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Starting an electrostatic cylinder problem

  1. Nov 19, 2012 #1
    1. The problem statement, all variables and given/known data
    http://img842.imageshack.us/img842/2816/unavngivettz.png [Broken]

    My problem is that I'm confused about a hint I was given in this problem. I usually use the law of cosine to find the length of [itex]\vec{r}-\vec{r'}[/itex] in sphere problems. But the hint I have says that I should make it [itex][r^2 + (z - z_0)^2]^{1/2}[/itex]

    Where could this be coming from? I can't quite get my head around the geometrical idea of this hint. Can't the law of cosine be used here?

    ([itex]\vec{r'}[/itex] is the vector to the charge distribution. [itex]\vec{r}[/itex] is the vector to everywhere in space, but since it is the potential at the axis of the cylinder it is probably what is described as z_0.)

    I have a hard time seeing where there is any right triangle here to use pythagoras approach on.

    (Here is a illustration of the problem:
    http://img820.imageshack.us/img820/3168/unavngivetwj.png [Broken])
    2. Relevant equations
    The volume part of this equation:
    http://img571.imageshack.us/img571/1306/unavngivetmg.png [Broken]

    3. The attempt at a solution
    I'm having trouble starting the problem.
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Nov 19, 2012 #2


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    I think the hint is based on using "cylindrical coordinates" ##(r, \theta, z)## where ##r## is the horizontal distance from the z-axis to the element of charge

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