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Homework Statement
We have an uncharged, conducting wire with radius a. We surround it by a linear dielectric material, ε_{r}, which goes out to radius b. We place this in an external electric field, E_{o}.
Homework Equations
We have electric potential inside (a < s < b)
V_{inbetween}=Acosφ + (B/s)cosφ
and outside (s > b)
V_{outside}=E_{o}scosφ + (D/s) cosφ
Our boundary conditions are:
V_{inbetween}=V_{outside}
ε_{r}E_{sin}=ε_{r}E_{sout}
when s = a, V = 0
when s = b, V = E_{o}scosφ
The Attempt at a Solution
I have solved for the constant and got:
A =  B/a^{2}
B = (E_{o}b^{2} + D)/(b^{2}(a^{2} + a^{2})
D = ((ε_{r}b^{2}E_{o} + ε_{r}BE_{o} + (E_{o}/a^{2}) + (E_{o}/a^{2}))b)/(b(a^{2} + b^{2}  ε_{r} + ε_{r}b)
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.
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