Discussion
Which one of the following shows the CORRECT relationship among velocity of light in a medium (\(v\)), permittivity of medium (\(\varepsilon\)) and magnetic permeability of medium (\(\mu\))?
Answer: D
The correct relation is \(v = \frac{1}{\sqrt{\mu\varepsilon}}\).
Maxwell's equations give the speed of an electromagnetic wave in a medium as \(v = \frac{1}{\sqrt{\mu\varepsilon}}\). In vacuum this is \(c = \frac{1}{\sqrt{\mu_0\varepsilon_0}} \approx 3 \times 10^{8}\) m/s, and the refractive index is \(n = \frac{c}{v} = \sqrt{\mu_r\varepsilon_r}\).
A dimension check rules out the rest: \(\mu\varepsilon\) has units of s2/m2, so only its inverse square root is a speed. \(\frac{1}{\mu\varepsilon}\) is a speed squared, \(\frac{1}{(\mu\varepsilon)^{2}}\) a fourth power and \(\frac{1}{(\mu\varepsilon)^{-2}}\) is \((\mu\varepsilon)^{2}\), not a speed at all.
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