A plane electromagnetic wave, $E_z=100 \cos \left(6 \times 10^8 t+4 x\right) Vm^{-1}$, propagating in a medium of dielectric constant is:
Answer & explanation
Correct answer: option 4
$E_z=100 \cos \left(6 \times 10^8 t+4 x\right) Vm^{-1}$
Comparing the given equation with $E_z=E_0 \cos (\omega t+kx)$,
We get
$\omega=6 \times 10^8 {rads}^{-1}, k=4 {radm}^{-1}$
Speed of electromagnetic wave in a medium is $v=\frac{\omega}{k}=\frac{6 \times 10^8 {rads}^{-1}}{4 {radm}^{-1}}=\frac{3 \times 10^8}{2} ms^{-1}$
Dielectric constant, $K=\left(\frac{c}{v}\right)^2=\left(\frac{3 \times 10^8 ms^{-1}}{\frac{3 \times 10^8}{2} ms^{-1}}\right)^2=4$