Q. An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, εᵣ = 9, has the electric field, $E_x=E_0\sin(kz-2\pi\times10^6t)$ V m⁻¹ where $E_0$ is the amplitude and k is the wave vector. Among the following options, the incorrect choice is
A) The direction of propagation of the electromagnetic wave is along +z
B) The speed of the electromagnetic wave inside the medium is $10^8$ m s⁻¹
C) The wavelength of the electromagnetic wave inside the medium is 300 m
D) The magnetic field is given by the relation $B_y=(E_0/v)\sin(kz-2\pi\times10^6t)$ where v is the speed of the electromagnetic wave inside the medium
Explanation
[Solution from source] $v=c/\sqrt{\varepsilon_r}=10^8$ m s⁻¹ and the phase (kz − ωt) means travel along +z. With f = 10⁶ Hz, λ = v/f = 100 m, not 300 m (300 m is the vacuum wavelength). B is along y with amplitude E₀/v. Answer (3).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.