$(45$ pts$.)$ A very long uncharged conducting wire of radius $a$ is surrounded by think insulation of a linear dielectric material $($with dielectric constant ${}_r)$ out to radius $b.$ This object is then placed into external otherwise uniform electric field vec$(E{)}_0.$ That electric field is perpendicular to the wire $($You can assume that electric field is in the $z-$direction$).($Hint: Set the ground level of electric potential at the surface of the wire.$)$ Use cylindrical coordinates to find

a$)$ Electric potential for $s>bs>bs=as=as=ba$

$fa$

$da$

$b$