First slide

Electromagnetic waves and its nature

Question

A plane electromagnetic ware travelling in a non-magnetic medium is given by $E = (9 \times 10^{8} {NC}^{- 1}) \sin [(9 \times 10^{8} {rads}^{- 1}) t - (6 m^{- 1}) x]$ where x is in metre and t is in second. The dielectric constant of the medium is

Moderate

Solution

$v = \frac{ω}{k} = \frac{9 \times 10^{8}}{6} = 1 .5 \times 10^{8} {ms}^{- 1}$
Refractive index $n = \frac{c}{v} = \frac{3 \times 10^{8}}{1 .5 \times 10^{8}} = 2$
Also $n = \sqrt{μ_{r} \in_{r}}$ . For a non-magnetic medium $μ_{r} = 1$ .
Therefore
$n = \sqrt{\in_{r}} \Rightarrow \in_{r} = n^{2} = (2)^{2} = 4$
$∴$ Dielectric constant $k = \in_{r} = 4$ .

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