?For the following exercises, consider the radial fields \(\mathbf{F}=\frac{\langle x
Chapter 6, Problem 325(choose chapter or problem)
For the following exercises, consider the radial fields \(\mathbf{F}=\frac{\langle x, y, z\rangle}{\left(x^{2}+y^{2}+z^{2}\right)^{\frac{p}{2}}}=\frac{\mathbf{r}}{|\mathbf{r}|^{p}}\) , where p is a real number.
Let S consist of spheres A and B centered at the origin with radii 0 < a < b. The total outward flux across S consists of the outward flux across the outer sphere B less the flux into S across inner sphere A.
Show that for p = 3 the flux across S is independent of a and b.
Text Transcription:
F = langle x, y, z rangle / (x^2 + y^2 + z^2)^pi/2 = r / |r|^p
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