Recent content by PowerWill

What do I do with the arctan at infinity? Do I just use \frac{\pi}{2} or do I have to be saucy about it?

You'll want to start by doing a quick graph of 2-x^3 and tan x. For (a), find where the two functions and the x-axis form a completely enclosed region. Use the points where these functions intersect each other and the x-axis as the limits for your integration, and simply integrate (you'll have...

Left my integral table at home, could someone tell me the value of these integrals? \int_0^{\infty} \frac{dx}{(x^2+b^2)^2} \int_0^{\infty} \frac{x^2}{(x^2+b^2)^2} dx and the same as the latter but with the denominator raised to the power 4. Thanks!

Dexter...you need to drop the intensity down a notch. And to the ninja, just convert x^2 + y^2 to r^2 and integrate over the same area in cylindrical.

That's cylindrical coordinates, sorry

Converting to rectangular coordinates would probably be easier

Nevermind I got it...I was trying to use spherical coordinates all the way through instead of the spherical components of the rectangular coordinates

I'm still rather confused...should I calculate the dot product by components or say it equals pcos \acute{\theta} and then try to find some weird relation between theta prime and theta? Or perhaps I'm missing something? Cuz either way I keep getting lost.

Working on Griffiths 3.33. I'm supposed to show that the Electric Field of a pure dipole can be written in the following coordinate free form: \vec{E}(\vec{r}) = \frac{1}{4 \pi \epsilon_0 r^3} [3(\vec{p} \cdot \hat{r})\hat{r} - \vec{p}] Where p is the dipole. I know that the potential...