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).