# What is the total charge on the surface?

1. Oct 30, 2011

### blueyellow

1. The problem statement, all variables and given/known data
A point charge q is embedded at the centre of a sphere of linear dielectric material (with susceptibility chi(subscript e) and radius R).

b)What is the total charge on the surface? [3 marks]
c) where is the compensating negative bound charge located? calculate it

3. The attempt at a solution

volume polarisation charge density=-div P
=1/r^2 d/dr((r^2)P) (partial derivative)
=1/r^2 d/dr [[(r^2 Q chi(e) epsilon0]/[4 pi epsilon(r) r^2]]
=1/R^2 d/dr [(q chi(e) epsilon0)/(4 pi epsilon (r))]
=1/R^2 *0
=0

surface charge polarisation density=[(q chi(e) epsilon0) r-hat.n]/(4 pi epsilon1 R^2)
=[(q chi(e) epsilon0)]/(4 pi epsilon1 R^2)

does that help to calculate the total bound charge on the surface at all?
because the surface polarisation charge density=0, the bound charge on the surface=0. three marks for saying just that?

please tell me if I'm wrong

Last edited: Oct 30, 2011