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Electrostatic Problem at point on a conical surface

  1. Mar 22, 2015 #1
    1. The problem statement, all variables and given/known data
    I am trying to understand a solved problem which is about finding electrostatic potential at point b of the following conical surface with a given surface charge:

    cone.jpg

    I have attached the worked solutions to this post. In the solutions, I don't understand how they have got the expression:

    ##\bar{r}=\sqrt{h^2+r^2-\sqrt{2}hr}##

    3. The attempt at a solution

    I appreciate it if anyone could explain how this expression was obtained.

    Looking at the expression it looks like Pythagoras was used here with ##\bar{r}## being the hypotenuse. But when the vertical side is ##h##, how do we get ##r^2-\sqrt{2}hr## as the other side? I'm very confused here.

    Any helps is greatly appreciated.
     

    Attached Files:

  2. jcsd
  3. Mar 22, 2015 #2

    TSny

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    The triangle formed by ##h##, ##r##, and ##\bar{r}## is not a right triangle. Can you see how the law of cosines can be used to get the expression for ##\bar{r}##?
     
    Last edited: Mar 22, 2015
  4. Mar 23, 2015 #3
    No, how can I use the law of cosines when the triangle is not a right angle? Should I be considering a different triangle? I really have no idea how the expression for ##\bar{r}## was obtained. :confused:
     
  5. Mar 23, 2015 #4

    BvU

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    triang1.jpg express r in ##\mathcal r##
     
  6. Mar 23, 2015 #5

    TSny

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    The law of cosines applies to all triangles, not just right triangles.

    See http://www.mathsisfun.com/algebra/trig-cosine-law.html
     
  7. Mar 23, 2015 #6
    Thank you so much BvU for the diagram. It makes perfect sense now.

    Thank you Tsny, I really appreciate the link.
     
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