Question

Consider a uniform plane wave traveling in the z-direction in a simple lossless nonmagnetic medium (i.e., µ=µ0 ) with a y-directed electric field of maximum amplitude of 60 V/m. If the wavelength is 20 cm and the velocity of propagation is 10^8 m/s, (a) determine the frequency of the wave and the relative permittivity of the medium and (b) write complete time-domain expressions for both the electric.

(E(z,t)) and magnetic
(H(z, t)) field components of the wave.

Answer 1

The amplitude of the electric field is 60 V/m, the frequency is 5 x 10^8 Hz, and the relative permittivity of the medium is 1 x 10^-16 F/m.

Step-by-step explanation:

The amplitude of the electric field is 60 V/m and the wavelength is 20 cm. To determine the frequency, we can use the formula: velocity = frequency x wavelength. Rearranging the formula, we get frequency = velocity / wavelength. Substituting the given values, we have frequency = 10^8 m/s / 0.20 m = 5 x 10^8 Hz.

The relative permittivity of the medium, also known as the dielectric constant, can be calculated using the formula: c = 1 / sqrt(relative permittivity x relative permeability). Since the medium is nonmagnetic (µ = µ0), the formula simplifies to c = 1 / sqrt(relative permittivity). Rearranging the formula, we get relative permittivity = 1 / (c^2). Substituting the given value of c, we have relative permittivity = 1 / (10^8 m/s)^2 = 1 x 10^-16 F/m.

In the time-domain, the complete expressions for the electric field (E(z,t)) and magnetic field (H(z,t)) components of the wave can be written as:

E(z,t) = Eo cos(kz - wt)

H(z,t) = (Eo / c) cos(kz - wt)

where Eo is the maximum amplitude of the electric field, k is the wave number (k = 2π / λ), z is the direction of propagation, t is time, and w is the angular frequency (w = 2πf).