Question

A plane electromagnetic wave in a non-magnetic dielectric medium is given by $\vec{E}=\vec{E}_{0}\left(4\times10^{-7}\,x-50t\right)$ with distance being in meter and time in seconds. The dielectric constant of the medium is:

• A. $2.4$
• B. $5.8$
• C. $8.2$
• D. $4.8$

Answer 1

The Correct Option is B

Given equation of wave
$\vec{ E }=\vec{ E }_{0}\left(4 \times 10^{-7} x -50 t \right)$
comparing with general equation of wave
$\vec{ E }=\vec{ E }_{0}( kx -\omega t )$
we get
$\omega=50 rad / s ; k =4 \times 10^{-7} m ^{-1}$
Thus velocity of wave
$V =\frac{\omega}{ k }=\frac{50}{4 \times 10^{-7}}=1.25 \times 10^{8} m / s$
So, refractive index of medium
$\mu=\frac{ e }{ V }=\frac{3 \times 10^{8}}{1.25 \times 10^{8}}=2.4$
using
$\mu^{2}= km . ke$
( $km$ and ke are di-magnetic and dielectric constants)
as medium is non diamagnetic, $km =1$
$\Rightarrow ke =\mu^{2}=(2.4)^{2} $
$\Rightarrow ke =5.76=5.8$