Along, straight, solid cylinder, oriented with its axis in the z−direction, carries a current whose current density is j⃗ . the current density, although symmetrical about the cylinder axis, is not constant but varies according to the relationship j⃗ =2i0πa2[1−(ra)2]k^for≤a=0 for≥a where a is the radius of the cylinder, r is the radial distance from the cylinder axis, and i0 is a constant having units of amperes.