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January 3rd, 2017, 07:24 AM  #1 
Member Joined: Oct 2016 From: Sverige Posts: 32 Thanks: 2  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. 
January 3rd, 2017, 08:45 AM  #2 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,878 Thanks: 766 
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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integrate, issue, sphere, urgent 
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