In region 1, z < 0, 1 = 2 10 11 F/m, 1 =

In region 1, z < 0, ∈₁ = 2 × 10⁻¹¹ F/m, μ₁ = 2 × 10⁻⁶ H/m, and σ₁ = 4×10⁻³ S/m; in region 2, z > 0, ∈₂ = ∈₁/2, μ₂ = 2μ₁, and σ₂ = σ₁/4. It is known that E₁ = (30a_x + 20a_y + 10a_z) cos 10⁹t V/m at P(0, 0, 0⁻).

(a) Find E_N1, E_t1, D_N1, and D_t1 at P₁.

(b) Find J_N1 and J_t1 at P₁.

(c) Find E_t2, D_t2, and J_t2 at P₂(0, 0, 0⁺).

(d) (Harder) Use the continuity equation to help show that J_N1 − J_N2 = ∂D_N2/∂t − ∂D_N1/∂t, and then determine D_N2, J_N2, and E_N2.