Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by
E = 20cos(2 × 10¹⁰ t - 200x) V/m. The dielectric constant of the medium is equal to : (Take μᵣ = 1)

Solution

Physics sir · 3 steps

Read the wave speed straight off the equation, get the refractive index, then square it.

1. Wave speed. For E = E₀cos(ω t - kx), the speed is v = ω/k. Here ω = 2 × 10¹⁰ rad s⁻¹ and k = 200 m⁻¹, so v = 10⁸ m s⁻¹.
2. Refractive index. n = c/v = (3 × 10⁸)/10⁸ = 3.

   n = √(μᵣ εᵣ) ⇒ εᵣ = n²/μᵣ

3. So. With μᵣ = 1, the dielectric constant is εᵣ = 3² = 9, option (a).

The idea to keep. In a medium, v = ω/k and n = c/v. Refractive index goes as the square root of the dielectric constant, so always square n to get εᵣ.

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