Consider a hollow metal cylinder of radius 1.0 mm that has a thin wire of radius 0.50 mm...

Consider a hollow metal cylinder of radius 1.0 mm that has a thin wire of radius 0.50 mm running down the center as sketched in Figure P18.48. This structure is a capacitor, with the wire acting as one “plate” and the cylinder acting as the other plate. Calculate the capacitance using the following steps. (a) Place charges on the wire and the cylinder and calculate the electric field between them. Assume the cylinder has a length L and assume L is very long. (b) Estimate qualitatively the electric potential difference between the wire and the cylinder, which can be done using a plot of the electric field as a function of radius. (c) Use the potential difference to estimate the capacitance C for L = 10 cm.