An infinitely long, straight cable is made out of a cylindrical core with radius a, surrounded by a thin cylindrical shell with radius b. Both the cylindrical core and cylindrical shell are centered along the z-axis. There is a volume current density ] = js³2 in the cylindrical core, and a surface current density K = -K2 (directed in the opposite direction). a) If the magnitude of the current running through the core (Icore) is twice the magnitude of the current running through the shell (Ishell), find an expression for the constant j in terms of K, the magnitude of the surface current density. b) Determine the magnetic field, B, in each region (s b). c) Find the magnetic vector potential, A, in each region, making sure that the boundary conditions at s = a and s= b are satisfied. b a

An infinitely long, straight cable is made out of a cylindrical core with radius a, surrounded by a thin cylindrical shell with radius b. Both the cylindrical core and cylindrical shell are centered along the z-axis. There is a volume current density ] = js³2 in the cylindrical core, and a surface current density K = -K2 (directed in the opposite direction). a) If the magnitude of the current running through the core (Icore) is twice the magnitude of the current running through the shell (Ishell), find an expression for the constant j in terms of K, the magnitude of the surface current density. b) Determine the magnetic field, B, in each region (s b). c) Find the magnetic vector potential, A, in each region, making sure that the boundary conditions at s = a and s= b are satisfied. b a