Text: 4, (25 points) The following question asks you to calculate the magnetic field created by a non-uniform current density inside of a long, cylindrical wire given by the following function J(s) = Joe^(-s/42) for S < S1, surrounded by a conducting shell with radius S2 carrying current Ishell in the 2 direction as shown in the figure below. This problem is best analyzed using cylindrical coordinates.
(a) Calculate the value of the constant A, given that the total current being carried by the cylinder is Icylinder. Your answer should only depend on Icylinder, S1, and Joe.
(b) Calculate the magnetic field, B(s), for S1 < S < S2 and for S > S2. For S < S1, is the magnetic field increasing or decreasing? What does the magnetic field look like far away, i.e., at S >> S2? Create a graph of the magnetic field intensity for all values and find where the magnetic field strength is largest if Icylinder = Ishell.