A positively charged thin cylindrical shell of length 50 \(\mathrm{cm}\) and radius \(1 \mathrm{~mm}\) has no end caps and a uniform surface charge density of \(3 \times 10^{-6} \mathrm{C} / \mathrm{m}^{2}\).

(a) What is the charge on the shell? Determine the electric field magnitude far from either end of the shell at 

(b) \(r=0.9 \mathrm{~mm}\)

(c) \(r=1.1 \mathrm{~mm}\), where \(r\) is the radial distance from the long central axis of the shell.