Question

Calculate the phase velocity of electromagnetic wave having electron density and frequency for $D$ layer, $N=400$ electron $/c{m}^3,v=300kHz$

• A. $3\times 10^{4}m{s}^{-1}$
• B. $3.75\times 10^{8}m{s}^{-1}$
• C. $6.8\times 10^{8}m{s}^{-1}$
• D. $1.1\times 10^{9}m{s}^{-1}$

Answer 1

Answer: (B)

$:\mu ={\mu }_0\sqrt{1-\frac{81.45N}{v^2}}$
Here, $N=400$ electron $c{m}^{-3}=400\times 10^6$ electron $m^{-3}$
$v=300kHz=300\times 10^{3}Hz,$ and ${\mu }_0=1$
$\Rightarrow \mu =1\sqrt{1-\frac{81.45\left(400\times 10^6\right)}{{\left(300\times 10^3\right)}^2}}=0.8$
$\Rightarrow c=\frac{c_0}{\mu }=\frac{3\times 10^{8}m{s}^{-1}}{0.8}=3.75\times 10^{8}m{s}^{-1}$