Write characteristics of electromagnetic waves. 

Characteristics of electromagnetic waves are as follows :

$(1)$ In electromagnetic waves electric field and magnetic field are perpendicular to each other as well as perpendicular to direction of propagation.

During charging process of capacitor electric field inside plate is perpendicular to plate and magnetic field produced due to displacement current is circular and parallel to close loop and in direction of plate hence $\vec{E}$ and $\vec{B}$ are perpendicular to each other.

$(2)$ Let plane electromagnetic wave propagates in $z$-direction. Here, electric field $\mathrm{E}_{x}$ is in $x$-direction and electromagnetic wave propagate in $z$-direction and varies according to sine function. Electric and magnetic field $\mathrm{E}_{x}$ and $\mathrm{B}_{y}$ are perpendicular to each other and perpendicular to direction of propagation ( $z$-axis). Hence, it can be represented mathematically,

$\mathrm{E}_{x}=\mathrm{E}_{0} \sin (k z-\omega t)$ $\mathrm{B}_{y}=\mathrm{B}_{0} \sin (k z-\omega t)$ $\therefore \overrightarrow{\mathrm{E}}=\mathrm{Exi}+0 j+0 \hat{k}=\mathrm{E}_{0} \sin (k z-\omega t) \hat{i}$ $\text { and } \overrightarrow{\mathrm{B}}=0+\mathrm{B} y j+0 \hat{k}=\mathrm{B}_{0} \sin (k x-\omega t) \hat{j}$

where $k=$ wave vector $=\frac{2 \pi}{\lambda}$

$\ldots$ $(3)$

It shows direction of propagation of wave. $\omega=$ angular frequency

$\frac{\omega}{k}=$ wave speed

$\omega=c k$

$\ldots$ $(4)$

where $c=\frac{1}{\sqrt{\mu_{0} \in_{0}}}$

$\omega=c k$ is standard equation for waves