$A$ lamp emits monochromatic green light uniformly in all directions. The lamp is $3\%$ efficient in converting electrical power to electromagnetic waves and consumes $100\,W$ of power. The amplitude of the electric field associated with the electromagnetic radiation at a distance of $5\,m$ from the lamp will be nearly.......$V/m$

Electromagnetic waves travel in a medium which has relative permeability $1.3$ and relative permittivity $2.14$. Then the speed of the electromagnetic wave in the medium will be

Given below are two statements:
Statement $I$: $A$ time-varying electric field is a source of a changing magnetic field and vice-versa. Thus,a disturbance in an electric or magnetic field creates $EM$ waves.
Statement $II$: In a material medium,the $EM$ wave travels with speed $v = \frac{1}{\sqrt{\mu_{0} \varepsilon_{0}}}$.
In the light of the above statements,choose the correct answer from the options given below:

If $\overrightarrow E$ and $\overrightarrow B$ are the electric and magnetic field vectors of electromagnetic waves,then the direction of propagation of the electromagnetic wave is along the direction of:

$A$ 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 $c = \frac{1}{\sqrt{\mu_0 \epsilon_0}}$.

An electromagnetic wave,going through vacuum,is described by $E = E_0 \sin(kx - \omega t)$. Which of the following is independent of wavelength?