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Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by

Question:

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by $E=20 \cos \left(2 \times 10^{10} \mathrm{t}-200 \mathrm{x}\right) \mathrm{V} / \mathrm{m}$. The dielectric constant of the medium is equal to :

$\left(\right.$ Take $\mu_{\mathrm{r}}=1$ )

  1. 9

  2. 2

  3. $\frac{1}{3}$

  4. 3

Correct Option: 1

Solution:

Speed of wave $=\frac{2 \times 10^{10}}{200}=10^{8} \mathrm{~m} / \mathrm{s}$

Refractive index $=\frac{3 \times 10^{8}}{10^{8}}=3$

Now refractive index $=\sqrt{\varepsilon_{\mathrm{r}} \mu_{\mathrm{r}}}$

$3=\sqrt{\varepsilon_{\mathrm{r}}(1)}$

$\Rightarrow \varepsilon_{\mathrm{r}}=9$

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