The velocity of electromagnetic radiation in a medium of permittivity $\varepsilon_0$ and permeability $\mu_0$ is given by :
A
$\dfrac{1}{\sqrt{\mu_0 \varepsilon_0}}$
B
$\sqrt{\dfrac{\mu_0}{\varepsilon_0}}$
C
$\sqrt{\dfrac{\varepsilon_0}{\mu_0}}$
D
$\sqrt{\mu_0 \varepsilon_0}$
The answer is A.
Solution
From Maxwell's equations, the speed of an electromagnetic wave in a medium of permittivity $\varepsilon$ and permeability $\mu$ is $v = \dfrac{1}{\sqrt{\mu\varepsilon}}$. Here the medium has permittivity $\varepsilon_0$ and permeability $\mu_0$. $C = \dfrac{1}{\sqrt{\mu_0 \varepsilon_0}}$ = velocity of the electromagnetic wave through the medium. Dimension check: $\mu_0\varepsilon_0$ has the dimensions of $\dfrac{1}{(\text{speed})^2}$, so only $\dfrac{1}{\sqrt{\mu_0\varepsilon_0}}$ has the dimensions of speed. Numerically this is $3 \times 10^{8}$ m/s for free space.
ConceptSpeed of EM waves
Electromagnetic Waves in past papers
49 questions from this chapter have appeared across 24 exam years.
