The peak electric field produced by the radiation coming from the $8\, W$ bulb at a distance of $10\, m$ is $\frac{x}{10} \sqrt{\frac{\mu_{0} c }{\pi}} \,\frac{ V }{ m }$. The efficiency of the bulb is $10\, \%$ and it is a point source. The value of $x$ is …… .

An antenna is placed in a dielectric medium of dielectric constant $6.25$. If the maximum size of that antenna is $5.0\, mm$. it can radiate a signal of minimum frequency of $GHz .$

(Given $\mu_{ r }=1$ for dielectric medium)

Identify the correct statements from the following descriptions of various properties of electromagnetic waves.

$A$. In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field.

$B.$ The energy in electromagnetic wave is divided equally between electric and magnetic fields.

$C.$ Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave.

$D.$ The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other.

$E.$ The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light.

Choose the most appropriate answer from the options given below:

An $EM$ wave propagating in $x$-direction has a wavelength of $8\,mm$. The electric field vibrating $y$ direction has maximum magnitude of $60\,Vm ^{-1}$. Choose the correct equations for electric and magnetic fields if the $EM$ wave is propagating in vacuum

An em wave is propagating in a medium with a velocity $\vec v =v\hat i.$ The instantaneous oscillating electric field of this em wave is along $+y$ axis. Then the direction of oscillating magnetic field of the em wave will be along