Question

The velocity of an electromagnetic wave in a medium with \(\varepsilon_r=2\) and \(\mu_r=18\) is

• A. \(1.5\times10^8\,\text{m s}^{-1}\)
• B. \(2\times10^8\,\text{m s}^{-1}\)
• C. \(0.5\times10^8\,\text{m s}^{-1}\)
• D. \(0.25\times10^8\,\text{m s}^{-1}\)

Hint:

For electromagnetic waves in a medium: \[ v=\frac{c}{\sqrt{\mu_r\varepsilon_r}} \] where \[ n=\sqrt{\mu_r\varepsilon_r} \] is the refractive index of the medium. Larger values of \(\mu_r\) and \(\varepsilon_r\) reduce the speed of the wave.

Answer 1

The Correct Option is C

Step 1:Substitute the given values. Given, \[ \mu_r=18 \] \[ \varepsilon_r=2 \] Therefore, \[ v= \frac{3\times10^8} {\sqrt{18\times2}} \] \[ v= \frac{3\times10^8} {\sqrt{36}} \] \[ v= \frac{3\times10^8}{6} \] \[ v=0.5\times10^8\,\text{m s}^{-1} \]

Step 2: State the answer. \[ { v=0.5\times10^8\,\text{m s}^{-1} } \] Hence, the correct option is \[ {(C)} \]