An electromagnetic wave travel in a medium with a speed of $2 \times 10^8 \mathrm{~ms}^{-1}$. The relative…

An electromagnetic wave travel in a medium with a speed of $2 \times 10^8 \mathrm{~ms}^{-1}$. The relative permeability of the medium is 1 . Then the relative permitivity is
  1. 1.75
  2. 2
  3. 2.25
  4. 2.75

Solution

For EM wave, $v=2 \times 10^8 \mathrm{~ms}^{-1}, \mu_{\mathrm{r}}=1$ $\begin{aligned} & \therefore v=\frac{1}{\sqrt{\mu \varepsilon}}=\left(\frac{1}{\sqrt{\mu_{\mathrm{o}} \varepsilon_{\mathrm{o}}}}\right)\left(\frac{1}{\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}}}\right)=\frac{c}{\sqrt{\mu_{\mathrm{r}} \varepsilon_{\mathrm{r}}}} \\ & 2 \times 10^8=\frac{3 \times 10^8}{\sqrt{1 \times \varepsilon_{\mathrm{r}}}} \quad \therefore \varepsilon_{\mathrm{r}}=\left(\frac{3}{2}\right)^2=2.25\end{aligned}$

Asked in: AP EAMCET 2024 (19 May Shift 2)

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