Q. The electric field of an electromagnetic wave in free space is given by E⃗ = 10 cos(10⁷t + kx) ĵ V/m, where t and x are in seconds and metres respectively. It can be inferred that (a) The wavelength λ is 188.4 m (b) The wave number k is 0.33 rad/m (c) The wave amplitude is 10 V/m (d) The wave is propagating along +x direction Which one of the following pairs of statements is correct?
A) (c) & (d)
B) (a) & (b)
C) (b) & (c)
D) (a) & (c)
Explanation
[Solution from source] Here ω = 10⁷ rad/s, so k = ω/c = 10⁷/(3 × 10⁸) = 0.033 rad/m and λ = 2π/k ≈ 188.4 m; the amplitude is 10 V/m. So the wavelength and amplitude statements are correct. The wave number is 0.033, not 0.33 rad/m, and the phase (ωt + kx) means the wave travels along −x, not +x. Answer (4).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.