An electromagnetic wave of frequency 5 , GHz , is travelling in a… - Vidyadip

MCQ

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 $\times 10^{7}\, m / s$

A
$12$
B
$18$
✓
$15$
D
$20$

✓

Answer

Correct option: C.

$15$

c
Given : Frequency of wave $f =5 GHz$

$=5 \times 10^{9} Hz$

Relative permittivity, $\in_{ r }=2$

and Relative permeability, $\mu_{ r }=2$

Since speed of light in a medium is given by,

$v =\frac{1}{\sqrt{\mu \in}}=\frac{1}{\sqrt{\mu_{ s } \mu_{0} \cdot \in_{ s } \in_{0}}}$

$v =\frac{1}{\sqrt{\mu_{ s } \in_{ x }}} \frac{1}{\sqrt{\mu_{0} \in_{0}}}=\frac{ C }{\sqrt{\mu_{ s } \in_{ r }}}$

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 $15$

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