An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, $\epsilon_r = 9$, has the electric field, $E_x = E_0\sin(kz - 2\pi \times 10^6 t)\ \text{V m}^{-1}$ where $E_0$ is the amplitude and $k$ is the wave vector. Among the following options, the incorrect choice is :
Answer: (B) The wavelength of the electromagnetic wave inside the medium is $300$ m
Speed: $v = \dfrac{c}{\sqrt{\epsilon_r}} = \dfrac{3 \times 10^8}{3} = 10^8\ \text{m s}^{-1}$. Statement (1) is correct.
Frequency: $2\pi f = 2\pi \times 10^6$, so $f = 10^6$ Hz.
$$\lambda = \frac{v}{f} = \frac{10^8}{10^6} = 100\ \text{m}$$
So statement (2), which says $300$ m, is incorrect. ($300$ m is the wavelength in vacuum.)
The phase $(kz - \omega t)$ shows that the wave travels along $+z$, so statement (4) is correct. With $\vec{E}$ along $x$ and propagation along $z$, $\vec{B}$ is along $y$ and in phase with $\vec{E}$, with amplitude $E_0/v$. Statement (3) describes this; the printed $B_0$ stands for this amplitude.
The incorrect choice is (2).
Solution by Sreeraj P, M.Sc Physics