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Finding radius a of non-conducting spherical shell

  1. Jun 12, 2012 #1
    1. The problem statement, all variables and given/known data

    A non-conducting spherical shell is uniformly charged.
    The electrostatic potential [itex]\phi[/itex] at the centre of the sphere is [itex]\phi[/itex]1 = 200V
    The potential at distance r = 50cm from the centre is [itex]\phi[/itex]2 = 40V
    Find the radius of sphere: a

    2. Relevant equations

    I seem to have missed this lecture.

    3. The attempt at a solution

    I understand that the potential (V) is a function of r (distance from centre) and satisfies:

    V(0) = 200V
    V(50) = 40V
    V(a) = 0V

    I've been reading up on this, but I can't seem to make sense out of this question. I can't seem to find a case for non conducting spherical shell. Would someone mind providing me a formula and clear steps to solve this problem?

    Thank you!
     
  2. jcsd
  3. Jun 12, 2012 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The "non-conducting" just means that you don't have to worry about the charge moving! Yes, V is a function of r- more specifically it is [itex]C/r^2[/itex].

    So you have [itex]C/r^2= 200[/itex] and [itex]C/(r- 40)^2= 40[/itex], two equations you can solve for C and r.

    Since you really only want to solve for r, I would recommending dividing one equation by another to eliminate C.
     
  4. Jun 13, 2012 #3
    Thanks for the quick reply!!! I understand how to do the question now. is C just some constant? Or is it charge (Q)?

    Not that it matters in this question but I'm certain I need to know this for other stuff.

    Thanks again!!!
     
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