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Potential of all space from sphere

  1. Mar 26, 2009 #1
    1. The problem statement, all variables and given/known data
    Consider a sphere or radius a. The top hemisphere has a uniform charge density [tex]\sigma[/tex], the bottom has -[tex]\rho[/tex]. Calculate the electric potential in all space.[tex]\sigma[/tex]


    2. Relevant equations
    Laplace's Equation:
    [tex]\nabla[/tex][tex]^{2}[/tex]=-4[tex]\pi\sigma[/tex]

    Potential (solved from Laplace's Equation):
    V=[tex]\int\frac{\rho(r)}{r}[/tex]d[tex]\tau[/tex]


    3. The attempt at a solution
    I solved laplace's equation to get the potential is the integral over rho/r. I want to integrate from 0 to a, and then a to R; where R is some arbitrary point. I want to just plug in [txt]\sigma[txt] times a, for the charge, and integrate it over r.

    I'm not sure how to treat the -[txt]\sigma[txt]. Any ideas?
     
  2. jcsd
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