A long, thin, positively charged wire runs along the long central axis of a hollow conducting cylinder of length \(10 \mathrm{~m}\), inner radius \(50 \mathrm{~mm}\), and outer radius \(70 \mathrm{~mm}\). The wire has a uniform linear charge density of \(+1.5 \mu \mathrm{C} / \mathrm{m}\), and the cylinder has zero net charge.

(a) Ignoring the regions near the two ends, calculate the surface charge density on the cylinder's inner and outer surfaces. Again ignoring the ends, determine the electric field magnitude at

(b) r=49 mm

(c) r=51 mm, and 

(d) r=100 mm, where r is the radial distance from the wire.