A filamentary conductor on the z axis carries a current of 16 A in the a_z direction, a conducting shell at ρ = 6 carries a total current of 12 A in the −a_z direction, and another shell at ρ = 10 carries a total current of 4 A in the −a_z direction.

(a) Find H for 0 < ρ < 12.

(b) Plot H_ϕ versus ρ.

(c) Find the total flux crossing the surface 1 < ρ < 7, 0 < z < 1, at fixed ϕ.