Q. The electric field part of an electromagnetic wave in a medium is represented by Ex = 0; Ey = 2.5 (N/C) cos[(2π × 10⁶ rad/s) t − (π × 10⁻² rad/m) x]; Ez = 0. The wave is:
A) moving along x direction with frequency 10⁶ Hz and wave length 100 m
B) moving along x direction with frequency 10⁶ Hz and wave length 200 m
C) moving along −x direction with frequency 10⁶ Hz and wave length 200 m
D) moving along y direction with frequency 2π × 10⁶ Hz and wave length 200 m
Explanation
[Solution from source] Comparing with E₀cos(ωt − kx): ω = 2π × 10⁶ rad/s gives f = 10⁶ Hz, and k = π × 10⁻² rad/m gives λ = 2π/k = 200 m. The (ωt − kx) form means propagation along +x. Taking f = 2π × 10⁶ Hz confuses ω with f. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.