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Electromag problem

  1. Nov 20, 2007 #1
    The problem statement, all variables and given/known data

    1, What is the electric field around the conducting sphere of radius R carrying a charge Q?
    2, What is the electric potential at the surface of the sphere if the potential infinately far away is zero?
    3, Hence obtain a formula for the capacitance of the sphere.
    4, Assuming the Earth to be a huge conducting sphere of radius 6.4*10^4 m surrounded by air find the capacitance of the earth.



    The attempt at a solution


    I have a solution for 1 which is E=kQ/r^2. I cannot do the rest of it, although i beleive that I have to use gausses law although i quite simply dont know how to do this. Any helps or suggestions would be more that welcome.

    Many Thanks.
     
  2. jcsd
  3. Nov 22, 2007 #2

    learningphysics

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    Homework Helper

    V(R) - V(infinity) = [tex]-\int_{\infty}^{R}\vec{E}(r)\cdot\vec{dr}[/tex]

    This is just the definition of electric potential.

    V(infinity) = 0, so:

    V(R) = [tex]-\int_{\infty}^{R}\vec{E}(r)\cdot\vec{dr}[/tex]

    Use your formula for E(r) from part a). Solve the integral.
     
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