The speed of electromagnetic wave in a medium (whose dielectric constant is $2.25$ and relative permeability is $4$ ) is equal to ………. $\times 10^8 \,m / s$

The electric fields of two plane electromagnetic plane waves in vacuum are given by

$\overrightarrow{\mathrm{E}}_{1}=\mathrm{E}_{0} \hat{\mathrm{j}} \cos (\omega \mathrm{t}-\mathrm{kx})$ and

$\overrightarrow{\mathrm{E}}_{2}=\mathrm{E}_{0} \hat{\mathrm{k}} \cos (\omega \mathrm{t}-\mathrm{ky})$

At $t=0,$ a particle of charge $q$ is at origin with a velocity $\overrightarrow{\mathrm{v}}=0.8 \mathrm{c} \hat{\mathrm{j}}$ ($c$ is the speed of light in vacuum). The instantaneous force experienced by the particle is 

In a plane electromagnetic wave travelling in free space, the electric field component oscillates sinusoidally at a frequency of $2.0 \times 10^{10}\,Hz$ and amplitude $48\,Vm ^{-1}$. Then the amplitude of oscillating magnetic field is : (Speed of light in free space $=3 \times 10^8\,m s ^{-1}$)

In propagation of electromagnetic waves the angle between the direction of propagation and plane of polarisation is

The intensity of a light pulse travelling along a communication channel decreases exponentially with distance $x$ according to the relation $I = {I_0}{e^{ – \alpha x}}$ , where $I_0$ is the intensity at $x = 0$ and $\alpha $ is the attenuation constant. The attenuation in $dB/km$ for an optical fibre in which the intensity falls by $50$ percent over a distance of $50\ km$ is