Question

A plane electromagnetic wave in a non-magnetic dielectric medium is given by $\vec{E}={\vec{E}}_0\left(4\times 10^{-7}x-50t\right)$ 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

Answer: (B)

Given equation of wave
$\vec{E}={\vec{E}}_0\left(4\times 10^{-7}x-50t\right)$
comparing with general equation of wave
$\vec{E}={\vec{E}}_0(kx-\omega t)$
we get
$\omega =50rad/s;k=4\times 10^{-7}{m}^{-1}$
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, $km=1$
$\Rightarrow ke={\mu }^2=(2.4{)}^2$
$\Rightarrow ke=5.76=5.8$