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Homework Help: Electrostatics problem (Spherical surface)

  1. Nov 17, 2009 #1
    1. The problem statement, all variables and given/known data
    Find the electric field a distance z above the center of a spherical surface of radius R, which carries a uniform charge density "sigma" Treat the case z<R(inside) as well z>R (outside). express your answers in terms of the total charge q on the sphere.[hint:use the law of cosines to write r interms of R and "theta". be sure to take the positive square root:
    sqrt(R^2+z^2-2Rz)=(R-z) if R>z and (z-R) for R<z]

    here is the solution for the problem:
    http://img689.imageshack.us/img689/2492/questionr.jpg [Broken]

    even with the solution i have problem understanding....
    what i don't understand is:
    1) how did he get dq=sigma*R^2*sin(theta)d(theta)d(phi)
    2)the reason for taking cos(curlyphi) ?
    my guess: to get the vertical component? since horizontal components cancels out
    3)is there a different way looking at this problem? i remember in college there is a simpler way doing this kind of problem....
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Nov 17, 2009 #2


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    Homework Helper

    1. R*sinθ*dφ and R*dθ are the length and width of the area da where the charge dq lies.
    2. You are correct.
    3. Yes, you could use Gauss' Law. This problem must be at a point in your course where you have not taken Gauss' Law - and it is good practise!
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