An electromagnetic wave travelling in a lossless dielectric medium of dielectric constant ε_r=9 has electric field E_x=E₀(kz-2π×10⁶t) Vm⁻¹, where E₀ is the amplitude and k the wave vector. Among the following, the INCORRECT choice is:

Solution & Explanation

This is a 'choose the INCORRECT statement' question, so test each. The wave is E_x = E₀ sin(kz − 2π×10⁶ t), giving angular frequency ω = 2π×10⁶ rad s⁻¹. Speed in the medium: v = c/√ε_r = (3×10⁸)/√9 = (3×10⁸)/3 = 10⁸ m s⁻¹ → statement 1 is CORRECT. Frequency: f = ω/2π = (2π×10⁶)/(2π) = 10⁶ Hz. Wavelength inside medium: λ = v/f = 10⁸/10⁶ = 100 m, NOT 300 m → statement 2 is the INCORRECT one (the answer). The B field accompanies E in phase with the same argument (kz − ωt) and B₀ = E₀/v, so statement 3 is correct in form. The argument (kz − ωt) means propagation along +z → statement 4 is correct. Hence the incorrect statement is the wavelength claim (option B).