$2.(10$ points$)$ An infinite, solid, conducting and grounded cylinder with radius $\backslash ($ R $\backslash )$ is placed near and parallel to an infinite charged wire with charge density $\backslash (\backslash$lambda $\backslash ).$ The wire is at a distance $\backslash ($ a $\backslash )$ from the axis of the conducting cylinder.

a$)(7$ pts$)$ Find the potential and electric field everywhere in this configuration. HINT: use method of images.

b$)(3$ pts$)$ Calculate the surface charge density on the grounded cylinder.