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Charge staggered over spherical volume.

  1. May 17, 2015 #1
    1. The problem statement, all variables and given/known data
    There is charge placed in a volume of a sphere, whose density changes by expression ρ(r)=ρ0a/r for 0<r≤a and ρ(0)=0. Where a and ρ0 are known variables , and r is a distance from the origin. Determine the potential of the point A(0,0,0) with regard to reference point at infinity.

    2. Relevant equations
    Gaussian law.

    3. The attempt at a solution
    I solved it this way:

    I separated potential into two parts like this:
    формула за потенцијал у задатку.png
    since there is different expression for changing of electric field at arbitrary point whose distance from origin is less than a, than for those whose distance is greater than a.

    For finding E i used Gaussian law,
    and this is what i got for E1:

    лијева страна.png
    десна страна.png прво поље.png

    Doing the same thing for the r greater than a, i got expression for E2 (difference is that i had different limits of integration when finding charge , it was from 0 to a instead of r since i took all of the charge there is):
    друго поље.png
    Placing it into first expression i got:

    укупни потенцијал.png

    Now my question is, is this correct, i mean is this correct approach for finding potential in examples like this?
     
  2. jcsd
  3. May 17, 2015 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    Everything looks good!
     
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