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An electromagnetic wave of frequency $5\, GHz ,$ is travelling in a medium whose relative electric permittivity and relative magnetic permeability both are $2 .$ Its velocity in this medium is $\times 10^{7}\, m / s$
$12$
$18$
$15$
$20$
Solution
Given : Frequency of wave $f =5 GHz$
$=5 \times 10^{9} Hz$
Relative permittivity, $\epsilon_{ r }=2$
and Relative permeability, $\mu_{ r }=2$
Since speed of light in a medium is given by,
$v =\frac{1}{\sqrt{\mu \in}}=\frac{1}{\sqrt{\mu_{ s } \mu_{0} \cdot \epsilon_{ s } \epsilon_{0}}}$
$v =\frac{1}{\sqrt{\mu_{ s } \epsilon_{ x }}} \frac{1}{\sqrt{\mu_{0} \epsilon_{0}}}=\frac{ C }{\sqrt{\mu_{ s } \epsilon_{ r }}}$
Where $C$ is speed of light is vacuum.
$\therefore v =\frac{3 \times 10^{8}}{\sqrt{4}}=\frac{30 \times 10^{7}}{2} m / s$
$=15 \times 10^{7} m / s$
$\therefore$ Ans. is $15$
