(Solved): A thin, long straight wire is surrounded by a long, hollow cylindrical metal cylinder whose axis co ...

A thin, long straight wire is surrounded by a long, hollow cylindrical metal cylinder whose axis coincides with that of the wire. There is a gap between the wire and the inner surface of the cylinder. The inner radius of the cylinder is \( a \) and the outer radius is \( b \). The wire carries a net charge per unit length of \( (+2 \mu) \mathrm{C} / \mathrm{m} \) while the cylinder has a uniformly distributed net charge per unit length of \( (-3 \mu) \mathrm{C} / \mathrm{m}, \mu \) is a constant. (a) Explain briefly why the above system is NOT being considered here as a cylindrical capacitor. [3 marks] (b) Use Gauss law to find the electric field in the gap between the wire and the cylinder, i.e. for \( rb \). [5 marks] (e) Sketch, showing the important values, the graph of electric field against \( r \). Note: you do not need to sketch the graph on graph paper, but your sketch must be clear and must contain the important values for electric field and for \( r \). [8 marks]