(Solved): (b) An infinitely long cylindrical shell with radius \( R_{i} \) and \( R_{0} \) is placed in free ...

(b) An infinitely long cylindrical shell with radius \( R_{i} \) and \( R_{0} \) is placed in free space such that its centre axis is along the \( z \)-axis. This shell is charged with a uniform volume charge density of \( \rho>0 \) for \( R_{i} \leq r \leq R_{0} \) (the shell is hollow inside) (i) What is the direction of electric field vector at a position \( r>R_{0} \) in the cylindrical coordinates? (ii) Use Gauss' law to obtain the electric field vector \( \mathrm{E} \) at a position \( r>R_{0} \).