Two long, hollow metal tubes share the same central axis. The smaller one has a radius of 1 mm, and the larger one has a radius of 20 mm. The space between them is filled with air. When a certain potential difference is applied, the smaller tube is maintained at zero potential, while the larger one is held at 150 V. Assume the tubes are very long compared with their diameters so that edge effects at the ends can be ignored. a) Explain why the electric potential inside the region between the tubes depends only on the distance from the axis. b) Starting from the fact that there are no free charges in the region, determine the general mathematical form of the potential as a function of radius. c) Apply the given boundary conditions to find the explicit potential function. d) Determine both the magnitude and direction of the electric field between the tubes. e) Briefly explain physically why the field points in the direction you found and how its magnitude changes with distance