First slide

Electromagnetic waves and its nature

Question

A plane electromagnetic wave propagating in a non-magnetic dielectric medium is given by $E = E_{0} \sin [4 \times 10^{- 7} x - 50 t]$ .Where $' x'$ is in meter and $' t'$ is in second. If the relative permeability of the medium, $μ_{r} = 1$ then the dielectric constant of the medium is

Moderate

A

2.42
B

5.76
C

8.26
D

4.84

Solution

Speed of electromagnetic wave in Vacuum is $C = \frac{1}{\sqrt{μ_{0} \in_{0}}}$
Speed of electromagnetic wave in a dielectric medium of dielectric constant (k) is given by $C' = \frac{1}{\sqrt{k μ_{0} \in_{0}}} = \frac{C}{\sqrt{k}}$
From given equation $C' = \frac{angular velocity}{wave number} = \frac{50}{4 \times 10^{- 7}} = \frac{5}{4} \times 10^{8} m / s$
And $C = 3 \times 10^{8} m / s$
Using, $C' = \frac{C}{\sqrt{k}}$
$\Rightarrow \frac{5}{4} \times 10^{8} = \frac{3 \times 10^{8}}{\sqrt{k}} \Rightarrow \frac{25}{16} = \frac{9}{k} \Rightarrow k = \frac{9 \times 16}{25} = 5.76$

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