In Section 9.1, Faraday’s law was used to show that the field E = −1/2 kB₀e^ktρa_ϕ results from the changing magnetic field B = B₀e^kta_z.

(a) Show that these fields do not satisfy Maxwell’s other curl equation.

(b) If we let B₀ = 1 T and k = 10⁶ s⁻¹, we are establishing a fairly large magnetic flux density in 1μs. Use the ∇ × H equation to show that the rate at which Bz should (but does not) change with ρ is only about 5 × 10⁻⁶ T per meter in free space at t = 0.