Question

A plane electromagnetic wave,
$E_z=100cos\left(6\times 10^{8}t+4x\right)V{m}^{-1}$, propagating in a medium of dielectric constant is

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

Answer 1

Answer: (D)

$E_z=100cos\left(6\times 10^{8}t+4x\right)V{m}^{-1}$
Comparing the given equation with
$E_z=E_{0}cos\left(\omega t+kx\right),$
We get
$\omega =6\times 10^{8}rad{s}^{-1},k=4rad{m}^{-1}$
Speed of electromagnetic wave in a medium is
$\upsilon =\frac{\omega }{k}=\frac{6\times 10^{8}rad{s}^{-1}}{4rad{m}^{-1}}=\frac{3\times 10^8}{2}m{s}^{-1}$
Dielectric constant,
$K={\left(\frac{c}{\upsilon }\right)}^2={\left(\frac{3\times 10^{8}m{s}^{-1}}{\frac{3\times 10^8}{2}m{s}^{-1}}\right)}^{{}^2}=4$