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

1. Sep 4, 2016

### JaneHall89

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. Sep 4, 2016

### drvrm

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

Last edited: Sep 4, 2016
3. Sep 4, 2016

### vela

Staff Emeritus
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.