Q122 / 180 · NEET 2026 (Re-NEET) · Physics
An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, $\epsilon_r=9$, has the electric field, $E_x=E_0\sin(kz-2\pi\times10^6 t)$ Vm$^{-1}$ where $E_0$ is the amplitude and $k$ is the wave vector. Among the following options, the incorrect choice is :
- AThe direction of propagation of the electromagnetic wave is along $+z$
- BThe speed of the electromagnetic wave inside the medium is $10^8$ ms$^{-1}$
- Correct answerCThe wavelength of the electromagnetic wave inside the medium is $300$ m
- DThe magnetic field is given by the relation $B_y=\dfrac{B_0}{v}\sin(kz-2\pi\times10^6 t)$ where $v$ is the speed of the electromagnetic wave inside the medium
Solution
From the given equation of the electric field $E_x = E_0 \sin(kz - 2\pi \times 10^6 t)$, the wave is propagating in the $+z$ direction.
The angular frequency is $\omega = 2\pi \times 10^6$ rad/s, which gives the frequency $f = \dfrac{\omega}{2\pi} = 10^6$ Hz.
The speed of the electromagnetic wave in the dielectric medium is given by $v = \dfrac{c}{\sqrt{\mu_r \epsilon_r}}$.
Assuming a non-magnetic medium ($\mu_r = 1$), we get $v = \dfrac{3 \times 10^8}{\sqrt{9}} = 10^8$ ms$^{-1}$.
The wavelength of the wave inside the medium is $\lambda = \dfrac{v}{f} = \dfrac{10^8}{10^6} = 100$ m.
Option (3) states the wavelength is $300$ m, which is incorrect.
The angular frequency is $\omega = 2\pi \times 10^6$ rad/s, which gives the frequency $f = \dfrac{\omega}{2\pi} = 10^6$ Hz.
The speed of the electromagnetic wave in the dielectric medium is given by $v = \dfrac{c}{\sqrt{\mu_r \epsilon_r}}$.
Assuming a non-magnetic medium ($\mu_r = 1$), we get $v = \dfrac{3 \times 10^8}{\sqrt{9}} = 10^8$ ms$^{-1}$.
The wavelength of the wave inside the medium is $\lambda = \dfrac{v}{f} = \dfrac{10^8}{10^6} = 100$ m.
Option (3) states the wavelength is $300$ m, which is incorrect.
Hence, the correct answer is option: 'C'.