Answer to Question #89920 in Electricity and Magnetism for Shivam Nishad

Question #89920
A uniform plane wave has a wavelength of 6cm in vacuum and 2 cm in a non-magnetic dielectric having permeability of free space. Calculate the dielectric constant of the dielectric and the phase velocity of propagation of the wave through it.
1
Expert's answer
2019-05-23T09:39:55-0400

Wavelength in vacuum:


λ0=cν=6cm\lambda_0 = \frac{c}{\nu} = 6\,\text{cm}


Frequency ν\nu of both waves are equal.

In dielectric medium, speed of light equals to

v=cn=cεμv = \frac{c}{n} = \frac{c}{\sqrt{\varepsilon \mu}}

As dielectric is non-magnetic, wavelength equals to


λm=vν=cνε=2cm\lambda_m=\frac{v}{\nu} = \frac{c}{\nu\sqrt{\varepsilon}} = 2\,\text{cm}

Therefore, dielectric constant


ε=λ0λmε=λ02λm2=9\sqrt{\varepsilon} = \frac{\lambda_0}{\lambda_m} \Rightarrow \varepsilon = \frac{\lambda_0^2}{\lambda_m^2} = 9

phase velocity of propagation of the wave:


v=cε=108m/sv = \frac{c}{\sqrt{\varepsilon }} = 10^8 \,\text{m/s}


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