A plane wave in free space with E→=(√π)(10.0xˆ+11.8yˆ) exp[ j( 4π×10^8t-kz)].where xˆ and y are unit vectors in the x and y-directions, respectively, is incident normally on a semi-infinite block of ice as shown in Figure. For ice, µ = µ0, σ = 0 and ε = 9 e0(1 – j0.001). (a) Calculate the average power density associated with the incident wave. (b) Calculate the skin depth in ice. (c) Estimate the average power density at a distance 5 times the skin depth in the ice block, measured from the interface.

Question

A plane wave in free space with [latex]\vec{E}=(\sqrt{\pi})(10.0 \hat{x}+11.8 \hat{y}) \exp \left[j\left(4 \pi imes 10^{8} t-k z ight) ight][/latex] .where [latex]\hat{x}[/latex] and y are unit vectors in the x and y-directions, respectively, is incident normally on a semi-infinite block of ice as shown in Figure. For ice, [latex]\mu=\mu_{0}, \sigma=0 ext { and } \varepsilon=9_{ e 0}(1- j 0.001)[/latex].

(a) Calculate the average power density associated with the incident wave.

(b) Calculate the skin depth in ice.

(c) Estimate the average power density at a distance 5 times the skin depth in the ice block, measured from the interface.

Accepted Answer

[latex]\vec{E}=24 e^{j(\omega t-\beta z)} \vec{a}_{y} \quad \omega=4 \pi imes 10^{8}[/latex]

[latex]E_{y}=11.8 \sqrt{\pi} \quad \beta=k=\omega \sqrt{H \omega}[/latex]

[latex]|E|_{2}=\left|E_{x} ight|^{2}+\left|E_{y} ight|^{2}=751.6, \eta=\eta_{0}=120 \pi[/latex]

Question 2.5.8: A plane wave in free space with E→=(√π)(10.0xˆ+11.8yˆ) exp[ ...

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