Consider an infinitely long straight cylinder of radius R carrying a current lo. The current is not uniform in cross-section. The density of current per unit of cross-sectional area, J, is 21. J = r2 A) Verify that the total current in the wire is in fact lo. B) Find the magnitude of the magnetic field as a function of r, the distance from the cylinder's axis, using Ampere's Law, for 0srsR. C) Find the magnitude of the magnetic field as a function of r, the distance from the cylinder's axis, using Ampere's Law, for r2 R.

Consider an infinitely long straight cylinder of radius R carrying a current lo. The current is not uniform in cross-section. The density of current per unit of cross-sectional area, J, is 21. J = r2 A) Verify that the total current in the wire is in fact lo. B) Find the magnitude of the magnetic field as a function of r, the distance from the cylinder's axis, using Ampere's Law, for 0srsR. C) Find the magnitude of the magnetic field as a function of r, the distance from the cylinder's axis, using Ampere's Law, for r2 R.