The electromagnetic waves travel in a medium at a speed of 2.0 × 10⁸ m/s. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :

Solution

Physics sir · 3 steps

The wave slows down by a factor √(μᵣ εᵣ), so square the ratio c/v.

1. Speed in a medium. In a medium, the speed of an electromagnetic wave depends on both the relative permeability μᵣ and the relative permittivity εᵣ.

   v = c/√(μᵣ εᵣ) ⇒ εᵣ = 1/μᵣ(c/v)²

2. Put in numbers. c/v = (3.0 × 10⁸)/(2.0 × 10⁸) = 1.5. With μᵣ = 1.0, εᵣ = (1.5)² = 2.25.
3. So. The relative permittivity of the medium is 2.25, which is option (a).

The idea to keep. The refractive index is n = c/v = √(μᵣ εᵣ). Find n from the speeds first, then square it. Do not forget the square.

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