- #1
Taylor_1989
- 402
- 14
Homework Statement
Consider an infinitely long one dimensional conducting wire with a homeogenous charge density ##\lambda##, running along the central axis of an infinitely long cyclindrical glass casing of radius b (glass is a dielectric material). Calculate:
a) The displacement vector inside the glass
b) the surface bound charges on the outer surface of the glass
Homework Equations
a) ##\oint D . dA=q##
b) ##\sigma_b=P.\hat n##
##P=\epsilon_0\chi_e E##
The Attempt at a Solution
[/B]
So my attempt for a) I drew a Gaussian surface in terms of a cylinder and calculate all three surfaces like so:
##\oint D . dA=\int_1 D dAcos\theta+\int_2 D dAcos\theta+\int_3 D dAcos\theta##
By calulating ##\theta ## for the respectable surfaces ##1=90, 2=0, 3=90##
Thus leaving me with ##\int_2 D dA=D\int_2 dA=D\times A=D(L)(2\pi r)=q##
##\lambda=\frac{q}{L}##
##D=\frac{\lambda}{2\pi r}## (electric displacement vector)
b) But I am not sure where to even start I have been reading a one book say that the surface charge cannot be calculate, but dosent really give an explanation and the other basically uses the two formulas which I have mentioned above. So I am a bit confused about the whole thing at the moment a would appreciate any help that anyone could give. I understand the equation I have given for part b are for a linear dielectric but I am just not 100% sure if the question I have been asked is a linear dielectric