- #1

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## Homework Statement

Find the divergence of [tex]\vec v = \frac{\hat{v}}{r}[/tex]

Then use the divergence theorem to look for a delta function at the origin.

## Homework Equations

[tex] \int ∇\cdot \vec v d\tau = \oint \vec v \cdot da [/tex]

## The Attempt at a Solution

I got the divergence easy enough: [tex] \frac{1}{r^2} [/tex]

And, really I have the integrals set up as well. But I'm getting hung up on my limits:

[tex] \int \frac {1}{r^2} d\tau = \oint \frac {1}{r} da [/tex]

[tex] \int_0^?\int_0^?\int_0^R \frac {1}{r^2} (r^2 sin(\theta) dr d\theta d\phi = \oint_0^?\oint_0^? \frac {1}{R} (R^2 sin(\theta) d\theta d\phi [/tex]

These are easy integrals so my only issue is limits. To me it seems like Phi and Theta should be 2 pi. But I know that when we did integrals with hemispheres that the integration was from 0 to half pi. Though, I felt it should have been to pi there instead. Essentially, my issue is visualization of this.