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Homework Help: Electric Potential

  1. Feb 7, 2010 #1
    1. The problem statement, all variables and given/known data

    What is the electric potential at the center of a uniformly charged sphere?

    2. Relevant equations


    3. The attempt at a solution

    Integrate from infinity to the center of the sphere and be sure to account for the changing electric potential. I was told that the answer might be zero, but I believe that that is not right. So, am I right?
  2. jcsd
  3. Feb 7, 2010 #2
    The answer is not zero, so you're right about that. Think about it this way: what if instead of a sphere of continual charge, you had billions of little, positive point charges in the shape of a sphere. You could calculate the voltage of each one and sum them together to get the total voltage at that point. Well, voltage for a positive charge is always positive and never zero. Therefore, all the point charges would always add and never subtract from the voltage at some point p inside the sphere.

    By the way, you know that voltage is the -integral of electric field dx. You also know form Gauss that that sphere of charge up until the surface behaves like a point charge. You also know that the electric field within a conducting sphere is zero. So your voltage calculation is the same as that of a point charge up until r = R (where R is the radius of the sphere) and then the voltage stops becoming bigger - it remains constant throughout the inside of the conductor. This makes sense since the E field is zero in there - it takes no work (no force) to move the charge around at a constant velocity(you needn't push or pull to prevent the electrical force from accelerating it)
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