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Simpleton's Thread with Problems

  1. Sep 10, 2009 #1
    Hi, here are a list of questions I have doubts about (I do not want to create one for every problem so as not the spam the forum)

    Q1.
    1. The problem statement, all variables and given/known data
    My senior gave me this problem.

    Given that the Earth's radius at the equator is Re, and the radius at the poles is Rp, express the ratio Re/Rp in terms of known constants.


    2. Relevant equations
    I have no idea how to do this problem at all. I don't even know where to start. I asked my senior and he said that over a sufficiently long timescale the rocky material of the earth can be taken to inelastically deform like a fluid. I don't get that how this information helps :(. Can someone tell me how you even start on these kind of problems?

    3. The attempt at a solution
    No Attempt.

    Q2.
    1. The problem statement, all variables and given/known data
    The problem I am talking about is this:

    Given a charged solid sphere with charge density rho and radius R, find the total electrical potential energy in the sphere.

    2. Relevant equations
    See below.

    3. The attempt at a solution
    I found the answer to this problem on this forum.

    You start from a small charged sphere of radius r. The amount of charge in it is 4/3*pi*r^3*rho. Then you add a small shell of charge over it, and you find the potential energy. This small shell will have a charge of 4*pi*r^2*dr*rho. Therefore, the potential energy between the sphere and the shell will be:

    k*4/3*pi*r^3*rho*4*pi*r^2*dr*rho/r = k*16/3*pi^2*rho^2*r^4^dr

    Integrating this from 0 to R, you get k*16/15*pi^2*rho^2*r^5

    However, what happens to the potential energy that is within the shell itself? I believe that there should be potential energy between the charges in each shell too, but it does not seem to be taken into account in this solving method.

    Q3)
    1. The problem statement, all variables and given/known data
    Find the potential energy of different charged geometric shapes with charge density rho (a line of charges, a sheet of charges, a pyramid, a square etc...)

    2. Relevant equations
    U = qV
    Gauss Law? integral E dA = Q/Eo

    3. The attempt at a solution
    I tried doing it for a line in the way the potential energy for the circle is done. I imagine I already have a rod, and I add a tiny bit to the top. However, in the sphere case, I can treat the sphere already there as a point charge, and so I can add the shell of charge easily. However, I don't know how to do so if it is a line, a sheet etc, as there seems to be no symmetry and stuff I can take advantage of.

    EDIT: For Q3, I think I just need some guidance, and maybe 1 sample solution to one of the problem. Then I try to work out the rest myself and post my answer here to see whether it is correct. Thanks.

    Thanks in advance.
     
    Last edited: Sep 10, 2009
  2. jcsd
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