(Solved): The refractive index \( N \) experienced by an electromagnetic wave in an isotropic plasma is given ...

The refractive index \( N \) experienced by an electromagnetic wave in an isotropic plasma is given by: \[ N=\left[1-\left(\frac{\omega_{P}}{\omega}\right)^{2}\right]^{\frac{1}{2}} \] The electron number density of the lowest layer of the ionosphere (the E-band) is of the order \( 2.5 \times 10^{10} \mathrm{~m}^{-3} \). Calculate the plasma frequency and hence explain what happens to a radio signal of frequency \( 5 \mathrm{MHz} \) emitted from the surface of the Earth when it interacts with this layer of the atmosphere. [4 marks] You may find the following useful: Plasma frequency: \( \omega_{p}=\sqrt{\frac{n_{e} e^{2}}{m_{e} \varepsilon_{0}}} \) \( \varepsilon_{0} \mu_{0}=\frac{1}{c^{2}} \) Electron charge: \( e=1.6 \times 10^{-19} \mathrm{C} \) Electron mass: \( m_{e}=9.1 \times 10^{-31} \mathrm{~kg} \) Permittivity of free space: \( \varepsilon_{0}=8.9 \times 10^{-12} \mathrm{~F}^{-\mathrm{m}^{-1}} \)