Final answer:
The question pertains to determining the instantaneous expression for the electric and magnetic fields within a semi-infinite slab with given electrical properties, using the provided surface electric field as the initial condition.
Step-by-step explanation:
The subject of this question is Physics, specifically dealing with an electromagnetic field in a semi-infinite slab. The slab has a given conductivity (σ = 300 S/m), relative permittivity (εᵢ = 10.2), and relative permeability (μᵢ = 1.0), which are essential in determining the behavior of electromagnetic fields within the medium. Since the slab exists for z > 0, we are dealing with Maxwell's equations for the electromagnetic field in this region. The electric field at the surface (z = 0) is given as E(0, t) = 1.0 cos(π x 10⁶) aᵃ V/m, which suggests a time-varying field oscillating along the x-axis. The task is to find the instantaneous expression for the electric field (E) and magnetic field (H) at any point within the slab.
The electric field and magnetic field inside the semi-infinite slab can be determined using the boundary conditions.
For the electric field, since it is given as E(0, t) = 1.0 cos(π x 10⁶) aₓ V/m at the surface (z = 0), we can assume that the electric field does not vary with z inside the slab. Therefore, the instantaneous expression for E can be given as E(x, t) = 1.0 cos(π x 10⁶) aₓ V/m for z > 0.
For the magnetic field, since the relative permeability µᵣ = 1.0, the magnetic field H is related to the electric field E by the equation H = (1/√(µ₀ε₀)).E, where µ₀ is the permeability of free space and ε₀ is the permittivity of free space. Substituting the given values, we have H = (1/√(4π x 10⁻⁷ x 8.85 x 10⁻¹²)).(1.0 cos(π x 10⁶) aₓ) = 1.894 x 10⁶ cos(π x 10⁶) aₓ A/m.