Electromagnetic waves travel in a medium which has relative permeability 1.6 and relative permittivity 2.5. The speed of the electromagnetic wave in the medium would be-
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 1.5 x 108 m/s
The speed of an electromagnetic wave in a medium is reduced from c by the square root of the product of the relative permeability and relative permittivity.
\( \displaystyle v = \frac{1}{\sqrt{\mu\varepsilon}} = \frac{c}{\sqrt{\mu_r \varepsilon_r}} \)
\( \displaystyle v = \frac{3\times10^{8}\,\mathrm{m\,s^{-1}}}{\sqrt{1.6 \times 2.5}} = \frac{3\times10^{8}\,\mathrm{m\,s^{-1}}}{\sqrt{4}} \)
\( \displaystyle v = 1.5\times10^{8}\,\mathrm{m\,s^{-1}} \)
Shortcut: No wave can travel faster than c in a material medium, which rules out 3.6 × 108 m/s; and \( \sqrt{\mu_r\varepsilon_r} = 2 \) cannot bring \( 3\times10^{8} \) down to \( 10^{6} \), which rules out the other two.