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

During the propagation of electromagnetic waves in a medium

A particle of charge $q$ and mass $m$ is moving along the $x-$ axis with a velocity $v,$ and enters a region of electric field $E$ and magnetic field $B$ as shown in figures below. For which figure the net force on the charge may be zero :-

Figure given shows the face of a cathode-ray oscilloscope tube, as viewed from in front. $i.e.$ the electron beam is coming out normally from the plane of the paper. The electron beam passes through a region where there are electric and magnetic fields directed as shown. The deflections of the spot from the center of the screen produced by the electric field $E$ and the magnetic field $B$ separately are equal in magnitude. Which one of the diagrams below shows a possible position of the spot on the screen when both fields are operating?

If the magnetic field in a plane electromagnetic wave is given by

$\overrightarrow{\mathrm{B}}=3 \times 10^{-8} \sin \left(1.6 \times 10^{3} \mathrm{x}+48 \times 10^{10} \mathrm{t}\right) \hat{\mathrm{j}}\; \mathrm{T}$

then what will be expression for electric field?

A plane electromagnetic wave of frequency $500\, MHz$ is travelling in vacuum along $y-$direction. At a particular point in space and

time, $\overrightarrow{ B }=8.0 \times 10^{-8} \hat{ z } \;T$. The value of electric field at this point is

(speed of light $\left.=3 \times 10^{8}\, ms ^{-1}\right)$

$\hat{ x }, \hat{ y }, \hat{ z }$ are unit vectors along $x , y$ and $z$ direction.