Electromagnetic waves travel in a medium with speed of 1.5 × 10⁸ m s⁻¹. The relative permeability of the medium is 2.0. The relative permittivity will be:

Solution

Physics sir · 3 steps

Square the speed ratio c/v and you get μᵣ εᵣ. Then divide out the one you know.

1. Speed in a medium. In vacuum c = 1/√(μ₀ ε₀). In a medium both constants are multiplied by their relative values, so the speed drops by a factor √(μᵣ εᵣ).

   v = c/√(μᵣ εᵣ) ⇒ μᵣ εᵣ = (c/v)²

2. Put in numbers. c/v = (3 × 10⁸)/(1.5 × 10⁸) = 2, so μᵣ εᵣ = 2² = 4.
3. So. With μᵣ = 2, εᵣ = 4/2 = 2. The answer is option (c), 2.

The idea to keep. In any medium c/v = √(μᵣ εᵣ). Square the speed ratio first, then divide by whichever relative constant is given.

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