The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,
Eᵧ = 20 sin (3 × 10⁶x - 4.5 × 10¹⁴t) V/m
(where x, t and other values have S.I. units). The dielectric constant of the medium i $s ____.$
(speed of light in free space is 3 × 10⁸ m/s)

Question

The electric field of a plane electromagnetic wave, travelling in an unknown non-magnetic medium is given by,

Eᵧ = 20 sin (3 × 10⁶x - 4.5 × 10¹⁴t) V/m

(where x, t and other values have S.I. units). The dielectric constant of the medium i $s ____.$

(speed of light in free space is 3 × 10⁸ m/s)

G1 Physics · Accepted Answer

Compare the given wave with E = E₀ sin(kx - ωt). Therefore, k = 3 × 10⁶ m⁻¹, ω = 4.5 × 10¹⁴ rad/s. The wave speed in the medium is v = ω/k = (4.5 × 10¹⁴)/(3 × 10⁶) = 1.5 × 10⁸ m/s. The refractive index is n = c/v = (3 × 10⁸)/(1.5 × 10⁸) = 2. For a non-magnetic medium, μᵣ = 1. Also, n² = μᵣεᵣ. Therefore, εᵣ = n² = 4. Hence the dielectric constant is 4.