Question

A plane electromagnetic wave,
$E_{z}=100cos\left(6\times10^{8}t+4x\right)V\,m^{-1}$, propagating in a medium of dielectric constant is

• A. $1.5$
• B. $2.0$
• C. $2.4$
• D. $4.0$

Answer 1

Answer: (D)

$E_{z}=100cos\left(6\times10^{8}t+4x\right)V\,m^{-1}$
Comparing the given equation with
$E_{z}=E_{0}cos\left(\omega t+kx\right),$
We get
$\omega=6\times10^{8}\,rad\,s^{-1}, k=4\,rad\,m^{-1}$
Speed of electromagnetic wave in a medium is
$\upsilon=\frac{\omega}{k}=\frac{6\times10^{8}\,rad\,s^{-1}}{4\,rad\,m^{-1}}=\frac{3\times10^{8}}{2}m\,s^{-1}$
Dielectric constant,
$K=\left(\frac{c}{\upsilon}\right)^{2}=\left(\frac{3\times10^{8}\,m\,s^{-1}}{\frac{3\times10^{8}}{2}m\,s^{-1}}\right)^{^2}=4$