Is permittivity/permeability ratio constant or not in media?

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In a vacuum, the ratio of electric permittivity (ε) and magnetic permeability (μ) remains constant, but this ratio varies in different media due to their atomic and molecular properties. The relative permittivity (ε_r) is frequency-dependent, significantly affecting materials like water, which has a high ε_r at low frequencies and a much lower value at optical frequencies due to molecular polarization dynamics. In contrast, the relative permeability (μ_r) is generally close to 1 across all frequencies, except in ferromagnetic materials. The differences in ε_r and μ_r highlight the complex interactions between electromagnetic fields and materials. Understanding these properties is crucial for applications in optics and electromagnetism.
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We have a constant ratio of them in vacuum. Is it same in a medium also? Or not? And in any case, what is the reason?
 
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In a medium, ##\epsilon## and ##\mu## are independent of each other, as far as I know. They depend on the atomic/molecular/bulk properties of the material.
 
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\epsilon_r (relative permittivity) is usually frequency-dependent, to a greater or lesser degree. A favourite example is water, whose \epsilon_r at very low frequencies is about 80, but at optical frequencies (around 5 \times 10^{14} Hz, is about 1.8. This is because water molecules are strongly polarised, and at low frequencies can align themselves strongly with the electric field. At high frequencies they can't flail about (librate?) fast enough to keep pace with the changing field. Except for ferromagnetic materials, \mu_r (relative permeability) is pretty much 1 at all frequencies.
 
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