A cylindrical shell of radius R and length L carries a surface charge density sigma. The cylinder is centered around the z-axis and its midpoint lies at the origin. (a) If the cylinder is made to spin around the z-axis with an angular velocity omega, determine the magnetic field at the origin. (b) Determine the magnetic field at the origin in the limit that L rightarrow infinity 3. Use Ampere's law to determine the magnetic field inside an infinite spinning cylinder identical to that of Question 2. (a) Determine the magnetic vector potential at the origin of the spinning cylindrical shell in Question 2. (b) Using your answer to Question 3, determine the magnetic vector potential inside an infinitely long spinning cylindrical shell. Verify that your answer is consistent with that of Question 3 using B