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January 3rd, 2017, 07:24 AM   #1
Joined: Oct 2016
From: Sverige

Posts: 28
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Integrate over sphere issue (URGENT)

So I'm suppose to integrate over a sphere w. radius 3.
It has the surface charge
$\displaystyle w = e^r * sinu * sin^2v$

To integrate I want to find:
n dS, n being normal vector, dS delta surface aka. du dv.

Normal vector = sphere coordinate normalized =
$\displaystyle n = (sinu * cosv, sinu*sinv, cosu)$
$\displaystyle n dS = n dudv$ ??

But in my book they get:
$\displaystyle ndS = (+- r^2sinu, 0, 0)$

I have no idea how they just deleted 2 out of 3 axis when integrating over a sphere.

All help is appreciated, got final exam in less than a week.
Addez123 is offline  
January 3rd, 2017, 08:45 AM   #2
Math Team
Joined: Jan 2015
From: Alabama

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In spherical coordinates, the radial axis is perpendicular to the sphere so the $\displaystyle \theta$ and $\displaystyle \phi$ components (called "u" and "v" here) are 0.
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