Final answer:
The velocity of an electromagnetic wave in a homogeneous half space can be calculated using the formula v = 1/√(με), where v is the velocity, μ is the permeability of the medium, and ε is the permittivity of the medium. To find the velocity, we need to calculate the permeability and permittivity of the medium using the given resistivity and the known values for permeability of free space and speed of light.
Step-by-step explanation:
The velocity of an electromagnetic (em) wave in a homogeneous half space can be calculated using the formula:
v = 1/√(με)
Where v is the velocity, μ is the permeability of the medium, and ε is the permittivity of the medium.
In this case, the resistivity of the half space is given as 100 ohm.m. The permeability of the medium can be calculated using the formula:
μ = μ0/ρ
Where μ0 is the permeability of free space and ρ is the resistivity of the medium.
Substituting the given values, we can find μ:
μ = (4π × 10-7 T∙m/A) / (100 ohm.m)
After finding μ, we can calculate the permittivity (ε) of the medium using the formula:
ε = 1/c² μ
Where c is the speed of light in vacuum.
Substituting the values, we can find ε:
ε = 1/((3 × 108 m/s)²) × (μ value)
Finally, substituting the values of μ and ε in the velocity formula, we can find the velocity of the electromagnetic wave.