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I Electric potential inside an insulating sphere

  1. Mar 22, 2016 #1
    In the example my textbook has, the electric potential is calculating by integrating the electric field from infinity to R, radius of sphere, and then integrating the electric field from R to r, radius of point inside sphere. What I don't understand is why is the field integrated from infinity to r, why not 0 to r? How do you decide on the reference point? In an uniform electric field, the potential is calculated by integrating from to 0 to r.
     
  2. jcsd
  3. Mar 22, 2016 #2

    Dale

    Staff: Mentor

    The integration is alwaysstarting from your reference (0 potential) location.
     
  4. Mar 22, 2016 #3
    All kinds of potential have an arbitrary zero point, which is essentially a constant of integration. Infinity is just a handy choice of a zero point. Since the field of a charge drops off to 0 at infinity, setting a reference point at infinity is like setting a 0 potential reference point where there is no charge at all.
     
  5. Mar 22, 2016 #4
    What about if you integrated the field from r=0 to r=R, radius of sphere? Why would that ot give you the right answer? Conceptually what is the difference in value?
     
  6. Mar 23, 2016 #5

    Dale

    Staff: Mentor

    You could certainly do that. The result would differ by a constant from the usual formula, which is fine. It would simply mean that you are taking the center as your reference instead of infinity.
     
  7. Mar 23, 2016 #6
    You might find a small problem at r=0.
     
  8. Mar 23, 2016 #7
    So it's just that integrating from infinity is more convenient as the voltage at infinity would be zero, correct?
     
  9. Mar 23, 2016 #8
  10. Mar 23, 2016 #9

    Dale

    Staff: Mentor

    I think that he is considering a sphere of charge, not a point charge. So there shouldn't be a problem at r=0.
     
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