Q154 / 160 · AP EAMCET 2024 (19 May Shift 2) · Physics

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

  • A
    1.75
  • B
    2
  • Correct answer
    C
    2.25
  • D
    2.75

Solution

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

Hence, the correct answer is option: 'C'.

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