Question 257: Magnetism and Matter

Question

If an optical medium possesses a relative permeability of $\frac{10}{\pi}$ and relative permittivity of $\frac{1}{0.0885}$, then the velocity of light is greater in vacuum than that in this medium by _________ times.
$$\left(\mu_0=4 \pi 	imes 10^{-7} \mathrm{H} / \mathrm{m}, \epsilon_0=8.85 	imes 10^{-12} \mathrm{~F} / \mathrm{m}, \mathrm{c}=3 	imes 10^8 \mathrm{~m} / \mathrm{s}ight)$$

Accepted Answer

$$\begin{aligned}
&	ext { Since velocity of light in terms of } \mu \& E 	ext { is }\
&\begin{aligned}
& V=\frac{1}{\sqrt{\mu \epsilon}}=\frac{1}{\sqrt{\mu_0 \mu_{\mathrm{r}}}} 	imes \frac{1}{\sqrt{\epsilon_0 \epsilon_{\mathrm{r}}}} \
& =\frac{1}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}} 	imes \frac{1}{\sqrt{\mu_0 \epsilon_0}} \
& =\frac{C}{\sqrt{\mu_{\mathrm{r}} \epsilon_{\mathrm{r}}}}=\frac{C}{\sqrt{\frac{10}{\pi} 	imes \frac{1}{0.0885}}} \
& =\frac{C}{\sqrt{36}}=\frac{C}{6}
\end{aligned}
\end{aligned}$$
$$\begin{aligned}
V & =\frac{C}{6} \
C & =6 V
\end{aligned}$$
Velocity of light in vacuum is greater by 6 times the velocity of light in medium
Answer is 6

Magnetism and Matter

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