Final answer:
The frequency of the wave is 5 x 10⁸ Hz and the relative permittivity of the medium is 9.
Step-by-step explanation:
We have been given that a uniform plane wave is traveling in the z-direction in a simple lossless nonmagnetic medium with a y-directed electric field of maximum amplitude of 60 V/m. The wavelength (λ) is given as 20 cm (or 0.2 meters), and the velocity of propagation (v) is given as 10⁸ m/s. To find the frequency (f) of the wave, we use the relationship:
c = λν
where c is the speed of light, λ is the wavelength, and ν (nu) is the frequency. Since the medium is lossless and nonmagnetic (μ = μ0), the speed of wave propagation in the medium will be equal to the speed of light in vacuum only if the relative permittivity (εr) is 1. For any other value of relative permittivity, the speed v is less than c.
The frequency (f) can be calculated as:
f = v / λ = (10⁸ m/s) / (0.2 m) = 5 x 10⁸ Hz
To find the relative permittivity (εr), we use the relationship between the speed of light, the permittivity and permeability of free space, and the relative permittivity:
v = c / √εr
Using the given speed of propagation and the speed of light in free space (c = 3 x 10⁸ m/s), εr is found by solving:
10⁸ m/s = (3 x 10⁸ m/s) / √εr
εr = (3 x 10⁸ / 10⁸)² = 9
Therefore, the relative permittivity of the medium is 9.