An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, εr = 9, has the electric field, Ex = E₀ sin (kz - 2π × 10⁶ t) V m⁻¹ where E₀ 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 10⁸ ms⁻¹ (c) The wavelength of the electromagnetic wave inside the medium is 300 m (d) The magnetic field is given by the relation By = B₀/v sin (kz - 2π × 10⁶ t) where v is the speed of the electromagnetic wave inside the medium

Answer: (c). Phase (kz - ω t) means propagation along +z, so (a) is correct. n = √(εr) = 3 ⇒ v = c/3 = 10⁸ m/s, so (b) is correct. ν = 2π × 10⁶2π = 10⁶ Hz ⇒ λ = v/ν = 100 m, not 300 m, so (c) is incorrect. For Ex along +z, B is along y with B = E/v, in phase with E, so (d) is the intended correct statement. So the answer is (c).

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Speed of EM Waves in a Medium

An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, $\varepsilon_r = 9$ , has the electric field, $E_x = E_0 \sin\left(kz - 2\pi \times 10^{6} t\right)\text{ V m}^{-1}$ where $E_0$ is the amplitude and $k$ is the wave vector. Among the following options, the incorrect choice is

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Answer: (c)

Phase $(kz - \omega t)$ means propagation along $+z$ , so (a) is correct.
$n = \sqrt{\varepsilon_r} = 3 \Rightarrow v = c/3 = 10^{8}$ m/s, so (b) is correct.
$\nu = \dfrac{2\pi \times 10^{6}}{2\pi} = 10^{6}$ Hz $\Rightarrow \lambda = v/\nu = 100$ m, not 300 m, so (c) is incorrect.
For $E_x$ along $+z$ , $B$ is along $y$ with $B = E/v$ , in phase with $E$ , so (d) is the intended correct statement.
So the answer is (c).

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