An infinitely long positively charged cylindrical shell of radius \(a\) has a uniform linear charge density \(\lambda_{a}\). An infinitely long cylindrical shell of radius \(b>a\) is concentric with the first and has a uniform linear charge density \(\lambda_{b}\).

(a) Determine \(\vec{E}\) in all regions.

(b) If \(\lambda_{a}=+5.0 \mathrm{nC} / \mathrm{m}\), which type of charge must the shell of radius \(b\) carry and what value must \(\lambda_{b}\) have in order for the electric field to be zero for radial distances \(r>b\) ?

(c) Sketch the electric field lines for this situation.