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.

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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