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

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 :-

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 $10m$  from the lamp will be........$V/m$

A beam of light travelling along $X$-axis is described by the electric field $E _{ y }=900 \sin \omega( t - x / c )$. The ratio of electric force to magnetic force on a charge $q$ moving along $Y$-axis with a speed of $3 \times 10^{7}\,ms ^{-1}$ will be.

[Given speed of light $=3 \times 10^{8}\,ms ^{-1}$ ]

A mathematical representation of electromagnetic wave is given by the two equations $E = E_{max}\,\, cos (kx -\omega\,t)$ and $B = B_{max} cos\, (kx -\omega\,t),$ where $E_{max}$ is the amplitude of the electric field and $B_{max}$ is the amplitude of the magnetic field. What is the intensity in terms of $E_{max}$ and universal constants $μ_0, \in_0.$

Write magnitude and dimensional formula of $\frac{1}{{\sqrt {{\mu _0}{ \in _0}} }}$