If ${\mu_r}$ is the relative permeability and $K$ is the dielectric constant of a medium,its refractive index $n$ is given by:

If a source is transmitting electromagnetic waves of frequency $8.2 \times 10^6 \ Hz$,then the wavelength of the electromagnetic waves transmitted from the source will be.....$m$.

$A$ plane $EM$ wave travelling in vacuum along $z$-direction is given by $\vec E = E_0 \sin(kz - \omega t) \hat i$ and $\vec B = B_0 \sin(kz - \omega t) \hat j$.
$(i)$ Evaluate $\int \vec E \cdot d\vec l$ over the rectangular loop $1234$ shown in the figure.
$(ii)$ Evaluate $\int \vec B \cdot d\vec s$ over the surface bounded by loop $1234$.
$(iii)$ Use $\int \vec E \cdot d\vec l = -\frac{d\phi_E}{dt}$ to prove $\frac{E_0}{B_0} = c$.
$(iv)$ By using a similar process and the equation $\int \vec B \cdot d\vec l = \mu_0 I + \mu_0 \epsilon_0 \frac{d\phi_E}{dt}$,prove that $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$.

$A$ plane electromagnetic wave travelling along the $X$-direction has a wavelength of $3 \ mm$. The variation in the electric field occurs in the $Y$-direction with an amplitude of $66 \ Vm^{-1}$. The equations for the electric and magnetic fields as a function of $x$ and $t$ are respectively:

Due to the presence of an em-wave whose electric component is given by $E = 100 \sin(\omega t - kx) \ NC^{-1}$,a cylinder of length $200 \ cm$ holds a certain amount of em-energy inside it. If another cylinder of the same length but half the diameter of the previous one holds the same amount of em-energy,the magnitude of the electric field of the corresponding em-wave should be modified as:

The electric field of a plane electromagnetic wave is given by $\overrightarrow{E} = E_{0}(\hat{x} + \hat{y}) \sin(kz - \omega t)$. Its magnetic field will be given by