In a dielectric medium, E⃗=30(2î+ĵ) sin{2π[5×10¹⁴t-(10⁷/3)z]} V m⁻¹. Take c=3×10⁸ m s⁻¹. Which statements are correct?
Select all that apply

Question

In a dielectric medium, E⃗=30(2î+ĵ) sin{2π[5×10¹⁴t−(10⁷/3)z]} V m⁻¹. Take c=3×10⁸ m s⁻¹. Which statements are correct?

G1 Physics · Accepted Answer

The phase is 2π[5×10¹⁴t−(10⁷/3)z], so the wave propagates along +z. Its speed is v=f/(1/λ)=5×10¹⁴/(10⁷/3)=1.5×10⁸ m s⁻¹, giving refractive index n=c/v=2; hence D is correct. For propagation along +z, B⃗=(1/v)k̂×E⃗. With E⃗=30(2î+ĵ)sin(phase), k̂×(2î+ĵ)=2ĵ−î. Thus B⃗=2×10⁻⁷(−î+2ĵ)sin(phase) T. Therefore Bₓ=−2×10⁻⁷sin(phase) T, so A is correct; Bᵧ is actually 4×10⁻⁷sin(phase) T, so B is false. The polarization angle is tan⁻¹(1/2)≈26.6°, so C is false. Correct options: A,D.