Final answer:
To calculate the speed of an electromagnetic wave in a medium with a dielectric constant of 2.07 and a relative permeability of 1, divide the speed of light in free space by the square root of the product of the dielectric constant and relative permeability. The result is approximately 2.07 x 10^8 m/s.
Step-by-step explanation:
To calculate the speed of an electromagnetic wave in a medium, we can use the formula where v is the speed of the wave, ε is the dielectric constant of the medium, and μ is the relative permeability of the medium:
v = × {1 √(ε_r ε_0 μ_r μ_0)}
For electromagnetic waves in free space, the speed is c = 2.998 × 10^8 m/s.
However, in a medium, this speed is reduced by a factor of √(ε_r μ_r), where ε_r is the relative permittivity (or dielectric constant) and μ_r is the relative permeability.
Given that the dielectric constant (ε_r) is 2.07 and the relative permeability (μ_r) is 1 for the medium in question, we can calculate the new speed of the electromagnetic wave using the following steps:
- First, we find the square root of the product of the dielectric constant and relative permeability: √(2.07 * 1) = √2.07.
- Then, we divide the speed of light in free space (c) by this factor: v = c / √2.07 = (2.998 × 10^8 m/s) / √2.07.
- Perform the calculation to find v.
The result is approximately 2.07 × 10^8 m/s, which is the speed of the electromagnetic wave in the given medium.