- #1

physicsisfun0

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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.