A toroidal core has a square cross section, 2.5 cm < < 3.5 cm, 0.5 cm

A toroidal core has a square cross section, 2.5 cm < ρ < 3.5 cm, −0.5 cm < z < 0.5 cm. The upper half of the toroid, 0 < z < 0.5 cm, is constructed of a linear material for which μ_r = 10, while the lower half, −0.5 cm < z < 0, has μ_r = 20. An mmf of 150 A· t establishes a flux in the a_ϕ direction. For z > 0, find:

(a) H_ϕ(ρ);

(b) B_ϕ(ρ);

(c) z > 0.

(d) Repeat for z > 0.

(e) Find total.