The surface charge density of an infinitely long conducting cylinder of radius $a$ is $s.$ The cylinder

is surrounded by a dielectric medium with $r=2$ and contains free charge. Find $ss$ if the tangent

component of the electric field at $ra$ is given by ${?}^{\text{v}\text{e}\text{c}(E)}t=sin$ r $3.$

The radii of two infinite$-$length cylindrical surfaces are $r=$a and $r=b(b>a),$ respectively, $sa$

and $sb$ carry surface charge densities.

$($a$)$ Determine vec$(E)$ everywhere

$($b$)$ What must be the relationship between a and $b$ for vec$(E)$ to be zero for $r>b?$