A long, straight, solid cylinder, oriented with its axis in the z-direction, carries a c...

A long, straight, solid cylinder, oriented with its axis in the z-direction, carries a current whose current density is . The current density, although symmetric about the cylinder axis, is not constant and varies according to the relationship

where the radius of the cylinder is a = 5.00 cm, r is the radial distance from the cylinder axis, b is a constant equal to 600 A/m, and δ is a constant equal to 2.50 cm. (a) Let I₀ be the total current passing through the entire cross section of the wire. Obtain an expression for I₀ in terms of b, d, and a. Evaluate your expression to obtain a numerical value for I₀. (b) Using Ampere’s law, derive an expression for the magnetic field in the region r ≥ a. Express your answer in terms of I₀ rather than b. (c) Obtain an expression for the current I contained in a circular cross section of radius r … a and centered at the cylinder axis. Express your answer in terms of I₀ rather than b. (d) Using Ampere’s law, derive an expression for the magnetic field in the region r ≤ a. (e) Evaluate the magnitude of the magnetic field at r = δ, r = a, and r = 2a.