pi / a^{p-3}\). It is instructive to do the calculation using both an explicit and parametric description of the sphere.

ANSWER:

Solution  60E

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