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Electric Potential on z-axis due to circular disk

  1. Dec 11, 2013 #1
    1. The problem statement, all variables and given/known data
    Hey guys, I am a little bit confused how my textbook arrived at the answer it did for this particular question. The disk is in the xy-plane with radius b and uniform charge density. They go

    [tex]V=\frac{\rho_S}{4πε}\int_0 ^{2π}\int_0 ^b\frac{r'}{(r'^2+z^2)^{1/2}}dr'd\phi'=\frac{ρ_S}{2ε}[(z^2+b^2)^{1/2}-|z|][/tex]

    Where does the|z| come from? When I evaluate the integral, I do not get that.
    I get
    [tex]\frac{ρ_S}{2ε}[(z^2+b^2)^{1/2}][/tex]
     
    Last edited: Dec 11, 2013
  2. jcsd
  3. Dec 11, 2013 #2

    collinsmark

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    Gold Member

    Try to evaluate your limits again.

    Here is a hint: Evaluating,

    [tex] \sqrt{z^2 + r^2} \ \ \bigg|_{r=0}^b [/tex]
    is not just [itex] \sqrt{z^2 + b^2} [/itex]. :wink:
     
  4. Dec 11, 2013 #3
    !!!!!!!!!!!!!!! Thank you!!!!!!!
     
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