Charge Density Triple Integral to infinity

Asked Apr 07 '14 at 02:46

Active Apr 07 '14 at 02:52

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OK, I'm given a charge density function $\displaystyle \frac{2\cdot10^{-4}}{1 + \rho^3}$, and the spherical coordinate of $0 \le \rho < \infty$. Task: find total charge of cloud.

Is the answer the following?

$$\int_0^{2\pi} \int_0^{\pi} \int_0^{\infty} \frac{2\cdot10^{-4}}{1+\rho^3} \rho^2 \sin \phi d\rho d\phi d\theta$$

If I set the problem up this way, the triple integral appears to diverge, which doesn't make sense because the charge density function definitely converges.

This is for Calc III

Thank you

edited Apr 07 '14 at 02:52

2012ssohn

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asked Apr 07 '14 at 02:46

Tony

It does diverge because you should end up with $\ln(1 + \rho^3)$ which does diverge. – Jared Apr 07 '14 at 02:53
So the issue is "How do I find the charge of the cloud if the integral diverges?" – Tony Apr 07 '14 at 02:58
Wait. I don't need p^2 and sin(phi) unless I'm converting from rectangular, do I? Is that where I screwed up? – Tony Apr 07 '14 at 03:00
You didn't screw up. The integral diverges, and hence the total charge is infinity. – Stephen Montgomery-Smith Apr 07 '14 at 03:09
Well, then, THANKS!! I didn't know that was a possible answer. Wish I could have the last two hours of my life back! – Tony Apr 07 '14 at 03:13

Charge Density Triple Integral to infinity

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