Question

A uniformly charged straight wire (radius a) has linear charge density lambda. The wire is coated with a dielectric material chi with external radius b.

I need to find the electric field everywhere and the volume and surface bound charge distrobutions but I do not know where to even start :(

Use Gauss law. I will be happy to critique your work. Use gaussian cylinders, you know the charge enclosed.

This is what I got:

r < a: E = lambda/(2*pi*r*Eo) r^

a < r < b: E = lambda / (2*pi*r*Eo(1+chi)) r^

r > b: E = lambda/(2*pi*Eo*r) r^


THen for the surface/volume bound charges:

sigma = lambda/(2*pi*r)
rho = lambda/(pi*r^2)
for r < a and replace the a for when r > a. I'm really not at all confident in my answer, I really did just kind of guess and hope for the best from a solved example in my book :(