The energy density associated with electric field $\overrightarrow{ E }$ and magnetic field $B$ of an electromagnetic wave in free space is given by ( $\epsilon_0-$ permittivity of free space, $\mu_0$ – permeability of free space)

Suppose that the electric field amplitude of an electromagnetic wave is $E_{0}=120\; N / C$ and that its frequency is $v=50.0\; MHz$.

$(a)$ Determine, $B_{0}, \omega, k,$ and $\lambda .$

$(b)$ Find expressions for $E$ and $B$

The magnetic field vector of an electromagnetic wave is given by ${B}={B}_{o} \frac{\hat{{i}}+\hat{{j}}}{\sqrt{2}} \cos ({kz}-\omega {t})$; where $\hat{i}, \hat{j}$ represents unit vector along ${x}$ and ${y}$-axis respectively. At $t=0\, {s}$, two electric charges $q_{1}$ of $4\, \pi$ coulomb and ${q}_{2}$ of $2 \,\pi$ coulomb located at $\left(0,0, \frac{\pi}{{k}}\right)$ and $\left(0,0, \frac{3 \pi}{{k}}\right)$, respectively, have the same velocity of $0.5 \,{c} \hat{{i}}$, (where ${c}$ is the velocity of light). The ratio of the force acting on charge ${q}_{1}$ to ${q}_{2}$ is :-

The magnetic field of an electromagnetic wave is given by

$\vec B = 1.6 \times {10^{ – 6}}\,\cos \,\left( {2 \times {{10}^7}z + 6 \times {{10}^{15}}t} \right)\left( {2\hat i + \hat j} \right)\frac{{Wb}}{{{m^2}}}$ The associated electric field will be

The magnetic field in a plane electromagnetic wave is $\mathrm{B}_y=\left(3.5 \times 10^{-7}\right) \sin \left(1.5 \times 10^3 \mathrm{x}+0.5\right.$ $\left.\times 10^{11} \mathrm{t}\right) \mathrm{T}$. The corresponding electric field will be