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A plane electromagnetic wave in a non-magnetic dielectric medium is given by $\vec E\, = \,{\vec E_0}\,(4 \times {10^{ - 7}}\,x - 50t)$ with distance being in meter and time in seconds. The dielectric constant of the medium is
$2.4$
$5.8$
$8.2$
$4.8$
Solution
Given equation of wave
$\vec{E}=\vec{E}_{0}(4 \times \overrightarrow{10} x-50 t)$
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,
$v=\frac{w}{k}=\frac{50}{4 \times 10^{-7}}=1.25 \times 10^{8} \mathrm{m} / \mathrm{s}$
so, refractive index of medium,
$\mu=\frac{e}{v}=\frac{3 \times 10^{8}}{1.25 \times 10^{8}}=2.4$
using, $u^{2}=k m . k e[\mathrm{km}$ and ke are magnetic and dielectric di – constants]
as medium is non diamagnetic, $k m=1$
$\Rightarrow k e=\mu^{2}=(2.4)^{2} \Rightarrow k e=5.76$
