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Potential Due to a Charged non conducting sphere

  1. Apr 15, 2010 #1
    1. The problem statement, all variables and given/known data

    \bold{V}\ =\ \frac{Q\,(3R^2\ -\ r^2)}{4\,\pi\,\varepsilon_0 \ \ {2R^3}}

    Potential inside the sphere.
    2. Relevant equations

    Electric field inside the sphere (non conducting):

    \bold{E}\ =\ \frac{Q.r}{4\,\pi\,\varepsilon_0\,R^3}


    \bold{V}\ = \int E.dr[/tex]

    In one dimension.
    3. The attempt at a solution

    Even when we use both the formula's I've given we don't get the one given in the book. Does anybody here have some suggestion to find, how they have derived it.
  2. jcsd
  3. Apr 15, 2010 #2
    How have you used the formulae you are given? What have you tried to do?

    Note that to calculate the potential you must integrate from infinity up to the point that you're concerned about - in this case the formula for the electric field changes between infinity and your point.
  4. Apr 15, 2010 #3
    Electric field is zero inside charged conducting sphere but not in the case of non conducting sphere.
  5. Apr 15, 2010 #4
    Yes, sorry, I misread your post - I've edited it now.
  6. Apr 15, 2010 #5
    Thanks, It is solved now. Actually we have to calculate it in two steps. work required to bring unit positive charge from infinity to the surface and then from surface to some point inside the sphere.

    BTW, thanks once again gadje. Sometime a very small hint can trigger our mind.
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