Along, 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, ris the radial distance from the cylinder axis, b is a constant equal to 600 A/m, and is a constant equal to 2.50 cm.
(a) Let be the total current passing through the entire cross section of the wire. Obtain an expression for in terms of b, d, and a. Evaluate your expression to obtain a numerical value for .
(b) Using Ampere’s law, derive an expression for the magnetic field in the region . Express your answer in terms of rather than b.
(c) Obtain an expression for the current | contained in a circular cross section of radius r... a and centered at the cylinder axis. Express your answer in terms of rather than b.
(d) Using Ampere’s law, derive an expression for the magnetic field in the region
(e) Evaluate the magnitude of the magnetic field at r- = 6, r= a, and r= 2a.