A long wire of radius 2a is constructed as shown with a cylindrical cavity of radius a along its entire length. A current I flows in the positive z-direction (that is, out of the page). What is the current density I in the wire? What is the magnetic field at (0, 0)? (Hint: Replace the cavity with a solid wire having current density -I z and another having current density - 2.) What is the magnetic field at (a, 0)? Derive an expression for the magnetic field at all points along the x-axis. What is the magnetic field at (a, a)?