The speed of an electromagnetic wave in a medium of dielectric constant 2.25 and relative permeability 4 is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( 10^{8}\,\mathrm{m\,s^{-1}} \)
The speed of an electromagnetic wave in a medium of permittivity \( \varepsilon \) and permeability \( \mu \) is \( v = 1/\sqrt{\mu\varepsilon} \). Writing \( \varepsilon = \varepsilon_r\varepsilon_0 \) and \( \mu = \mu_r\mu_0 \), and using \( c = 1/\sqrt{\mu_0\varepsilon_0} \):
\( \displaystyle v = \frac{c}{\sqrt{\mu_r\varepsilon_r}} = \frac{3\times10^{8}\,\mathrm{m\,s^{-1}}}{\sqrt{4\times2.25}} = \frac{3\times10^{8}}{3}\,\mathrm{m\,s^{-1}} = 10^{8}\,\mathrm{m\,s^{-1}} \)
The dielectric constant is \( \varepsilon_r \).
Shortcut: The speed in a medium is always less than \( c = 3\times10^{8}\,\mathrm{m\,s^{-1}} \), which removes Options (1) and (2) at once. Of the two left, \( \sqrt{4\times2.25} = 3 \) gives \( c/3 \), that is \( 10^{8}\,\mathrm{m\,s^{-1}} \).