Question

An electromagnetic wave of frequency $3.0MHz$ passes from vacuum into a non-magnetic medium with permittivity, $ϵ=16{ϵ}_0.$ Where, ${ϵ}_0$ is the free space permittivity. The change in wavelength is

• A. -75 m
• B. +75 m
• C. -50 m
• D. +50 m

Answer 1

Answer: (A)

Given, frequency of EM wave,
$f=3MHz$
$=3\times 10^{6}Hz$
and permittivity of non-magnetic medium,
$\epsilon =16{\epsilon }_0$
Wavelength of EM wave,
$\lambda =\frac{c}{f}=\frac{3\times 10^8}{3\times 10^6}$
$\lambda =100m$
Velocity of electromagnetic $(EM)$ into non-magnetic material,
$v=\frac{c}{\sqrt{{\epsilon }_r}}=\frac{3\times 10^8}{\sqrt{16}}\left[\because {\epsilon }_r=\frac{\epsilon }{{\epsilon }_0}=16\right]$
$=\frac{3}{4}\times 10^{8}m/s$
$\therefore$ Wavelength, ${\lambda }^{{}^{\prime }}=\frac{v}{f}=\frac{\frac{3}{4}\times 10^8}{3\times 10^6}=25m$
$\therefore$ Change in wavelength $={\lambda }^{\prime }-\lambda$
$=25-100=-75m$