A coaxial cable consists of a solid inner conductor of radius $R_{i}$ surrounded by a concentric outer conducting shell of radius $R_{0}$. Insulating material fills the space between the conductors. The inner conductor carries current to the right, and the outer conductor carries the same current to the left down the outer surface of the cable (Figure 19-39). Using Ampère's law, derive an expression for the magnitude of the magnetic field in three separate regions of space: inside the inner conductor, between the two conductors, and outside of the outer conductor.