IGNOU BPHCT 133 2026 - A uniform plane wave of travelling in free space strikes a

Question

A uniform plane wave of $100\text{ MHz}$ travelling in free space strikes a large block of a material having $\varepsilon = 9\varepsilon_0$ , $\mu = 4\mu_0$ and $\sigma = 0$ normal to the surface. If the incident electric field vector is given by
$$\vec{E} = 1000\cos(\omega t - \beta y)\hat{z}\text{ Vm}^{-1}$ $
write the complete expressions for the incident, reflected and transmitted field vector

19 Jan 2026

Answer :

Word Count : 528

When a uniform plane electromagnetic wave propagates in free space and strikes a boundary with a different material, the behavior of the wave can be analyzed using Maxwell’s equations and the boundary conditions at the interface. Let us denote the free space with permittivity (\varepsilon_0), permeability (\mu_0), and assume the material has permittivity (\varepsilon), permeability (\mu), and conductivity (\sigma). The wave is assumed to strike the boundary normally, so the analysis simplifies to one-dimensional propagation along the (z)-axis. The incident electric field vector is given as (\mathbf{E}_i = \mathbf{E}_0 e^{-j k_0 z} \hat{x}), where (\mathbf{E}_0) is the amplitude, (k_0 = \omega \sqrt{\mu_0 \varepsilon_0}) is the wave number in free space, (\omega) is the angular frequency, and (\hat{x}) indicates polarization along the x-direction. The corresponding incident magnetic field can be obtained from the Maxwell-Faraday equation for plane waves: [ \mathbf{H}_i = \frac{1}{\eta_0} \hat{k} \times \mathbf{E}_i ] where (\eta_0 = \sqrt{\mu_0 / \varepsilon_0}) is the intrinsic impedance of free space, and (\hat{k}) is the propagation direction (here (\hat{z})). Since the wave

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