An electromagnetic wave of frequency 5 GHz, is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are 2. Its velocity in this medium is ____________ × 10⁷ m/s.

Solution

Physics sir · 3 steps

Speed in a medium depends only on its permittivity and permeability, so the 5 GHz frequency plays no part.

1. Speed in a medium. In a medium, an EM wave slows down by the factor √(εᵣ μᵣ), which is the refractive index of the medium.

   v = c/√(εᵣ μᵣ)

2. Put in numbers. Here εᵣ μᵣ = 2 × 2 = 4, so √4 = 2. Then v = (3 × 10⁸)/2 = 1.5 × 10⁸ m s⁻¹.
3. So. 1.5 × 10⁸ m s⁻¹ = 15 × 10⁷ m s⁻¹, so the answer is 15.

The common slip: 7.5. Dividing c by εᵣ μᵣ = 4 without taking the square root gives 7.5 × 10⁷ m s⁻¹, so 7.5 instead of 15.

The idea to keep. For an EM wave in a medium, v = c/√(εᵣ μᵣ). The frequency changes the wavelength, never the speed, so do not get distracted by it.

Answer from the NTA final answer key. Solution by PrepWiser.