Why is the potential at the surface zero in this question....

[JaneHall89]

Homework Statement

[/B]
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

Homework Equations

∫∫ D ⋅ dA = ∫∫∫ ρ dV

D = E εε₀

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

 

[drvrm]

Assuming the potential at the surface is zero,

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
http://web.mit.edu/8.02-esg/Spring03/www/8.02ch24we.pdf

 

[vela]

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?

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.