Practice portal › Electromagnetic Waves › The Plane Wave: Reading the Equation

An electromagnetic wave travelling in a lossless dielectric medium having a dielectric
constant εᵣ=9 has the electric field
Eₓ=E₀ sin (kz-2π×10⁶t) V m⁻¹
where E₀ is the amplitude and k is the wave vector. Among the following options, the
incorrect choice is

Asked in RE-NEET 2026 · Reading omega, k, nu, lambda and v

• (1) The direction of propagation of the electromagnetic wave is along +z
• (2) The speed of the electromagnetic wave inside the medium is 10⁸ m s⁻¹
• (3) The wavelength of the electromagnetic wave inside the medium is 300 m
• (4) The magnetic field is given by the relation B_y=(E₀)/v sin (kz-2π×10⁶t), where v is the speed of the electromagnetic wave inside the medium

Step-by-step solution

Why the other options are wrong

• (1) comes from is correct: the phase is kz-ω t, so a point of constant phase moves towards +z as t grows.
• (2) comes from is correct: v=c/(√εᵣ)=(3×10⁸)/3=10⁸ m s⁻¹.
• (4) comes from is correct: the amplitudes are tied by B₀=(E₀)/v, so this is the right magnetic field. The paper prints B₀ in the numerator here and footnotes its own typo; the corrected form is used above, since as printed it would give a second incorrect statement and the question asks for only one.

Reading this solution needs no sign-in. You only sign in to practise against the clock and keep your progress.