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24 August, 15:38

The electric field of a plane wave propagating in a lossless, nonmagnetic, dielectric material with εr = 2.56 is given byE = ŷ20 cos (6π.10^9 t - kz) (V/m). Determine f in terms of Hz. a. Determine f in terms of Hzb. Determine up in terms of m/s. c. Determine λ in terms of meters. d. Determine k in terms of rad/m e. Determine eta in terms of Ohm.

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  1. 24 August, 15:47
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    f in term of Hz = 3GHz

    f in term of Hzb = 3GHz. b

    up in term of m/s = 1.875*10 ∧ 8 m/s

    λ in term of meters = 3.12cm equivalent to 6.25m

    k in terms of rad/m = 201.4 rad / m

    beta in terms of Ohm = 235.62 Ω

    Explanation:

    NOTE: Where the signs used and identified in the solving of this questions asked are in relation and related in meaning to those in the narrative of the question.

    w = 2πf = 6π * 10 ∧ 9 rad/sec

    f = 3 * 10 ∧ 9 Hz = 3GHz

    Up = c / √∈r = 3 * 10 ∧ 8 / √2.56 = 1.875*10 ∧ 8 m/s

    λ = Up / f = 1.875 * 10 ∧ 8 / 6 * 10 ∧ 9 = 3.12cm equivalent to 6.25m

    k = 2π / λ = 2π / 3.12*10 ∧-2 = 201.4 rad / m equivalent to 100.5

    η = η° / √∈r = 377 / 1.6 = 235.62 Ω.

    b) H = - ˆx = 20 / η cos (6π * 10 ∧9. t - kz)

    = - ˆx = 20 / 235.62 cos (6π * 10 ∧9. t - 201.4 z)

    = - ˆx 8.49 * 10 ∧-2 cos (6π * 10 ∧9. t - 201.4 z) (A/m).
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