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Homework Help: Why is the potential at the surface zero in this question...

  1. Sep 4, 2016 #1
    1. The problem statement, all variables and given/known data

    Consider an isotropic, homogenous dielectric sphere of radius R and constant relative permittivity ε, also permeated by a uniform free charge density ρ. Give an expression for the electrostatic potential V at the centre of the sphere by line integration of the electric field

    2. Relevant equations
    ∫∫ D ⋅ dA = ∫∫∫ ρ dV

    D = E εε0
    3. The attempt at a solution

    Using ∫∫ D ⋅ dA = ∫∫∫ ρ dV

    D × 4πr2 = ρ 4 πr3 / 3

    D = ρr / 3

    Using D = E εε0

    E = ρr / 3 εε0

    My example answer states the following ' Assuming the potential at the surface is zero, and using a line integral to find potential V

    V = - ∫ E ⋅ dl = ∫R0 ρr / 3 εε0 ⋅dr

    Why is the potential the surface be zero? Also the potential at infinity is suppose to be zero so how can we also have zero at the surface

    I know that a single charge has E =0 at the centre and it decreases radially out, but this question I am clueless
    Last edited: Sep 4, 2016
  2. jcsd
  3. Sep 4, 2016 #2
    i can not visualize the statement...pl. attach a copy of the exact page.

    (one guess is there: assume R to be very large then one can take the potential to be vanishingly small and then can calculate the work done)

    pl. you may take help of the following -page-23 of
    Last edited: Sep 4, 2016
  4. Sep 4, 2016 #3


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    You can arbitrarily set the zero of potential anywhere you like. You can choose to set the zero to be at infinity or at the surface, but once you make a choice, you have to be consistent. If the potential is zero at the surface, it's not going to be zero at infinity.
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