Homework Help: Surface bound charge on the outer surface of a dielectric

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1. Oct 25, 2017

JKC

1. The problem statement, all variables and given/known data

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.

2. Relevant equations

Included in attempt

3. 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 + σfree

From here on I don't really know how to approach this problem. Apologies for the scrappy attempt.

2. Oct 25, 2017

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.