Surface bound charge on the outer surface of a dielectric

[JKC]

Homework Statement

With regards to a one dimensional conducting wire with a homogeneous charge density λ surrounded by a cylindrical glass dielectric of radius R, find:

(a). The displacement vector inside the dielectric

(b). The surface bound charges on the surface of the dielectric

Sorry for the lack of equations and mathematical explanation. Trying to put everything mathematically and graphically would have been quite long. Rest assure I have everything that I'm describing in the attempt written in the correct notation on paper.[/B]

Homework Equations

Included in attempt

The Attempt at a Solution

(a).

Drawing a cylindrical Gaussian surface inside the dielectric of radius r and length L.

Surface integral (displacement vector, D) dot product dS (differential of surface) = charge enclosed

dS = 2πr L

Qenc= λ L

⇒ surface integral D (2πr L) = λ L

D = λ/2πr

For the displacement vector D(bar) = λ/2πr r(bar)

(b).

I'm slightly confused as to where to approach this one from:

D(vector) = εE(field vector) + P(vector)

E and P are the electric field and dipole moment.Surface bound charge = σ = P(vector) n(normal vector)

σ = σbound + σfreeFrom here on I don't really know how to approach this problem. Apologies for the scrappy attempt.

 

[TSny]

OK for part (a)

For part (b) try to make use of either the dielectric constant of the glass or the electric susceptibility of the glass.