The ratio of the speeds of electromagnetic waves in a vacuum and in a medium with dielectric constant $K=3$ and permeability $\mu=2\mu_{0}$ is (where $\mu_{0}$ is the permeability of vacuum).

Out of the following options,which one can be used to produce a propagating electromagnetic wave?

An electromagnetic wave travelling in the $x-$ direction has a frequency of $2 \times 10^{14} \, Hz$ and an electric field amplitude of $27 \, Vm^{-1}$. From the options given below,which one describes the magnetic field for this wave?

For an electromagnetic wave travelling in free space,the relation between average energy densities due to electric $(U_{e})$ and magnetic $(U_{m})$ fields is

If the electric field of a plane electromagnetic wave is $E_z = 60 \sin(0.5 \times 10^3 x + 1.5 \times 10^{11} t) \ Vm^{-1}$,then the magnetic field of the wave is

The Poynting vector $\vec S$ is defined as a vector whose magnitude is equal to the wave intensity and whose direction is along the direction of wave propagation. Mathematically,it is given by $\vec S = \frac{1}{{\mu _0}}(\vec E \times \vec B)$. Show the nature of the $\vec S$ vs $t$ graph.