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  • A plane electromagnetic wave in a non-magnetic dielectric medium is given by <img alt="\vec{E}=\vec{E_{0}}\left ( 4\times 10^{-7}x-50t \right )" src="https://learn.careers360.com/latex-image/?

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 : 

Option: 1

2.4


Option: 2

5.8


Option: 3

8.2


Option: 4

4.8


Answers (1)

best_answer

Given equation of wave 

\vec{E}=\vec{E}_{0}(4 \times 1 \overrightarrow{0} x-50 t)

Comparing with general equation of wave,

\\ \vec{E}=\vec{E}_{0}(k x-w t)$ \\ \\ we get, $w=50$ rad/s. $k=4 \times 10^{-7} m^{-1}$ \\ \\ Thus velocity of wave, $v=\frac{w}{k}=\frac{50}{4 \times 10^{-7}}=1.25 \times 10^{8} m / s$

\\ so, \ refractive \ index \ of \ medium, \\ \mu=\frac{e}{v}=\frac{3 \times 10^{8}}{1.25 \times 10^{8}}=2.4$\\ \\ using, $u^{2}=k m \cdot k e \quad[ km \text { and ke are magnetic and dielectric di - constants }]$\\ \\ as medium is non diamagnetic, $k m=1$ $\Rightarrow k e=\mu^{2}=(2.4)^{2} \Rightarrow k e=5.76$

Posted by

SANGALDEEP SINGH

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