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Finding electric potential between two concentric spheres.

  1. Mar 18, 2017 #1
    1. The problem statement, all variables and given/known data
    A spherical shell with inner radius A and outer radius 3A which has a uniform charge density, i.e charge per unit volume, p0. Find difference in electric potential between the center of the shell and a point a distance 2A from the center.

    2. Relevant equations
    The answer given is. -(p0A2)/3ε0

    3. The attempt at a solution
    I am completely lost as to what I'm supposed to do here. I would think you'd find the potential at 2A and subtract it from that at the center. But how exactly do you do that?
    I integrated the elctric field due to a charged sphere along 2A to A. So that makes:
    ∫E dr= ∫(ρr)/3ε0)dr=V
    That makes:

    [(ρr2)/6ε)] from 2A to A which does not equal the answer.
    I think I'm stumped here. Any help would be greatly appreciated!
  2. jcsd
  3. Mar 18, 2017 #2


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    Welcome to PF!

    Your expression for the electric field does not look correct. E for a uniformly charged shell is different than E for a uniformly charged solid sphere.
  4. Mar 18, 2017 #3
    I was not aware of the difference. I'll look it up.
  5. Mar 18, 2017 #4


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    Or, apply Gauss' law to find E inside the shell.
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