Assignment:
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 the variables a, b, c, r, lambda, and constants pi and epsilon_0.
- Find the direction of the electric field at any point between the cylinders a distance r from the axis.
- 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 the variables a, b, c, r, lambda, and constants pi and epsilon_0.
- Find the direction of the electric field at any point outside the outer cylinder a distance r from the axis.
- Find the charge per unit length on the inner surface and on the outer surface of the outer cylinder.
Provide complete and step by step solution for the question and show calculations and use formulas.