A long, straight, solid cy1inder, oriented with its axis in the z-direction, carries a current whose current density is J. The current density, although symmetrical 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 6 is a constant equal to 250 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, 8, and a. Evaluate your expression to obtain a numerical value for Io.
(b) Using Ampere's law, derive an expression for the magnetic field B in the region r "'= a. Express your answer in terms of 10 rather than b.

lela-a) for r S a for rza