(Solved): Please do all the parts. Detailed answer is highly appreciated.  1. A cylindrical conductor w ...

Please do all the parts. Detailed answer is highly appreciated. 

1. A cylindrical conductor with length \( b \) has a net charge of \( +2 q \). The axis of the cylinder runs along the \( z \) axis, and its lower end is in the \( x y \) plane. See figure. An external charge \( +q \) is then placed on the \( z \) axis. a distance \( b \) above the top end of the cylinder. This polarizes the conductor along the \( z \) axis. Give answers in terms of \( q, k_{e} \) and \( b \). (a) Draw a view of the \( x z \) plane showing the conductor, the external charge, and the charge on the bottom and lower ends of the cylinder. (b) Assuming that the magnitude of charge at the top end of the cylinder is equal to the magnitude of the external charge, find the charge on the bottom end of the cylinder. The sign is important. Hint: The cylinder is an isolated system, so its net charge is conserved. Insulators and Conductors Worksheet - PHYS \( 421 \quad 1 \) (c) Find the electric force by the external charge on the cylinder. Give answer in vector form. Treat the external charge, the charge at the bottom end, and the charge at the top as point charges.