Solution Found!
Radial fields and spheres Consider the radial field F = r/
Chapter 11, Problem 60E(choose chapter or problem)
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.
Questions & Answers
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
Step 1