We have an uncharged, conducting wire with radius a. We surround it by a linear dielectric material, εr, which goes out to radius b. We place this in an external electric field, Eo.
We have electric potential inside (a < s < b)
Vinbetween=Acosφ + (B/s)cosφ
and outside (s > b)
Voutside=-Eoscosφ + (D/s) cosφ
Our boundary conditions are:
when s = a, V = 0
when s = b, V = -Eoscosφ
The Attempt at a Solution
I have solved for the constant and got:
A = - B/a2
B = (-Eob2 + D)/(b2(a-2 + a-2)
D = -((εrb2Eo + εrBEo + (Eo/a2) + (Eo/a2))b)/(b(a-2 + b-2 - εr + εrb)
Is this correct? Once I know these, I can find electric potential and electric field. From there, how would I go about solving for surface density on the dielectric of a bound and free charge, when s=a and s=b.