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Just need a check Finding total charge when given distribution

  1. Sep 15, 2010 #1
    1. The problem statement, all variables and given/known data

    We have a sphere (radius R) where charge is placed inside of it, ρ(r)=ρ0 cos(θ/3) sin(φ/2). Find the total charge. Your answer will be in terms of R and p0.


    2. Relevant equations



    3. The attempt at a solution


    I think I did it correctly, but I would just like to make sure I did (and thus ensure my understanding). My answer is marked by the star, and everything below it is just my integration work that was required by the problem.
     

    Attached Files:

  2. jcsd
  3. Sep 15, 2010 #2

    gabbagabbahey

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    I think you'll want to double check your integration of

    [tex]\int_0^{\pi}\cos\left(\frac{\theta}{3}\right)\sin\theta d\theta[/tex]
     
  4. Sep 15, 2010 #3
    Hmm I tried to go over it again and I got the same result. Was it somewhere on the first integration by parts where I messed up? Thanks
     
  5. Sep 15, 2010 #4
    Ohhh I was double checking the wrong part. I ended up making a mistake at the very bottom. It changed my result from that integration to 27/16 and my final answer is now...

    (Rho)(R^3)(9/4) C

    I hope this should be correct now....
     
  6. Sep 15, 2010 #5

    gabbagabbahey

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    Looks good to me.

    For future reference, you could have avoided IBP by using a trig identity:

    [tex]\sin\theta\cos\left(\frac{\theta}{3}\right)=\frac{\sin\left(\frac{4\theta}{3}\right)+\sin\left(\frac{2\theta}{3}\right)}{2}[/tex]
     
  7. Sep 15, 2010 #6
    Ohh ok thanks. I don't even think I have ever come across that identity before.
     
  8. Sep 16, 2010 #7

    gabbagabbahey

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    Its just an application of the identity

    [tex]\sin\theta\cos\left(\phi\right)=\frac{ \sin\left(\theta+\phi)+\sin\left(\theta-\phi\right)}{2}[/tex]
     
  9. Sep 16, 2010 #8
    Oh ok thanks a lot.
     
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