Question
An electromagnetic wave travelling in a lossless dielectric medium having a dielectric constant, $\varepsilon_{r} = 9$, has the electric field, $E_{x} = E_{0}sin\left( kz - 2\pi \times 10^{6}t \right) \vee m^{- 1}$ where $E_{0}$ is the amplitude and $k$ is the wave vector. Among the following options, the incorrect choice is
Options
Solution
Sol. [Key Concept: EM wave in a dielectric — v = c/√εᵣ]
$\ \Rightarrow E_{x} = E_{0}sin\left( kz - 2\pi \times 10^{6}t \right) = E_{0}sin(kz - \omega t)$
⇒ Direction of propagation of wave is along +z axis.
⇒ Speed of wave in medium
$$\begin{matrix} & v_{m} = \frac{v_{0}}{\sqrt{\varepsilon_{r}}} = \frac{c}{\sqrt{9}} = \frac{3 \times 10^{8}}{3} \\ & v_{m} = 10^{8}\text{ }m/s \end{matrix}$$
⇒ Wavelength in medium $= \lambda_{m}$
$${\lambda_{m} = \frac{v_{m}}{f_{0}} = \frac{10^{8}}{\frac{2\pi \times 10^{6}}{2\pi}} = 100\text{ }m\left\lbrack \because f_{0} = \text{~}\text{constant}\text{~} \right\rbrack } $$∴ Wavelength of the electromagnetic wave inside the medium is 100 m .
Note: Among the options, in the expression $B_{y} = \frac{B_{0}}{v}sin\left( kz - 2\pi \times 10^{6}t \right),B_{0}$ should be replaced by $E_{0}$.
Create a free account to view solution
View Solution Free