(Solved): A long coaxial cable consists of an inner cylindrical conductor with radius \( a \) and an outer co ...

A long coaxial cable consists of an inner cylindrical conductor with radius \( a \) and an outer coaxial cylinder with inner radius \( b \) and outer radius \( c \). The outer cylinder is mounted on insulating supports and has no net charge. The inner cylinder has a uniform positive charge per unit length \( \lambda \) Calculate the magnitude of the electric field at any point between the cylinders a distance \( r \) from the axis Express your answer in terms of some or all of the variables \( a, b, c, r, \lambda \) and constants \( \pi \) and \( \epsilon 0 \). Calculate the magnitude of the electric field at any point outside the outer cylinder a distance \( r \) from the axis. Express your answer in terms of some or all of the variables \( a, b, c, r, \lambda \) and constants \( \pi \) and \( \epsilon_{0} \). Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder. Express your answers in terms of some or all of the variables \( a, b, c, r, \lambda \) and constants \( \pi \) and \( \epsilon_{0} \). Enter your answers separated by a comma.