A plane electromagnetic wave propagates through a lossless nonmagnetic dielectric medium of relative permittivity εᵣ = 9. Its electric field is Eₓ = E₀ sin(kz - 2π × 10⁶t) V m⁻¹. Which stated choice is incorrect? [The printed option 3 contains an additional symbol error.]
Options

Question

A plane electromagnetic wave propagates through a lossless nonmagnetic dielectric medium of relative permittivity εᵣ = 9. Its electric field is Eₓ = E₀ sin(kz - 2π × 10⁶t) V m⁻¹. Which stated choice is incorrect? [The printed option 3 contains an additional symbol error.]

Options

G1 Physics · Accepted Answer

Step 1: Assuming relative permeability μᵣ = 1, wave speed v = c/√εᵣ = (3 × 10⁸)/3 = 10⁸ m s⁻¹, so option 1 is true. Step 2: Angular frequency ω = 2π × 10⁶ rad s⁻¹, so frequency f = 10⁶ Hz. Step 3: Actual wavelength λ = v/f = 10⁸/10⁶ = 100 m, not 300 m. Therefore option 2 is false, matching the printed key. Step 4: Phase (kz − ωt) represents +z propagation, so option 4 is true. Step 5: Physically, magnetic-field amplitude is B₀ = E₀/v, giving Bᵧ = (E₀/v)sin(kz − ωt). The source prints B₀/v in op…

A plane electromagnetic wave propagates through a lossless nonmagnetic dielectric medium of relative permittivity εᵣ = 9. Its electric field is Eₓ = E₀ sin(kz − 2π × 10⁶t) V m⁻¹. Which stated choice is incorrect? [The printed option 3 contains an additional symbol error.]